WEBVTT Kind: captions; Language: en-US

NOTE
Created on 2024-02-07T20:59:36.8732843Z by ClassTranscribe

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Alright, good morning everybody.

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So we're going to do another

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consolidation and review session.

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I'm going, it's going to be sort of

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like just a different perspective on

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some of the things we've seen and then

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and then I'll talk about the exam a

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little bit as well.

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So far we've been talking about this

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whole function quite a lot.

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That we have some data, we have some

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model F, we have some parameters Theta.

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We have something that we're trying to

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predict why we have some loss that

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defines how good our prediction is.

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And we're trying to solve for some

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parameters that minimize the loss.

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Given our model and our data and our

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parameters and our labels.

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And so it's all, it's pretty

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complicated.

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There's a lot there.

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And if I were going to reteach the

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class, I would probably start more

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simply by just talking about X.

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So let's just talk about X for now.

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So for example, when you have one bit

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and another bit and they like each

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other very much and they come together,

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it makes 3.

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I'm just kidding.

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That's how integers are made.

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So let's talk about the data for a bit.

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So first, like, what is data?

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This sounds like kind of elementary,

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but it's actually not a very easy

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question to answer, right?

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So if we talk about one way that we can

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think about it is that we can think

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about data is information that helps us

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make decisions.

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Another way that we can think about it

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is data is just numbers, right?

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Like if it's stored on.

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If you have data stored on a computer,

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it's just like a big sequence of bits.

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And that's all that's really all data

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is.

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It's just a bunch of numbers.

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So for people, if we think about how do

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we represent data, we store it in terms

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of media that we can see, read or hear.

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So we might have images.

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We might have like text documents, we

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might have audio files, we could have

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plots and tables.

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So there are things that we perceive

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and then we make sense of it based on

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our perception.

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And we can.

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The data can take different forms

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without really changing its meaning.

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So we can resize an image, we can

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refreeze a paragraph, we can speed up

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an audio book, and all of that changes

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the form of the data a bit, but it

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doesn't really change much of the

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information that data contained.

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And sometimes we can change the data so

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that it becomes more informative to us.

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So we can denoise an image, we can

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clean it up.

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We can try to identify the key points

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and insights in a document.

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Cliff notes.

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We can remove background noise from

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audio.

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And none of these operations really add

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information to the data.

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If anything, they take away

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information, they prune it.

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But they reorganize it, and they

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removed distracting information so that

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it's easier for us to extract

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information that we want from that

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data.

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So that's from the, that's from our

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perspective as people.

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For computers, data are just numbers,

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so the numbers don't really mean

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anything by themselves.

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They're just bits, right?

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The meaning comes from the way the

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numbers were produced and how they can

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inform what they can tell us about

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other numbers, essentially.

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So.

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There you could have like each.

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Each number could be informative on its

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own, or it could only be informative if

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you view it in patterns of other groups

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of numbers.

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So one bit.

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If you have a whole bit string, the

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bits individually may not mean

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anything, but those bits may form

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characters, and those characters may

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form words, and those words may tell us

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something useful.

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So just like just like just like we can

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resize images and speed up audio and

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things like that to change the form of

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the data without changing the

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information and the data, we can also

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transform data without changing its

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information and computer programs.

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So, for example, we can add or multiply

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a vector by a constant value, and as

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long as we do that consistently, it

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doesn't really change the information

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that's contained in that data.

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So there's nothing inherently different

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about, for example, if I represent a

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vector or I represent the negative

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vector, as long as I'm consistent.

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We can represent the data in different

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ways, As for example 16 or 32 bit

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floats or integers.

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We might lose a little bit, but not

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very much.

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We can compress the document or store

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it in a different file format, so

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there's lots of different ways to

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represent the same data without

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changing the information.

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That is stored in that data or that's

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represented by that data?

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And justice like sometimes we can

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create summaries or ways to make data

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more informative for people.

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We can also sometimes transform the

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data to make it more informative for

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computers.

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So we can center and rescale the images

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of digits so that they're easier to

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compare each other to each other.

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For example, we can normalize the data,

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for example, subtract the means and

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divide by a stern deviations of the

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features of like cancer cell

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measurements that make similarity

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measurements better reflect malignancy.

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And we can do feature selection or

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create new features out of combinations

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of inputs.

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So this is kind of like analogous to

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creating a summary of a document.

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Or denoising the image so that we can

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see it better, or enhancing or things

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like that, right?

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Makes it easier to extract information

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from the same data.

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And sometimes they also change the

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structure of the data to make it easier

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to process.

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So we might naturally think of the

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image as a matrix because we where each

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of these grid cells represent some

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intensity at some position in the

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image.

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And this feels natural because the

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image is like takes up some area.

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It's like it makes sense to think of it

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in terms of rows and columns, but we

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can equivalently represent it as a

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vector, which is what we did for the

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homework and what we often do.

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And you just reshape it, and this is

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more convenient.

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So the matrix form is more convenient

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for local pattern analysis if we're

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trying to look for edges and things

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like that.

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The vector form is more convenient if

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we're trying to apply a linear model to

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it, because we can just do that as a as

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a dot product operation.

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So either way, it doesn't change the

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information and the data.

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But this form like makes no sense to us

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as people.

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But for computers it's more convenient

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to do certain kinds of operations if

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you represent it as a vector versus a

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matrix.

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So let's talk about how some different

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forms of information are represented.

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So as I mentioned a little bit in the

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last class, we can represent images as

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3D matrices.

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Where the three dimensions are the row,

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the column and the color.

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So if we have some intensity pattern

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like this, then the bright values are

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typically one or 255 depending on your

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representation.

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The dark values will be very low, like

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0 or in this case the darkest values

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are only about .3.

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And you represent that for the entire

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image area, and that gives you.

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If you're representing a grayscale

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image, you would just have one color

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dimension, so you'd have a number of

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rows by number of columns by one.

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If you have an RGB image, then you

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would have one matrix for each of the

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color dimensions.

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So you'd have a 2D matrix for R2D

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matrix for G and a 2D matrix for B.

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Text can be represented as a sequence

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of integers.

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And it's actually, I'm going to talk

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we'll learn a lot more about word

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representations next week and how to

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process language, but it's actually a

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more subtle problem than you might

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think at first.

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So you might think well represent each

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word as an integer.

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But then that becomes kind of tricky

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because you can have lots of similar

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words swims and swim and swim, and

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those will all be different integers.

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And those integers are kind of like

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arbitrary tokens.

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Don't necessarily have any similarity

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to each other.

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And then if you try to represent things

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as integers, and then you run into

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names and lots of different varieties

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of ways that we put characters

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together, then you have difficulty

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representing all of those.

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You need an awful lot of integers.

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So you can go to another extreme and

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represent the characters as.

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You can just represent the characters

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as byte values.

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So you can represent dog eat as like

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four 15727 using 27 as space 125.

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So you could just represent the

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characters as a bite stream and process

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it that way.

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That's one extreme.

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The other extreme is that you represent

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each complete word as an integer value

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and so you pre assign you have some.

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Vocabulary where you have like all the

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words that you think you might

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encounter.

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You assign each word to some integer,

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and then you have an integer sequence

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that you're going to process.

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And if you see some new set of

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characters that is not any rockabilly,

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you assign it to an unknown token, a

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token called Unknown or UNK typically.

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And then there's also like intermediate

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things, which I'll talk about more when

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I talk about language, where you can

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group common groups of letters into

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their own little groups and represent

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each of those.

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So you can represent, for example,

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bedroom 1521 as bed, one token for bed,

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or one integer for bed, one integer for

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room, and then four more integers for

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1521.

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And with this kind of representation

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you can model any kind of like

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sequence.

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The characters just really weird

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sequences like random letters will take

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a lot of different integers to

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represent, while something, well,

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common words will only take one integer

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each.

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And then we also may want to represent

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audio.

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So audio we can represent in different

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ways, we can represent it as amplitude

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versus time.

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The wave form, and this is usually the

00:12:48.870 --> 00:12:50.590
way that it's stored is just you have

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an amplitude at some high frequency or

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you can represent it as a spectrogram

00:12:58.530 --> 00:13:00.660
as like a frequency, amplitude versus

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time like what's the power and the.

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And the low notes versus the high notes

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at each time step.

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And then there's lots of other kinds of

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data.

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So we can represent measurements and

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continuous values as floating point

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numbers, temperature length, area,

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dollars, categorical values like color,

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like whether something's happy or sad

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or big or small, those can be

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represented as integers.

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And here the distinction is that when

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you're representing categorical values

00:13:34.052 --> 00:13:36.210
as integers, these integers.

00:13:36.840 --> 00:13:38.620
The distance between integers doesn't

00:13:38.620 --> 00:13:40.920
imply similarity usually, so you don't

00:13:40.920 --> 00:13:42.790
necessarily say that zero is more

00:13:42.790 --> 00:13:45.150
similar to one than it is to two when

00:13:45.150 --> 00:13:46.910
you're representing categorical values.

00:13:47.960 --> 00:13:49.530
But if you're representing continuous

00:13:49.530 --> 00:13:51.110
values, then you see that some

00:13:51.110 --> 00:13:52.820
Euclidean distance between those values

00:13:52.820 --> 00:13:53.710
is meaningful.

00:13:55.920 --> 00:13:57.820
And all of these different types of

00:13:57.820 --> 00:14:00.120
values, the text, the images and the

00:14:00.120 --> 00:14:02.560
measurements can be reshaped and

00:14:02.560 --> 00:14:04.670
concatenated into a long feature

00:14:04.670 --> 00:14:05.050
vector.

00:14:05.050 --> 00:14:06.610
And that's often what we do.

00:14:06.610 --> 00:14:09.240
We take everything, every kind of

00:14:09.240 --> 00:14:11.300
information that we think can be

00:14:11.300 --> 00:14:13.900
applicable to solve some problem or

00:14:13.900 --> 00:14:15.500
predict some why that we're interested

00:14:15.500 --> 00:14:15.730
in.

00:14:16.440 --> 00:14:20.190
At some point we take that information,

00:14:20.190 --> 00:14:22.640
we reshape it into a big vector, and

00:14:22.640 --> 00:14:24.970
then we do a prediction based on that

00:14:24.970 --> 00:14:25.410
vector.

00:14:33.060 --> 00:14:34.640
Weird screeching sound.

00:14:35.270 --> 00:14:35.840


00:14:37.010 --> 00:14:39.780
So this is the same information.

00:14:39.780 --> 00:14:41.440
Content can be represented in many

00:14:41.440 --> 00:14:41.910
ways.

00:14:43.150 --> 00:14:45.930
Essentially, if the original numbers

00:14:45.930 --> 00:14:47.502
can be recovered, then it means that

00:14:47.502 --> 00:14:49.475
the change in representation doesn't

00:14:49.475 --> 00:14:50.980
change the information content.

00:14:50.980 --> 00:14:52.729
So any kind of transformation that we

00:14:52.730 --> 00:14:54.419
apply that we can invert, that we can

00:14:54.420 --> 00:14:56.350
get back to the original is not

00:14:56.350 --> 00:14:57.720
changing the information, it's just

00:14:57.720 --> 00:14:59.510
reshaping the data in some way that

00:14:59.510 --> 00:15:01.550
might make it easier or maybe harder to

00:15:01.550 --> 00:15:02.210
process.

00:15:03.570 --> 00:15:05.795
And we can store all types of data as

00:15:05.795 --> 00:15:07.100
1D vectors and arrays.

00:15:07.850 --> 00:15:10.800
And so we'll typically have like as our

00:15:10.800 --> 00:15:15.480
data set will have some set of vectors,

00:15:15.480 --> 00:15:17.630
a matrix where the columns are

00:15:17.630 --> 00:15:20.320
individual data samples and the rows

00:15:20.320 --> 00:15:22.570
correspond to different features as

00:15:22.570 --> 00:15:24.340
representing a set of data.

00:15:25.500 --> 00:15:27.820
And you don't, really.

00:15:27.820 --> 00:15:30.060
You never really need to use matrices

00:15:30.060 --> 00:15:31.680
or other data structures, but they just

00:15:31.680 --> 00:15:33.690
make it easier for us to code, and so

00:15:33.690 --> 00:15:34.170
it doesn't.

00:15:34.170 --> 00:15:36.080
Again, like there's nothing inherent

00:15:36.080 --> 00:15:37.740
about those structures that adds

00:15:37.740 --> 00:15:39.800
information to the data, it's just for

00:15:39.800 --> 00:15:40.570
convenience.

00:15:42.980 --> 00:15:45.000
So all of that so far is kind of

00:15:45.000 --> 00:15:49.019
describing a data .1 piece of data that

00:15:49.020 --> 00:15:51.460
we might use to make a prediction to

00:15:51.460 --> 00:15:52.980
gather some information from.

00:15:53.750 --> 00:15:55.660
But in machine learning, we're usually

00:15:55.660 --> 00:15:56.035
dealing.

00:15:56.035 --> 00:15:58.385
We're often dealing with data sets, so

00:15:58.385 --> 00:16:01.340
we want to learn from some set of data

00:16:01.340 --> 00:16:03.676
so that when we get some new data

00:16:03.676 --> 00:16:05.540
point, we can make some useful

00:16:05.540 --> 00:16:07.060
prediction from that data point.

00:16:08.850 --> 00:16:12.144
So we can write this as that we have

00:16:12.144 --> 00:16:14.436
some where X is a set of data.

00:16:14.436 --> 00:16:17.607
The little X here, or actually I have X

00:16:17.607 --> 00:16:18.670
is not a set of data, sorry.

00:16:18.670 --> 00:16:21.190
The little X is a data point with M

00:16:21.190 --> 00:16:24.120
features, so it has some M scalar

00:16:24.120 --> 00:16:27.304
values and it's drawn from some

00:16:27.304 --> 00:16:29.720
distribution D so for example, your

00:16:29.720 --> 00:16:32.114
distribution D could be all the images

00:16:32.114 --> 00:16:34.650
that are on the Internet and you're

00:16:34.650 --> 00:16:36.207
just like downloading random images

00:16:36.207 --> 00:16:37.070
from the Internet.

00:16:37.120 --> 00:16:38.820
And then one of those random images is

00:16:38.820 --> 00:16:39.820
a little X.

00:16:41.330 --> 00:16:43.650
We can sample many of these X's so we

00:16:43.650 --> 00:16:45.040
could download different documents from

00:16:45.040 --> 00:16:45.442
the Internet.

00:16:45.442 --> 00:16:47.170
We could download like emails to

00:16:47.170 --> 00:16:49.000
classify spam or not spam.

00:16:49.000 --> 00:16:51.769
We could take pictures, we could take

00:16:51.770 --> 00:16:54.830
measurements, and then we get a

00:16:54.830 --> 00:16:57.180
collection of those data points and

00:16:57.180 --> 00:16:59.830
that gives us some big X.

00:16:59.830 --> 00:17:03.610
It's a set of these X little X vectors

00:17:03.610 --> 00:17:06.890
from one to N, from zero to N guess it

00:17:06.890 --> 00:17:08.290
should be 0 to minus one.

00:17:09.170 --> 00:17:11.830
And that's John.

00:17:11.830 --> 00:17:13.790
It's all drawn from some distribution D

00:17:13.790 --> 00:17:15.260
so there's always some implicit

00:17:15.260 --> 00:17:16.865
distribution even if we don't know what

00:17:16.865 --> 00:17:19.190
it is, some source of the data that

00:17:19.190 --> 00:17:19.950
we're sampling.

00:17:19.950 --> 00:17:21.936
And typically we assume that we don't

00:17:21.936 --> 00:17:23.332
have all the data, we just have like

00:17:23.332 --> 00:17:25.020
some of it, we have some representative

00:17:25.020 --> 00:17:26.200
sample of that data.

00:17:27.380 --> 00:17:28.940
So we can repeat the collection many

00:17:28.940 --> 00:17:30.980
times, or we can collect one big data

00:17:30.980 --> 00:17:33.670
set and split it, and then we'll often

00:17:33.670 --> 00:17:36.173
split it into some X train, which are

00:17:36.173 --> 00:17:37.950
the samples that we're going to learn

00:17:37.950 --> 00:17:40.935
from an ex test, which are the samples

00:17:40.935 --> 00:17:42.820
that we're going to use to see how we

00:17:42.820 --> 00:17:43.350
learned.

00:17:44.950 --> 00:17:47.210
And usually we assume that all the data

00:17:47.210 --> 00:17:49.518
samples within X train and X test come

00:17:49.518 --> 00:17:51.240
from the same distribution and are

00:17:51.240 --> 00:17:52.505
independent of each other.

00:17:52.505 --> 00:17:54.620
So that term is called IID or

00:17:54.620 --> 00:17:56.470
independent identically distributed.

00:17:56.470 --> 00:17:59.760
And essentially that just means that no

00:17:59.760 --> 00:18:01.510
data point tells you anything about

00:18:01.510 --> 00:18:03.590
another data point if you the sampling

00:18:03.590 --> 00:18:04.027
distribution.

00:18:04.027 --> 00:18:06.654
So they come from the same

00:18:06.654 --> 00:18:07.092
distribution.

00:18:07.092 --> 00:18:09.865
So maybe they have they may have

00:18:09.865 --> 00:18:12.077
similar values to each other, but if

00:18:12.077 --> 00:18:13.466
know that distribution then they're

00:18:13.466 --> 00:18:14.299
then they're independent.

00:18:14.360 --> 00:18:16.050
If you randomly download images from

00:18:16.050 --> 00:18:16.660
the Internet.

00:18:17.410 --> 00:18:19.105
Each image tells you something about

00:18:19.105 --> 00:18:20.460
images, but they don't really tell you

00:18:20.460 --> 00:18:22.336
directly anything about the other

00:18:22.336 --> 00:18:24.149
images about a specific other image.

00:18:27.230 --> 00:18:29.540
So let's look at an example from this

00:18:29.540 --> 00:18:33.550
Penguins data set that we use in the

00:18:33.550 --> 00:18:34.000
homework.

00:18:34.820 --> 00:18:36.640
And I'm not actually going to analyze

00:18:36.640 --> 00:18:38.120
it in a way that directly helps you

00:18:38.120 --> 00:18:38.720
with your homework.

00:18:38.720 --> 00:18:40.220
It's just an example that you may be

00:18:40.220 --> 00:18:40.760
familiar with.

00:18:41.830 --> 00:18:43.010
But let's look at this.

00:18:43.010 --> 00:18:44.670
So we have this.

00:18:44.670 --> 00:18:46.970
It's represented in this like Panda

00:18:46.970 --> 00:18:49.370
framework, but basically just a tabular

00:18:49.370 --> 00:18:49.820
framework.

00:18:50.490 --> 00:18:53.020
So we have a whole bunch of data points

00:18:53.020 --> 00:18:55.360
where we know the species, the island,

00:18:55.360 --> 00:18:56.600
the.

00:18:57.400 --> 00:18:58.810
I don't even know what a Coleman is.

00:18:58.810 --> 00:18:59.950
Maybe the beak or something.

00:19:01.270 --> 00:19:03.130
Cullman length and depth probably not

00:19:03.130 --> 00:19:05.290
to be, I don't know, flipper length,

00:19:05.290 --> 00:19:07.700
body mass and the sets of the Penguin

00:19:07.700 --> 00:19:08.700
which may be unknown.

00:19:10.120 --> 00:19:11.920
And so the first thing we do, which is

00:19:11.920 --> 00:19:14.158
in the starter code, is we try to

00:19:14.158 --> 00:19:17.830
process the process the data into a

00:19:17.830 --> 00:19:19.830
format that is more convenient for

00:19:19.830 --> 00:19:20.510
machine learning.

00:19:21.570 --> 00:19:24.270
And so for example like the.

00:19:25.220 --> 00:19:29.770
The SK learn learn methods for training

00:19:29.770 --> 00:19:32.790
trees does not deal with like multi

00:19:32.790 --> 00:19:34.450
valued categorical variables.

00:19:34.450 --> 00:19:35.850
So it can't deal with that.

00:19:35.850 --> 00:19:37.325
There are like 3 different islands.

00:19:37.325 --> 00:19:39.065
It means you to turn it into binary

00:19:39.065 --> 00:19:39.540
variables.

00:19:40.340 --> 00:19:42.430
And so the first thing that you often

00:19:42.430 --> 00:19:44.340
do when you're trying to analyze a

00:19:44.340 --> 00:19:48.020
problem is you, like, reformat the data

00:19:48.020 --> 00:19:51.250
in a way that allows you to process the

00:19:51.250 --> 00:19:53.370
data or learn from the data more

00:19:53.370 --> 00:19:54.130
conveniently.

00:19:54.980 --> 00:19:58.900
So in this code we read the CSV that

00:19:58.900 --> 00:20:02.280
gives us some tabular format for the

00:20:02.280 --> 00:20:03.190
Penguin data.

00:20:04.230 --> 00:20:08.290
And then I just form this into an array

00:20:08.290 --> 00:20:10.490
so I get extracted features.

00:20:10.490 --> 00:20:12.160
These are all the different columns of

00:20:12.160 --> 00:20:13.253
that Penguin data.

00:20:13.253 --> 00:20:15.072
I put it in a Numpy array.

00:20:15.072 --> 00:20:18.435
I get the species because that's what

00:20:18.435 --> 00:20:20.100
the problem was to predict.

00:20:20.100 --> 00:20:22.389
And then I get the unique values of the

00:20:22.390 --> 00:20:23.300
island.

00:20:23.300 --> 00:20:26.840
I get the unique values of the sex

00:20:26.840 --> 00:20:28.880
which will be male, female and unknown.

00:20:28.880 --> 00:20:32.760
And I initialize some array where I'm

00:20:32.760 --> 00:20:34.000
going to store my data.

00:20:34.430 --> 00:20:36.722
Then I loop through all the elements or

00:20:36.722 --> 00:20:38.250
all the data points, and I know that

00:20:38.250 --> 00:20:39.830
there's one data point for each Y

00:20:39.830 --> 00:20:41.440
value, so I looked through the length

00:20:41.440 --> 00:20:41.800
of Y.

00:20:42.950 --> 00:20:44.770
And then I just replace the island

00:20:44.770 --> 00:20:46.890
names with an indicator variable with

00:20:46.890 --> 00:20:48.960
three indicator variables so I forget

00:20:48.960 --> 00:20:49.353
what the.

00:20:49.353 --> 00:20:50.720
I guess they're down here so if the

00:20:50.720 --> 00:20:51.930
island is Biscoe.

00:20:52.690 --> 00:20:54.830
Then the first value will be zero, I

00:20:54.830 --> 00:20:55.560
mean will be one.

00:20:56.460 --> 00:20:58.292
F and otherwise it will be 0.

00:20:58.292 --> 00:21:00.690
If the island is dream then the second

00:21:00.690 --> 00:21:02.850
value will be one and otherwise it will

00:21:02.850 --> 00:21:03.390
be 0.

00:21:03.390 --> 00:21:06.620
And if the island is Torgerson then the

00:21:06.620 --> 00:21:09.028
third value will be one and otherwise

00:21:09.028 --> 00:21:10.460
it will be 0.

00:21:10.460 --> 00:21:12.120
So exactly one of these should be equal

00:21:12.120 --> 00:21:13.646
to 1 and the other should be equal to

00:21:13.646 --> 00:21:13.820
0.

00:21:14.710 --> 00:21:16.154
Then I fell in the floating point

00:21:16.154 --> 00:21:17.980
values for these other things and then

00:21:17.980 --> 00:21:19.830
I do the same for this X.

00:21:19.830 --> 00:21:22.420
So one of these three values, female,

00:21:22.420 --> 00:21:24.892
male or unknown will be a one and the

00:21:24.892 --> 00:21:26.160
other two will be a 0.

00:21:26.950 --> 00:21:28.590
And so at the end of this I have this

00:21:28.590 --> 00:21:32.650
like now this data vector where each

00:21:32.650 --> 00:21:33.380
column.

00:21:34.050 --> 00:21:36.340
Will be either like a binary number or

00:21:36.340 --> 00:21:39.103
a floating point number that tells me

00:21:39.103 --> 00:21:42.360
like what island or what sex and what

00:21:42.360 --> 00:21:46.870
the Penguin had and then the I'll have

00:21:46.870 --> 00:21:50.620
a row for each data sample and for Y

00:21:50.620 --> 00:21:52.440
I'll just have her vote for each data

00:21:52.440 --> 00:21:55.360
sample that has the name of the thing

00:21:55.360 --> 00:21:56.920
I'm trying to predict, the species.

00:22:01.580 --> 00:22:04.390
So if we have some data set like that,

00:22:04.390 --> 00:22:06.040
then how do we measure it?

00:22:06.040 --> 00:22:09.156
So there's some simple things we can

00:22:09.156 --> 00:22:09.468
do.

00:22:09.468 --> 00:22:11.235
One is we can just measure the shape so

00:22:11.235 --> 00:22:15.520
we can see this has 341 data samples

00:22:15.520 --> 00:22:17.070
and I've got 10 features.

00:22:18.070 --> 00:22:20.730
I can also start to think about it now

00:22:20.730 --> 00:22:21.710
as the distribution.

00:22:21.710 --> 00:22:23.520
So it's no longer just like an

00:22:23.520 --> 00:22:25.500
individual point or an individual set

00:22:25.500 --> 00:22:27.940
of values, but it's a distribution.

00:22:27.940 --> 00:22:29.377
There's some probability that I'll

00:22:29.377 --> 00:22:31.674
observe some sets of values, and some

00:22:31.674 --> 00:22:33.520
probability that I'll observe other

00:22:33.520 --> 00:22:34.309
sets of values.

00:22:35.020 --> 00:22:37.100
And so one really simple way that I can

00:22:37.100 --> 00:22:39.460
measure the distribution is by looking

00:22:39.460 --> 00:22:41.213
at the mean and the standard deviation.

00:22:41.213 --> 00:22:43.950
If it were a Gaussian distribution

00:22:43.950 --> 00:22:46.015
where the values are independent from

00:22:46.015 --> 00:22:47.665
each other and different if the

00:22:47.665 --> 00:22:49.071
different features are independent from

00:22:49.071 --> 00:22:50.860
each other in a Gaussian, this would

00:22:50.860 --> 00:22:52.300
tell me everything there is to know

00:22:52.300 --> 00:22:53.780
about the distribution.

00:22:53.780 --> 00:22:55.996
But in practice you rarely have a

00:22:55.996 --> 00:22:56.339
Gaussian.

00:22:56.340 --> 00:22:58.210
Usually it's a bit more complicated.

00:22:58.210 --> 00:22:59.206
Still, it's a useful thing.

00:22:59.206 --> 00:23:02.680
So it tells me that like the body mass

00:23:02.680 --> 00:23:05.630
average is 4200 grams.

00:23:05.950 --> 00:23:08.185
And the steering deviation is 800, so

00:23:08.185 --> 00:23:10.890
there's so the average is like 4.1

00:23:10.890 --> 00:23:12.720
kilograms, but there's like a

00:23:12.720 --> 00:23:14.110
significant variance there.

00:23:18.640 --> 00:23:23.121
One of the key things to know is that

00:23:23.121 --> 00:23:25.580
the is that I'm just getting an

00:23:25.580 --> 00:23:27.270
empirical estimate of this

00:23:27.270 --> 00:23:29.855
distribution, so I don't know what the

00:23:29.855 --> 00:23:30.686
true mean is.

00:23:30.686 --> 00:23:32.625
I don't know what the true standard

00:23:32.625 --> 00:23:33.179
deviation is.

00:23:33.180 --> 00:23:34.970
All I know is what the mean and the

00:23:34.970 --> 00:23:37.240
standard deviation is of my sample, and

00:23:37.240 --> 00:23:39.240
if I were to draw different samples, I

00:23:39.240 --> 00:23:41.530
would get different estimates of the

00:23:41.530 --> 00:23:42.780
mean and the standard deviation.

00:23:43.750 --> 00:23:46.770
So in the top row, I'm resampling this

00:23:46.770 --> 00:23:49.640
data using this convenient sample

00:23:49.640 --> 00:23:52.720
function that the PANDA framework has,

00:23:52.720 --> 00:23:54.693
and then taking the mean each time.

00:23:54.693 --> 00:23:57.310
So you can see that one time 45% of the

00:23:57.310 --> 00:23:59.480
Penguins come from Cisco, another time

00:23:59.480 --> 00:24:02.770
it's 54%, and another time it's 44%.

00:24:02.770 --> 00:24:05.330
So this is drawing 100 samples with

00:24:05.330 --> 00:24:06.070
replacement.

00:24:06.990 --> 00:24:10.570
And by the way, is like is like

00:24:10.570 --> 00:24:11.220
bootstrapping.

00:24:11.220 --> 00:24:12.795
If I want to say what's the variance of

00:24:12.795 --> 00:24:13.232
my estimate?

00:24:13.232 --> 00:24:16.240
If I had 100 samples of data, I could

00:24:16.240 --> 00:24:18.920
repeat this random sampling 100 times

00:24:18.920 --> 00:24:20.800
and then take the variance of my mean

00:24:20.800 --> 00:24:22.528
and that would give me the variance of

00:24:22.528 --> 00:24:24.718
my estimate, even though I don't have

00:24:24.718 --> 00:24:27.360
like even even though I have a rather

00:24:27.360 --> 00:24:29.270
small sample to draw that estimate

00:24:29.270 --> 00:24:29.820
from.

00:24:31.210 --> 00:24:33.040
If I have more data, I'm going to get

00:24:33.040 --> 00:24:34.900
more accurate estimates.

00:24:34.900 --> 00:24:39.189
So if I sample 1000 samples, I'm

00:24:39.190 --> 00:24:40.780
drawing samples with replacement.

00:24:42.390 --> 00:24:44.749
Then the averages become much more

00:24:44.750 --> 00:24:45.140
similar.

00:24:45.140 --> 00:24:49.650
So now Biscoe goes from 475 to 473 to

00:24:49.650 --> 00:24:52.220
484, so it's a much smaller range than

00:24:52.220 --> 00:24:54.382
it was when I drew 100 samples.

00:24:54.382 --> 00:24:56.635
So in general like, the more I'm able

00:24:56.635 --> 00:24:59.970
to draw, the tighter my estimate of the

00:24:59.970 --> 00:25:01.260
distribution will be.

00:25:01.870 --> 00:25:03.525
But it's always an estimate of the

00:25:03.525 --> 00:25:03.757
distribution.

00:25:03.757 --> 00:25:05.120
It's not the true distribution.

00:25:08.870 --> 00:25:10.560
So there's also other ways that we can

00:25:10.560 --> 00:25:12.100
try to measure this data set.

00:25:12.100 --> 00:25:16.120
So one idea is to try to measure the

00:25:16.120 --> 00:25:18.110
entropy of a particular variable.

00:25:19.420 --> 00:25:21.610
If the variable is discrete, which

00:25:21.610 --> 00:25:24.015
means that it has like integer values,

00:25:24.015 --> 00:25:26.400
it has a finite number of values.

00:25:27.450 --> 00:25:29.870
And then we can measure it by counting.

00:25:29.870 --> 00:25:34.100
So we can say that the entropy will be

00:25:34.100 --> 00:25:36.040
the negative sum all the different

00:25:36.040 --> 00:25:37.670
values of that variable of the

00:25:37.670 --> 00:25:39.360
probability of that value times the log

00:25:39.360 --> 00:25:40.470
probability of that value.

00:25:41.340 --> 00:25:42.550
And I can count it like this.

00:25:42.550 --> 00:25:44.300
I can just say in this case these are

00:25:44.300 --> 00:25:47.080
binary, so I just count how many times

00:25:47.080 --> 00:25:49.190
XI equals zero or the fraction of times

00:25:49.190 --> 00:25:51.030
that's the probability of X I = 0.

00:25:52.240 --> 00:25:54.494
The fraction times XI equals one and

00:25:54.494 --> 00:25:57.222
then my cross and then my not cross

00:25:57.222 --> 00:25:57.675
entropy.

00:25:57.675 --> 00:25:59.623
My entropy is the negative probability

00:25:59.623 --> 00:26:02.090
of XI equals zero times the log base

00:26:02.090 --> 00:26:04.290
two probability of XI equals 0 minus

00:26:04.290 --> 00:26:07.269
probability XI equals one times log

00:26:07.269 --> 00:26:09.310
probability of XI equal 1.

00:26:10.770 --> 00:26:13.460
The log base two thing is like a

00:26:13.460 --> 00:26:15.360
convention, and it means that this

00:26:15.360 --> 00:26:17.600
entropy is measured in bits.

00:26:17.600 --> 00:26:20.550
So it's essentially how many bits you

00:26:20.550 --> 00:26:23.686
would need theoretically to be able to

00:26:23.686 --> 00:26:25.570
like disambiguate this value or specify

00:26:25.570 --> 00:26:26.310
this value.

00:26:27.030 --> 00:26:29.690
If you had a, if your data were all

00:26:29.690 --> 00:26:31.540
ones, then you really don't need any

00:26:31.540 --> 00:26:32.929
bits to represent it because it's

00:26:32.930 --> 00:26:33.870
always A1.

00:26:33.870 --> 00:26:35.930
But if it's like a completely random

00:26:35.930 --> 00:26:38.469
value, 5050 chance that it's a zero or

00:26:38.469 --> 00:26:40.942
one, then you need one bit to represent

00:26:40.942 --> 00:26:42.965
it because you until you observe it,

00:26:42.965 --> 00:26:44.245
you have no idea what it is, so you

00:26:44.245 --> 00:26:47.030
need a full bit to represent that bit.

00:26:48.460 --> 00:26:50.470
So if I look at Island Biscoe, it's

00:26:50.470 --> 00:26:53.010
almost a 5050 chance, so the entropy is

00:26:53.010 --> 00:26:53.510
very high.

00:26:53.510 --> 00:26:54.580
It's .999.

00:26:55.280 --> 00:26:57.050
If I look at a different feature index,

00:26:57.050 --> 00:26:58.400
the one for Torgerson.

00:26:59.510 --> 00:27:02.460
Only like 15% of the Penguins come from

00:27:02.460 --> 00:27:05.100
tergesen and so the entropy is much

00:27:05.100 --> 00:27:05.690
lower.

00:27:05.690 --> 00:27:07.020
It's .69.

00:27:11.760 --> 00:27:14.140
We can also measure the entropy of

00:27:14.140 --> 00:27:16.130
continuous variables.

00:27:16.130 --> 00:27:19.030
So if I have, for example the Cullman

00:27:19.030 --> 00:27:19.700
length.

00:27:19.700 --> 00:27:21.500
Now I can't just like count how many

00:27:21.500 --> 00:27:23.450
times I observe each value of Coleman

00:27:23.450 --> 00:27:25.030
length, because those values may be

00:27:25.030 --> 00:27:25.420
unique.

00:27:25.420 --> 00:27:26.880
I'll probably observe each value

00:27:26.880 --> 00:27:27.620
exactly once.

00:27:28.730 --> 00:27:31.589
And so instead we need to we need to

00:27:31.590 --> 00:27:34.130
have other ways of estimating that

00:27:34.130 --> 00:27:35.560
continuous distribution.

00:27:36.890 --> 00:27:39.610
So mathematically, the entropy of the

00:27:39.610 --> 00:27:42.630
variable X is now the negative integral

00:27:42.630 --> 00:27:44.760
over all the possible values X of

00:27:44.760 --> 00:27:47.395
probability of X times log probability

00:27:47.395 --> 00:27:48.550
of X.

00:27:48.550 --> 00:27:51.300
But this becomes a kind of complicated

00:27:51.300 --> 00:27:55.110
in a way because our data, while the

00:27:55.110 --> 00:27:56.780
values may be continuous, we don't have

00:27:56.780 --> 00:27:58.850
access to a continuous or infinite

00:27:58.850 --> 00:27:59.510
amount of data.

00:28:00.160 --> 00:28:02.350
And so we always need to estimate this

00:28:02.350 --> 00:28:04.520
continuous distribution based on our

00:28:04.520 --> 00:28:05.400
discrete sample.

00:28:07.160 --> 00:28:08.500
There's a lot of different ways of

00:28:08.500 --> 00:28:10.550
doing this, but one of the most common

00:28:10.550 --> 00:28:14.467
is to break up our continuous variable

00:28:14.467 --> 00:28:17.882
into smaller discrete variables into

00:28:17.882 --> 00:28:20.430
smaller discrete ranges, and then count

00:28:20.430 --> 00:28:22.220
for each of those discrete ranges.

00:28:22.220 --> 00:28:23.460
So that's what I did here.

00:28:24.260 --> 00:28:27.320
So I get the XI for the.

00:28:27.320 --> 00:28:28.690
This is for the Coleman length.

00:28:30.780 --> 00:28:33.060
I forgot to include this printed value,

00:28:33.060 --> 00:28:35.790
but there's if I the printed value here

00:28:35.790 --> 00:28:37.600
is just like a lot I think like all the

00:28:37.600 --> 00:28:38.420
values are unique.

00:28:39.230 --> 00:28:42.000
And I'm creating like empty indices

00:28:42.000 --> 00:28:44.604
because I'm being lazy here for the X

00:28:44.604 --> 00:28:47.915
value and for the probability of each X

00:28:47.915 --> 00:28:48.290
value.

00:28:49.190 --> 00:28:51.000
And I'm setting a step size of 1.

00:28:52.010 --> 00:28:54.635
Then I loop from the minimum value plus

00:28:54.635 --> 00:28:57.167
half a step to the maximum value minus

00:28:57.167 --> 00:28:58.094
half a step.

00:28:58.094 --> 00:28:59.020
I take steps.

00:28:59.020 --> 00:29:01.799
So I take steps of 1 from maybe like

00:29:01.800 --> 00:29:05.348
whoops, from maybe like 30, stop from

00:29:05.348 --> 00:29:07.340
maybe 30 to 60.

00:29:07.340 --> 00:29:10.460
And for each of those steps I count how

00:29:10.460 --> 00:29:14.870
many times I see a value within a range

00:29:14.870 --> 00:29:16.750
of like my current value minus half

00:29:16.750 --> 00:29:18.050
step plus half step.

00:29:18.050 --> 00:29:20.485
So for example, the first one will be

00:29:20.485 --> 00:29:21.890
from say like.

00:29:21.950 --> 00:29:24.860
How many times do I observe the common

00:29:24.860 --> 00:29:27.900
length between like 31 and 32?

00:29:28.670 --> 00:29:30.676
And so that will be my mean.

00:29:30.676 --> 00:29:32.370
So this is I'm estimating the

00:29:32.370 --> 00:29:34.010
probability that it falls within this

00:29:34.010 --> 00:29:34.440
range.

00:29:35.380 --> 00:29:37.130
And then I can turn this into a

00:29:37.130 --> 00:29:39.940
continuous distribution by dividing by

00:29:39.940 --> 00:29:40.850
the step size.

00:29:42.310 --> 00:29:43.820
So that will make it comparable.

00:29:43.820 --> 00:29:44.960
If I were to choose different step

00:29:44.960 --> 00:29:47.050
sizes, I should get like fairly similar

00:29:47.050 --> 00:29:47.620
plots.

00:29:47.620 --> 00:29:50.330
And the one -, 20 is just to avoid a

00:29:50.330 --> 00:29:52.140
divide by zero without really changing

00:29:52.140 --> 00:29:52.610
much else.

00:29:54.690 --> 00:29:58.290
So then I plot it and the cross entropy

00:29:58.290 --> 00:30:01.727
is just the negative sum of all of

00:30:01.727 --> 00:30:04.750
these different probabilities that the

00:30:04.750 --> 00:30:06.875
discrete probabilities now of these

00:30:06.875 --> 00:30:10.010
different ranges times the log 2

00:30:10.010 --> 00:30:12.460
probability of each of those ranges.

00:30:13.090 --> 00:30:17.120
And then I need to multiply that by the

00:30:17.120 --> 00:30:18.680
step size as well, which in this case

00:30:18.680 --> 00:30:19.380
is just one.

00:30:24.540 --> 00:30:27.018
OK, and then so I get an estimate.

00:30:27.018 --> 00:30:28.540
So this is the plot.

00:30:28.540 --> 00:30:30.950
This is the probability.

00:30:30.950 --> 00:30:32.840
It's my estimate of the continuous

00:30:32.840 --> 00:30:36.345
probability now of each variable of

00:30:36.345 --> 00:30:37.270
each value of X.

00:30:37.950 --> 00:30:39.520
And then this is my estimate of the

00:30:39.520 --> 00:30:40.180
entropy.

00:30:45.190 --> 00:30:48.320
So as I mentioned, I would like

00:30:48.320 --> 00:30:50.640
continuous features are kind of tricky

00:30:50.640 --> 00:30:52.360
because it depends on.

00:30:52.360 --> 00:30:54.240
I can estimate their probabilities in

00:30:54.240 --> 00:30:56.310
different ways and that will give me

00:30:56.310 --> 00:30:58.790
different distributions and different

00:30:58.790 --> 00:31:00.400
measurements of things like entropy.

00:31:01.340 --> 00:31:04.420
So if I chose a different step size, if

00:31:04.420 --> 00:31:06.950
I step in .1, that means I'm going to

00:31:06.950 --> 00:31:08.719
count how many times I observe this

00:31:08.720 --> 00:31:11.220
continuous variable in little tiny

00:31:11.220 --> 00:31:11.660
ranges.

00:31:11.660 --> 00:31:14.010
How many times do I observe it between

00:31:14.010 --> 00:31:16.222
40.0 and 40.1?

00:31:16.222 --> 00:31:18.030
And sometimes I might have no

00:31:18.030 --> 00:31:19.630
observations because I only have like

00:31:19.630 --> 00:31:22.216
300 data points and so that's why when

00:31:22.216 --> 00:31:24.370
I plot it as a line plot, I get this

00:31:24.370 --> 00:31:25.965
like super spiky thing because I've got

00:31:25.965 --> 00:31:27.640
a bunch of zeros, but I didn't observe

00:31:27.640 --> 00:31:29.390
anything in those tiny step sizes.

00:31:29.390 --> 00:31:30.950
And then there's other times when I

00:31:30.950 --> 00:31:31.200
observe.

00:31:31.250 --> 00:31:32.260
Several points.

00:31:32.930 --> 00:31:34.630
Inside of a tiny step size.

00:31:36.100 --> 00:31:37.710
So these are different representations

00:31:37.710 --> 00:31:40.780
of the same data and it's kind of like

00:31:40.780 --> 00:31:43.312
up to us to decide to think about like

00:31:43.312 --> 00:31:45.690
which of these is a better

00:31:45.690 --> 00:31:47.360
representation, which one do we think

00:31:47.360 --> 00:31:49.290
more closely reflects the true

00:31:49.290 --> 00:31:50.100
distribution?

00:31:51.310 --> 00:31:53.600
And I guess I'll ask you, so do you

00:31:53.600 --> 00:31:55.750
think if I had to rely on one of these

00:31:55.750 --> 00:31:58.632
as a probability density estimate of

00:31:58.632 --> 00:32:01.360
this, of this variable, would you

00:32:01.360 --> 00:32:03.790
prefer the left side or the right side?

00:32:06.800 --> 00:32:07.090
Right.

00:32:08.680 --> 00:32:09.930
All right, I'll take a vote.

00:32:09.930 --> 00:32:11.590
So how many prefer the left side?

00:32:13.000 --> 00:32:14.850
How many prefer the right side?

00:32:14.850 --> 00:32:16.750
That's interesting.

00:32:17.770 --> 00:32:20.455
OK, so it's mixed and there's not

00:32:20.455 --> 00:32:22.650
really a right answer, but I personally

00:32:22.650 --> 00:32:23.853
would prefer the left side.

00:32:23.853 --> 00:32:25.960
And the reason is just because I don't

00:32:25.960 --> 00:32:26.433
really think.

00:32:26.433 --> 00:32:28.580
It's true that there's like a whole lot

00:32:28.580 --> 00:32:31.898
of Penguins that would have a length of

00:32:31.898 --> 00:32:32.750
like 40.5.

00:32:32.750 --> 00:32:35.190
But then it's almost impossible for a

00:32:35.190 --> 00:32:37.059
Penguin to have a length of 40.6.

00:32:37.059 --> 00:32:38.900
But then 40.7 is like pretty likely.

00:32:38.900 --> 00:32:41.185
Again, that's not, that's not my model

00:32:41.185 --> 00:32:42.440
of how the world works.

00:32:42.440 --> 00:32:44.370
I tend to think that this distribution

00:32:44.370 --> 00:32:45.870
should be pretty smooth, right?

00:32:45.870 --> 00:32:47.020
It might be a multimodal.

00:32:47.080 --> 00:32:50.486
Distribution you might have like the

00:32:50.486 --> 00:32:53.250
adult males, the adult females, and the

00:32:53.250 --> 00:32:54.850
kid Penguins.

00:32:54.850 --> 00:32:56.260
Maybe that's what it is.

00:32:57.300 --> 00:32:58.140
I don't really know.

00:32:58.140 --> 00:32:58.466
I'm not.

00:32:58.466 --> 00:32:59.700
I don't study Penguins.

00:32:59.700 --> 00:33:00.770
But it's possible.

00:33:03.440 --> 00:33:04.040
That's right.

00:33:07.480 --> 00:33:11.030
So the as I mentioned, the entropy

00:33:11.030 --> 00:33:12.350
measures how many bits?

00:33:12.350 --> 00:33:13.130
Question.

00:33:14.390 --> 00:33:14.960
Yeah.

00:33:30.580 --> 00:33:34.050
So that's a good question, comment so.

00:33:35.640 --> 00:33:37.275
The so you might choose.

00:33:37.275 --> 00:33:38.960
So you're saying that you chose this

00:33:38.960 --> 00:33:40.870
because the entropy is lower.

00:33:41.620 --> 00:33:45.100
The.

00:33:46.510 --> 00:33:48.210
So that kind of like makes sense

00:33:48.210 --> 00:33:51.420
intuitively, but I would say the reason

00:33:51.420 --> 00:33:54.369
that I wouldn't choose the entropy

00:33:54.370 --> 00:33:55.832
value as a way of choosing the

00:33:55.832 --> 00:33:58.095
distribution is that these entropy

00:33:58.095 --> 00:33:59.740
values are actually not like the true

00:33:59.740 --> 00:34:00.590
entropy values.

00:34:00.590 --> 00:34:02.920
They're just the estimate of the

00:34:02.920 --> 00:34:04.470
entropy based on the distribution that

00:34:04.470 --> 00:34:06.050
we estimated.

00:34:06.050 --> 00:34:08.160
And for example, if I really want to

00:34:08.160 --> 00:34:10.941
minimize this distribution or the

00:34:10.941 --> 00:34:12.800
entropy, I would say that my

00:34:12.800 --> 00:34:14.510
distribution is just like a bunch of

00:34:14.510 --> 00:34:16.050
delta functions, which means that.

00:34:16.100 --> 00:34:17.600
They say that each data point that I

00:34:17.600 --> 00:34:20.235
observed is equally likely.

00:34:20.235 --> 00:34:22.887
So if I have 300 data points and each

00:34:22.887 --> 00:34:24.518
one has a probability of one out of

00:34:24.518 --> 00:34:27.360
300, and that will minimize my entropy.

00:34:27.360 --> 00:34:29.660
But it will also mean that basically

00:34:29.660 --> 00:34:31.070
all I can do is represent those

00:34:31.070 --> 00:34:32.700
particular data points and I won't have

00:34:32.700 --> 00:34:34.540
any generalization to new data.

00:34:34.540 --> 00:34:37.386
So I think that's a really good point

00:34:37.386 --> 00:34:38.200
to bring up.

00:34:39.540 --> 00:34:42.970
That the we have to like, always

00:34:42.970 --> 00:34:45.430
remember that the measurements that we

00:34:45.430 --> 00:34:47.290
make on data are not like true

00:34:47.290 --> 00:34:47.560
measurements.

00:34:47.560 --> 00:34:48.012
They're not.

00:34:48.012 --> 00:34:49.585
They don't tell us anything, or they

00:34:49.585 --> 00:34:51.354
tell us something, but they don't

00:34:51.354 --> 00:34:52.746
reveal the true distribution.

00:34:52.746 --> 00:34:54.690
They only reveal what we've estimated

00:34:54.690 --> 00:34:55.939
about the distribution.

00:34:55.940 --> 00:34:57.907
And those estimates depend not only on

00:34:57.907 --> 00:34:59.519
the data that we're measuring, but the

00:34:59.520 --> 00:35:00.570
way that we measure it.

00:35:01.820 --> 00:35:04.593
So that's like a really tricky, that's

00:35:04.593 --> 00:35:07.590
like a really tricky concept that is

00:35:07.590 --> 00:35:09.329
kind of like the main concept that.

00:35:10.330 --> 00:35:12.280
That I'm trying to illustrate.

00:35:15.110 --> 00:35:17.257
All right, so the entropy measures like

00:35:17.257 --> 00:35:20.270
how many bits are required to store an

00:35:20.270 --> 00:35:22.872
element of data, the true entropy.

00:35:22.872 --> 00:35:25.320
So the true entropy again, if they

00:35:25.320 --> 00:35:27.250
were, if we were able to know the

00:35:27.250 --> 00:35:28.965
distribution, which we almost never

00:35:28.965 --> 00:35:29.350
know.

00:35:29.350 --> 00:35:31.960
But if we knew it, and we had an ideal

00:35:31.960 --> 00:35:34.230
way to store the data, then the entropy

00:35:34.230 --> 00:35:35.900
tells us how many bits we would need in

00:35:35.900 --> 00:35:37.390
order to store that data in the most

00:35:37.390 --> 00:35:38.750
compressed format possible.

00:35:43.500 --> 00:35:46.600
So does this mean that the entropy is a

00:35:46.600 --> 00:35:48.780
measure of information?

00:35:50.290 --> 00:35:50.970
So.

00:35:52.540 --> 00:35:54.419
How many people would say that the

00:35:54.420 --> 00:35:56.113
entropy is a measure?

00:35:56.113 --> 00:35:58.130
Is the information that the data

00:35:58.130 --> 00:35:59.140
contains?

00:36:00.740 --> 00:36:02.000
If yes, raise your hand.

00:36:04.860 --> 00:36:07.890
If no raise, raise your hand.

00:36:07.890 --> 00:36:10.260
OK, so most people more people say not,

00:36:10.260 --> 00:36:11.400
so why not?

00:36:13.870 --> 00:36:14.580
Just measures.

00:36:15.690 --> 00:36:16.130
Cortana.

00:36:19.330 --> 00:36:21.230
The information environment more like.

00:36:22.430 --> 00:36:25.340
The incoming data has like that

00:36:25.340 --> 00:36:25.710
element.

00:36:27.760 --> 00:36:29.580
The company information communication,

00:36:29.580 --> 00:36:32.200
but not correct, right?

00:36:32.200 --> 00:36:33.640
Yeah, so I think that I think what

00:36:33.640 --> 00:36:36.700
you're saying is that the entropy

00:36:36.700 --> 00:36:38.920
measures essentially like how hard it

00:36:38.920 --> 00:36:40.170
is to predict some variable.

00:36:40.820 --> 00:36:43.680
But it doesn't mean that variable like

00:36:43.680 --> 00:36:45.320
tells us anything about anything else,

00:36:45.320 --> 00:36:46.080
right?

00:36:46.080 --> 00:36:47.870
It's just how hard this variable is

00:36:47.870 --> 00:36:49.040
fixed, right?

00:36:49.040 --> 00:36:53.230
And so you could say so again that both

00:36:53.230 --> 00:36:54.680
of those answers can be correct.

00:36:55.530 --> 00:36:58.860
For example, if I have a random array,

00:36:58.860 --> 00:37:00.820
you would probably say like.

00:37:00.820 --> 00:37:02.210
Intuitively this doesn't contain

00:37:02.210 --> 00:37:02.863
information, right?

00:37:02.863 --> 00:37:05.370
If I just say I generated this random

00:37:05.370 --> 00:37:06.910
variable, it's a bunch of zeros and

00:37:06.910 --> 00:37:07.300
ones.

00:37:07.300 --> 00:37:09.260
I 5050 chance it's each one.

00:37:09.960 --> 00:37:13.120
Here's a whole TB of this like random

00:37:13.120 --> 00:37:15.325
variable that I generated for you now.

00:37:15.325 --> 00:37:16.810
Like how much is this worth?

00:37:17.430 --> 00:37:18.690
You would probably be like, it's not

00:37:18.690 --> 00:37:20.080
really worth anything because it

00:37:20.080 --> 00:37:21.926
doesn't like tell me anything about

00:37:21.926 --> 00:37:23.290
anything else, right?

00:37:23.290 --> 00:37:26.700
And so the IT contains in this case,

00:37:26.700 --> 00:37:29.060
like knowing the value of this random

00:37:29.060 --> 00:37:30.907
variable only gives me information

00:37:30.907 --> 00:37:32.250
about itself, it doesn't give me

00:37:32.250 --> 00:37:33.410
information about anything else.

00:37:34.210 --> 00:37:36.390
And so information is always a relative

00:37:36.390 --> 00:37:37.040
term, right?

00:37:37.840 --> 00:37:41.335
Information is the amount of

00:37:41.335 --> 00:37:43.630
uncertainty about something that's

00:37:43.630 --> 00:37:45.760
reduced by knowing something else.

00:37:45.760 --> 00:37:48.190
So if I know the temperature of today,

00:37:48.190 --> 00:37:50.090
then that might reduce my uncertainty

00:37:50.090 --> 00:37:52.810
about the temperature of tomorrow or

00:37:52.810 --> 00:37:54.010
whether it's a good idea to wear a

00:37:54.010 --> 00:37:55.740
jacket when I go out, right?

00:37:55.740 --> 00:37:57.330
So the temperature of today gives me

00:37:57.330 --> 00:37:58.383
information about that.

00:37:58.383 --> 00:38:00.839
But the but knowing the temperature of

00:38:00.839 --> 00:38:02.495
today does not give me any information

00:38:02.495 --> 00:38:04.260
about who's the President of the United

00:38:04.260 --> 00:38:04.895
States.

00:38:04.895 --> 00:38:07.040
So it has information about certain

00:38:07.040 --> 00:38:07.930
things and doesn't have.

00:38:07.980 --> 00:38:09.300
Information about other things.

00:38:12.900 --> 00:38:14.570
So we have this measure called

00:38:14.570 --> 00:38:19.410
information gain, which is a measure of

00:38:19.410 --> 00:38:23.221
how much information does one variable

00:38:23.221 --> 00:38:25.711
give me about another variable, or one

00:38:25.711 --> 00:38:28.201
set of variables give me about another

00:38:28.201 --> 00:38:29.979
variable or set of variables.

00:38:31.690 --> 00:38:35.820
So the information gain of Y given X is

00:38:35.820 --> 00:38:36.480
the.

00:38:37.590 --> 00:38:39.790
Is the entropy of Y my initial

00:38:39.790 --> 00:38:41.515
uncertainty and being able to predict

00:38:41.515 --> 00:38:41.850
Y?

00:38:42.860 --> 00:38:44.980
Minus the entropy of Y given X.

00:38:45.570 --> 00:38:47.230
In other words, like how uncertain am I

00:38:47.230 --> 00:38:50.320
still about why after I know X and this

00:38:50.320 --> 00:38:51.970
difference is the information gain.

00:38:51.970 --> 00:38:54.940
So if I want to know what is the

00:38:54.940 --> 00:38:57.280
temperature going to be in 5 minutes.

00:38:57.280 --> 00:38:59.389
So knowing the temperature right now

00:38:59.390 --> 00:39:01.450
has super high information gain, it

00:39:01.450 --> 00:39:04.350
reduces my entropy almost completely.

00:39:04.350 --> 00:39:05.530
Where knowing the temperature right

00:39:05.530 --> 00:39:07.418
now, if I want to know the temperature

00:39:07.418 --> 00:39:09.900
in 10 days, my information gain would

00:39:09.900 --> 00:39:10.380
be low.

00:39:10.380 --> 00:39:12.233
It might tell me like some guess about

00:39:12.233 --> 00:39:13.890
what season it is that can help a

00:39:13.890 --> 00:39:15.809
little bit, but it's not going to be

00:39:15.810 --> 00:39:16.400
very.

00:39:16.790 --> 00:39:18.450
Highly predictive of the temperature in

00:39:18.450 --> 00:39:18.910
10 days.

00:39:22.270 --> 00:39:25.140
So we can so we can also, of course

00:39:25.140 --> 00:39:25.980
compute this.

00:39:27.800 --> 00:39:28.590
With code.

00:39:28.590 --> 00:39:30.430
So here I'm computing the information

00:39:30.430 --> 00:39:32.560
gain over binary variables.

00:39:34.990 --> 00:39:39.020
Of some feature I = 0 in this case.

00:39:40.280 --> 00:39:41.800
With respect to male, female.

00:39:41.800 --> 00:39:44.120
So how much does a particular variable

00:39:44.120 --> 00:39:46.390
tell me about whether whether a Penguin

00:39:46.390 --> 00:39:47.840
is male or female?

00:39:49.010 --> 00:39:51.430
And so here this was a little bit

00:39:51.430 --> 00:39:53.600
tricky code wise because there was also

00:39:53.600 --> 00:39:56.760
unknown so I have to like ignore the

00:39:56.760 --> 00:39:57.680
unknown case.

00:39:57.680 --> 00:40:00.947
So I take I create a variable Y that is

00:40:00.947 --> 00:40:03.430
one if the Penguin is male and -, 1 if

00:40:03.430 --> 00:40:04.090
it's female.

00:40:05.160 --> 00:40:09.567
And then I extracted out the values of

00:40:09.567 --> 00:40:09.905
XI.

00:40:09.905 --> 00:40:13.150
So I got XI where I = 0 in this case.

00:40:13.150 --> 00:40:16.822
And then I took all the Xis where Y was

00:40:16.822 --> 00:40:19.321
male, where it was male and where it

00:40:19.321 --> 00:40:19.945
was female.

00:40:19.945 --> 00:40:21.507
So this is the male.

00:40:21.507 --> 00:40:23.159
I happens to correspond to island of

00:40:23.160 --> 00:40:23.690
Bisco.

00:40:23.690 --> 00:40:26.260
So this is like the bit string of the

00:40:26.260 --> 00:40:26.550
weather.

00:40:26.550 --> 00:40:28.650
Penguins came from the island of Biscoe

00:40:28.650 --> 00:40:30.490
and were male, and this is whether they

00:40:30.490 --> 00:40:32.190
came from Cisco and they were female.

00:40:34.110 --> 00:40:34.740
And.

00:40:35.810 --> 00:40:37.870
Then I'm counting how many times I see

00:40:37.870 --> 00:40:40.232
either male or female Penguins, and so

00:40:40.232 --> 00:40:42.127
I can use that to get the probability

00:40:42.127 --> 00:40:43.236
that a Penguin is male.

00:40:43.236 --> 00:40:44.700
And of course the probability that's

00:40:44.700 --> 00:40:46.092
female is 1 minus that.

00:40:46.092 --> 00:40:48.850
So I compute my entropy of Penguins

00:40:48.850 --> 00:40:50.400
being male or female.

00:40:50.400 --> 00:40:53.220
So probability y = 1 times log

00:40:53.220 --> 00:40:54.289
probability that minus.

00:40:55.070 --> 00:40:58.123
1 minus probability of y = 1 times log

00:40:58.123 --> 00:40:58.760
probability of that.

00:41:00.390 --> 00:41:03.180
And then I can get the probability that

00:41:03.180 --> 00:41:07.340
a male Penguin.

00:41:07.500 --> 00:41:08.260


00:41:09.460 --> 00:41:13.190
So this is the this is just the

00:41:13.190 --> 00:41:15.562
probability that a Penguin comes from

00:41:15.562 --> 00:41:15.875
Biscoe.

00:41:15.875 --> 00:41:17.940
So the probability that the sum of all

00:41:17.940 --> 00:41:20.015
the male and female Penguins that do

00:41:20.015 --> 00:41:21.603
not, sorry that do not come from Biscoe

00:41:21.603 --> 00:41:22.230
that are 0.

00:41:22.940 --> 00:41:24.070
Divide by the number.

00:41:25.070 --> 00:41:27.720
And then I can get the probability that

00:41:27.720 --> 00:41:28.820
a Penguin is.

00:41:29.950 --> 00:41:33.006
Is male given that it doesn't come from

00:41:33.006 --> 00:41:34.450
Biscoe, and the probability that

00:41:34.450 --> 00:41:36.410
Penguin is male given that it comes

00:41:36.410 --> 00:41:37.150
from Biscoe.

00:41:38.010 --> 00:41:40.550
And then finally I can compute my

00:41:40.550 --> 00:41:44.630
entropy of Y given X, which I can say

00:41:44.630 --> 00:41:46.240
there's different ways to express that.

00:41:46.240 --> 00:41:49.465
But here I express as the sum over the

00:41:49.465 --> 00:41:52.490
probability of whether the Penguin

00:41:52.490 --> 00:41:54.845
comes from VISCO or not, times the

00:41:54.845 --> 00:41:57.730
probability that the Penguin is male or

00:41:57.730 --> 00:42:00.290
female given that it came from Biscoe

00:42:00.290 --> 00:42:03.016
or not, times the log of that

00:42:03.016 --> 00:42:03.274
probability.

00:42:03.274 --> 00:42:05.975
And so I end up with this big term

00:42:05.975 --> 00:42:08.300
here, and so that's the entropy.

00:42:08.350 --> 00:42:12.720
The island given or the entropy of the

00:42:12.720 --> 00:42:15.510
sex of the Penguin given, whether it

00:42:15.510 --> 00:42:16.640
came from Biscoe or not.

00:42:17.240 --> 00:42:20.080
And if I compare those, I see that I

00:42:20.080 --> 00:42:21.297
gained very little information.

00:42:21.297 --> 00:42:23.560
So the so knowing what island of

00:42:23.560 --> 00:42:25.080
Penguin came from doesn't tell me much

00:42:25.080 --> 00:42:26.440
about whether it's male or female.

00:42:26.440 --> 00:42:28.420
That's not like a huge surprise,

00:42:28.420 --> 00:42:30.710
although it's not always exactly true.

00:42:30.710 --> 00:42:36.508
For example, something 49% of people in

00:42:36.508 --> 00:42:40.450
the United States are male and I think

00:42:40.450 --> 00:42:42.880
51% of people in China are male.

00:42:42.880 --> 00:42:44.570
So sometimes there is a slight

00:42:44.570 --> 00:42:45.980
distribution difference depending on

00:42:45.980 --> 00:42:47.150
where you come from and maybe that.

00:42:47.230 --> 00:42:49.220
The figure for some kinds of animals.

00:42:50.000 --> 00:42:51.740
But in any case, like quantitatively we

00:42:51.740 --> 00:42:54.010
can see knowing this island.

00:42:54.010 --> 00:42:55.690
Knowing that island tells me almost

00:42:55.690 --> 00:42:57.230
nothing about whether Penguins likely

00:42:57.230 --> 00:42:58.850
to be male or female, so the

00:42:58.850 --> 00:43:00.530
information gain is very small.

00:43:01.730 --> 00:43:03.230
Because it doesn't reduce the number of

00:43:03.230 --> 00:43:05.160
bits I need to represent whether each

00:43:05.160 --> 00:43:06.360
Penguin is male or female.

00:43:08.780 --> 00:43:10.590
We can also compute the information

00:43:10.590 --> 00:43:13.510
gain in a continuous case, so.

00:43:15.230 --> 00:43:18.550
So here I have again the same initial

00:43:18.550 --> 00:43:21.500
processing to get the male, female, Y

00:43:21.500 --> 00:43:22.020
value.

00:43:22.640 --> 00:43:24.980
And now I do a step through the

00:43:24.980 --> 00:43:28.110
different discrete ranges of the

00:43:28.110 --> 00:43:29.600
variable Kalman length.

00:43:30.710 --> 00:43:32.590
And I compute the probability that a

00:43:32.590 --> 00:43:34.300
variable falls within this range.

00:43:36.100 --> 00:43:38.855
And I also compute the probability that

00:43:38.855 --> 00:43:41.300
a Penguin is male given that it falls

00:43:41.300 --> 00:43:42.060
within a range.

00:43:42.670 --> 00:43:46.480
So that is, out of how many times does

00:43:46.480 --> 00:43:49.240
the value fall within this range and

00:43:49.240 --> 00:43:52.330
the Penguin is male divide by the

00:43:52.330 --> 00:43:53.855
number of times that it falls within

00:43:53.855 --> 00:43:55.665
this range, which was the last element

00:43:55.665 --> 00:43:56.440
of PX.

00:43:57.160 --> 00:43:59.320
And then I add this like very tiny

00:43:59.320 --> 00:44:01.110
value to avoid divide by zero.

00:44:02.830 --> 00:44:05.300
And then so now I have the probability

00:44:05.300 --> 00:44:07.340
that's male given each possible like

00:44:07.340 --> 00:44:08.350
little range of X.

00:44:09.100 --> 00:44:12.590
And I can then compute the entropy as a

00:44:12.590 --> 00:44:15.606
over probability of X times

00:44:15.606 --> 00:44:16.209
probability.

00:44:16.210 --> 00:44:19.240
Or the entropy of Y is computed as

00:44:19.240 --> 00:44:22.243
before and then the entropy of Y given

00:44:22.243 --> 00:44:24.681
X is the sum over probability of X

00:44:24.681 --> 00:44:26.815
times probability of Y given X times

00:44:26.815 --> 00:44:29.330
the log probability of Y given X.

00:44:31.430 --> 00:44:32.880
And then I can look at the information

00:44:32.880 --> 00:44:33.770
gain.

00:44:33.770 --> 00:44:38.660
So here here's the probability of X.

00:44:39.040 --> 00:44:39.780


00:44:40.400 --> 00:44:43.160
And here's the probability of y = 1

00:44:43.160 --> 00:44:43.680
given X.

00:44:44.570 --> 00:44:46.380
And the reason that these are different

00:44:46.380 --> 00:44:49.608
ranges is that is that probability of X

00:44:49.608 --> 00:44:52.260
is a continuous variable, so it should

00:44:52.260 --> 00:44:55.371
integrate to one, and probability of y

00:44:55.371 --> 00:44:58.600
= 1 given X will be somewhere between

00:44:58.600 --> 00:44:59.830
zero and one.

00:44:59.830 --> 00:45:01.442
But it's only modeling this discrete

00:45:01.442 --> 00:45:04.390
variable, so given a particular XY is

00:45:04.390 --> 00:45:06.429
equal to either zero or one, and so

00:45:06.430 --> 00:45:07.880
sometimes the probability could be as

00:45:07.880 --> 00:45:10.073
high as one and other times it could be

00:45:10.073 --> 00:45:10.381
0.

00:45:10.381 --> 00:45:12.660
It's just a discrete value condition on

00:45:12.660 --> 00:45:14.690
X where X is a continuous.

00:45:14.750 --> 00:45:17.280
Variable, but it's sometimes useful to

00:45:17.280 --> 00:45:20.150
plot these together, so lots and lots

00:45:20.150 --> 00:45:21.890
of times when I'm trying to solve some

00:45:21.890 --> 00:45:24.180
new problem, one of the first things

00:45:24.180 --> 00:45:26.510
I'll do is create plots like this for

00:45:26.510 --> 00:45:28.020
the different features to give me an

00:45:28.020 --> 00:45:30.650
understanding of like how linearly.

00:45:30.880 --> 00:45:32.725
How linear is the relationship between

00:45:32.725 --> 00:45:37.280
the features and the and the thing that

00:45:37.280 --> 00:45:38.160
I'm trying to predict?

00:45:39.070 --> 00:45:40.780
In this case, for example, there's a

00:45:40.780 --> 00:45:44.220
strong relationship, so if the common

00:45:44.220 --> 00:45:47.920
length is very high, then this Penguin

00:45:47.920 --> 00:45:49.310
is almost certainly male.

00:45:51.280 --> 00:45:52.330
If the.

00:45:53.150 --> 00:45:55.980
If the common length is moderately

00:45:55.980 --> 00:45:59.090
high, then it's pretty likely to be

00:45:59.090 --> 00:45:59.840
female.

00:46:00.900 --> 00:46:05.219
And if it's even lower, if it's even

00:46:05.220 --> 00:46:09.610
smaller, then it's kind of like roughly

00:46:09.610 --> 00:46:12.522
more evenly likely to be male and

00:46:12.522 --> 00:46:13.040
female.

00:46:13.040 --> 00:46:16.360
So again, this may not be too, this

00:46:16.360 --> 00:46:17.990
might not be super intuitive, like, why

00:46:17.990 --> 00:46:19.320
do we have this step here?

00:46:19.320 --> 00:46:22.454
But if you take my hypothesis that the

00:46:22.454 --> 00:46:25.580
adult male Penguins have large common

00:46:25.580 --> 00:46:27.481
links, and then adult female Penguins

00:46:27.481 --> 00:46:29.010
have the next largest.

00:46:30.070 --> 00:46:31.670
And then so there's like these

00:46:31.670 --> 00:46:32.980
different modes of the distribution,

00:46:32.980 --> 00:46:35.260
see these three humps, so this could be

00:46:35.260 --> 00:46:37.630
the adult male, adult female and the

00:46:37.630 --> 00:46:39.380
kids, which have a big range because

00:46:39.380 --> 00:46:41.290
they're different, different ages.

00:46:41.960 --> 00:46:44.300
And if you know it's a kid, then it

00:46:44.300 --> 00:46:44.640
doesn't.

00:46:44.640 --> 00:46:45.820
You don't really know if it's male or

00:46:45.820 --> 00:46:46.150
female.

00:46:46.150 --> 00:46:48.080
It could be a different, you know,

00:46:48.080 --> 00:46:51.980
bigger child or smaller child will kind

00:46:51.980 --> 00:46:54.290
of conflate with the gender.

00:46:56.150 --> 00:46:57.932
So if I looked at this then I might say

00:46:57.932 --> 00:46:58.861
I don't want to.

00:46:58.861 --> 00:47:00.610
I don't want to use this as part of a

00:47:00.610 --> 00:47:01.197
logistic regressor.

00:47:01.197 --> 00:47:03.650
I need a tree or I need to like cluster

00:47:03.650 --> 00:47:05.455
it or process this feature in some way

00:47:05.455 --> 00:47:06.990
to make this information more

00:47:06.990 --> 00:47:08.600
informative for my machine learning

00:47:08.600 --> 00:47:08.900
model.

00:47:10.510 --> 00:47:12.515
I'll take a break in just a minute, but

00:47:12.515 --> 00:47:13.930
I want to show him one more thing

00:47:13.930 --> 00:47:14.560
first.

00:47:14.560 --> 00:47:20.330
So again, like this is very subject to

00:47:20.330 --> 00:47:22.310
how I estimate these distributions.

00:47:22.310 --> 00:47:26.225
So if I choose a different step size,

00:47:26.225 --> 00:47:28.737
so here I choose a broader one, then I

00:47:28.737 --> 00:47:29.940
get a different probability

00:47:29.940 --> 00:47:32.060
distribution, I get a different P of X

00:47:32.060 --> 00:47:33.480
and I get a different conditional

00:47:33.480 --> 00:47:34.230
distribution.

00:47:34.910 --> 00:47:38.135
This P of X it's probably a bit too

00:47:38.135 --> 00:47:40.150
this step size is probably too big

00:47:40.150 --> 00:47:41.760
because it seemed like there were three

00:47:41.760 --> 00:47:44.530
modes which I can sort of interpret in

00:47:44.530 --> 00:47:45.050
some way.

00:47:45.050 --> 00:47:47.500
Making some guess where here I just had

00:47:47.500 --> 00:47:49.690
one mode I like basically smoothed out

00:47:49.690 --> 00:47:52.270
the whole distribution and I get a very

00:47:52.270 --> 00:47:56.240
different kind of like very much

00:47:56.240 --> 00:47:59.385
smoother probability of y = 1 given X

00:47:59.385 --> 00:48:00.010
estimate.

00:48:00.010 --> 00:48:02.082
So just using my intuition I think this

00:48:02.082 --> 00:48:03.580
is probably a better estimate than

00:48:03.580 --> 00:48:05.500
this, but it's something that you could

00:48:05.500 --> 00:48:06.050
validate.

00:48:06.110 --> 00:48:07.440
With their validation set, for example,

00:48:07.440 --> 00:48:09.430
to see given these two estimates of the

00:48:09.430 --> 00:48:11.520
distribution, which one better reflects

00:48:11.520 --> 00:48:12.850
some held out set of data.

00:48:12.850 --> 00:48:14.850
That's one way that you can that you

00:48:14.850 --> 00:48:16.850
can try to get a more concrete answer

00:48:16.850 --> 00:48:18.210
to what's the better way.

00:48:19.350 --> 00:48:21.437
And then these different ways of

00:48:21.437 --> 00:48:22.910
estimating this distribution lead to

00:48:22.910 --> 00:48:24.190
very different estimates of the

00:48:24.190 --> 00:48:25.150
information gain.

00:48:25.150 --> 00:48:28.142
So estimating it with a smoother with

00:48:28.142 --> 00:48:30.543
this bigger step size gives me a

00:48:30.543 --> 00:48:32.920
smoother distribution that reduces my

00:48:32.920 --> 00:48:35.200
information gain quite significantly.

00:48:39.480 --> 00:48:42.110
So let's take let's take a 2 minute

00:48:42.110 --> 00:48:42.680
break.

00:48:42.680 --> 00:48:46.200
I've been talking a lot and you can

00:48:46.200 --> 00:48:47.910
think about this like how can the

00:48:47.910 --> 00:48:49.430
information gain be different?

00:48:50.300 --> 00:48:52.100
Depending on our step size and what

00:48:52.100 --> 00:48:55.240
does this kind of like imply about our

00:48:55.240 --> 00:48:56.420
machine learning algorithms.

00:48:57.900 --> 00:48:59.390
Right, so I'll set it.

00:48:59.390 --> 00:49:01.480
I'll set a timer.

00:49:01.480 --> 00:49:03.240
Feel free to get up and stretch and

00:49:03.240 --> 00:49:05.170
talk or clear your brain or whatever.

00:49:59.230 --> 00:50:01.920
So why is the information, our

00:50:01.920 --> 00:50:04.655
information gain get improved from this

00:50:04.655 --> 00:50:06.060
slide to this slide?

00:50:06.060 --> 00:50:08.430
I'm kind of confused like these are

00:50:08.430 --> 00:50:09.275
different things.

00:50:09.275 --> 00:50:11.630
So here it's here, it's based on the

00:50:11.630 --> 00:50:12.246
common length.

00:50:12.246 --> 00:50:13.970
So I'm measuring the information gain

00:50:13.970 --> 00:50:15.645
of the Cullman length.

00:50:15.645 --> 00:50:17.850
So how much does Coleman length tell me

00:50:17.850 --> 00:50:19.900
about the male, female and then in the

00:50:19.900 --> 00:50:20.870
previous slide?

00:50:21.280 --> 00:50:22.515
Based on the island.

00:50:22.515 --> 00:50:25.723
So if I know in one case it's like if I

00:50:25.723 --> 00:50:27.300
know what island that came from, how

00:50:27.300 --> 00:50:29.505
much does that tell me about its

00:50:29.505 --> 00:50:31.080
whether it's male or female.

00:50:31.080 --> 00:50:32.850
And in this case, if I know the Cullman

00:50:32.850 --> 00:50:34.456
length, how much does that tell me

00:50:34.456 --> 00:50:35.832
about whether it's male or female?

00:50:35.832 --> 00:50:36.750
I see I see.

00:50:36.750 --> 00:50:39.093
So we changed to another feature.

00:50:39.093 --> 00:50:39.794
Yeah.

00:50:39.794 --> 00:50:42.770
So that I should have said that more

00:50:42.770 --> 00:50:43.090
clearly.

00:50:43.090 --> 00:50:45.690
But the I here is the feature index.

00:50:45.940 --> 00:50:46.353
I see.

00:50:46.353 --> 00:50:47.179
I see, I see.

00:50:47.180 --> 00:50:48.360
That makes sense, yeah.

00:50:50.170 --> 00:50:53.689
OK, it says we need like a check,

00:50:53.690 --> 00:50:53.980
right?

00:50:53.980 --> 00:50:54.805
Yeah.

00:50:54.805 --> 00:50:57.483
So I'm able to make the decision tree

00:50:57.483 --> 00:51:00.390
and I get, I get this like I get the

00:51:00.390 --> 00:51:02.226
first check is just less or equal to

00:51:02.226 --> 00:51:05.560
26, but the second check it differs

00:51:05.560 --> 00:51:07.897
from one side, it'll be like less than

00:51:07.897 --> 00:51:10.530
equal to 14.95 of depth and then one

00:51:10.530 --> 00:51:11.476
side it will be.

00:51:11.476 --> 00:51:13.603
So you want to look down on the tree

00:51:13.603 --> 00:51:14.793
here like here.

00:51:14.793 --> 00:51:17.050
You have basically a perfect

00:51:17.050 --> 00:51:18.760
classification here.

00:51:18.820 --> 00:51:21.050
Right here you have perfect

00:51:21.050 --> 00:51:22.860
classifications into Gen.

00:51:22.860 --> 00:51:23.260
2.

00:51:24.000 --> 00:51:28.360
And so these are two decisions that you

00:51:28.360 --> 00:51:28.970
could use.

00:51:28.970 --> 00:51:30.460
For example, right?

00:51:30.460 --> 00:51:32.710
Each of these paths give you a decision

00:51:32.710 --> 00:51:33.590
about whether it's a Gen.

00:51:33.590 --> 00:51:34.330
2 or not.

00:51:36.470 --> 00:51:39.660
So a decision is 1 path through the OR

00:51:39.660 --> 00:51:41.650
rule is like one path through the tree.

00:51:42.660 --> 00:51:46.200
So in so in the case of the work would

00:51:46.200 --> 00:51:48.026
you just because we need like a two

00:51:48.026 --> 00:51:48.870
check thing right?

00:51:48.870 --> 00:51:50.793
So are two check thing would be this

00:51:50.793 --> 00:51:53.770
and this for example if this is greater

00:51:53.770 --> 00:51:57.010
than that and if this is less than that

00:51:57.010 --> 00:51:58.420
then it's that.

00:52:03.860 --> 00:52:06.510
Yeah, I need to start, OK.

00:52:08.320 --> 00:52:10.760
Alright, so actually so one thing I

00:52:10.760 --> 00:52:12.585
want to clarify based is a question is

00:52:12.585 --> 00:52:14.460
that the things that I'm showing here

00:52:14.460 --> 00:52:15.631
are for different features.

00:52:15.631 --> 00:52:17.595
So I is the feature index.

00:52:17.595 --> 00:52:19.390
So the reason that these have different

00:52:19.390 --> 00:52:21.303
entropies, this was for island, we're

00:52:21.303 --> 00:52:22.897
here, I'm talking about Coleman length.

00:52:22.897 --> 00:52:24.970
So different features will give us

00:52:24.970 --> 00:52:26.655
different, different information gains

00:52:26.655 --> 00:52:28.300
about whether the Penguin is male or

00:52:28.300 --> 00:52:30.753
female and the particular feature index

00:52:30.753 --> 00:52:32.270
is just like here.

00:52:34.260 --> 00:52:35.550
All right, so.

00:52:36.750 --> 00:52:39.380
So why does someone have an answer?

00:52:39.380 --> 00:52:41.655
So why is it that the information gain

00:52:41.655 --> 00:52:43.040
is different depending on the step

00:52:43.040 --> 00:52:43.285
size?

00:52:43.285 --> 00:52:45.050
That seems a little bit unintuitive,

00:52:45.050 --> 00:52:45.350
right?

00:52:45.350 --> 00:52:45.870
Because.

00:52:46.520 --> 00:52:47.560
The same data.

00:52:47.560 --> 00:52:48.730
Why does it?

00:52:48.730 --> 00:52:50.830
Why does information gain depend on

00:52:50.830 --> 00:52:51.290
this?

00:52:51.290 --> 00:52:52.110
Yeah?

00:52:52.600 --> 00:52:56.200
If we have for a bigger step that we

00:52:56.200 --> 00:52:58.130
might overshoot and like, we might not

00:52:58.130 --> 00:52:59.330
capture those like.

00:53:01.000 --> 00:53:03.400
Local like optimized or like local?

00:53:09.790 --> 00:53:10.203
Right.

00:53:10.203 --> 00:53:13.070
So the answer was like, if we have a

00:53:13.070 --> 00:53:15.930
bigger step size, then we might like be

00:53:15.930 --> 00:53:17.525
grouping too many things together so

00:53:17.525 --> 00:53:19.905
that it no longer like contains the

00:53:19.905 --> 00:53:21.610
information that is needed to

00:53:21.610 --> 00:53:24.580
distinguish whether a Penguin is male

00:53:24.580 --> 00:53:25.417
or female, right?

00:53:25.417 --> 00:53:27.515
Or it contains less of that

00:53:27.515 --> 00:53:28.590
information, right.

00:53:28.590 --> 00:53:30.560
And so, like, the key concept that's

00:53:30.560 --> 00:53:33.020
really important to know is that.

00:53:33.590 --> 00:53:34.240


00:53:35.310 --> 00:53:37.820
Is that the information gain?

00:53:37.820 --> 00:53:41.008
It depends on how we use the data.

00:53:41.008 --> 00:53:43.130
It depends on how we model the data.

00:53:43.130 --> 00:53:45.110
So that the information gain is not

00:53:45.110 --> 00:53:47.400
really inherent in the data itself or

00:53:47.400 --> 00:53:48.400
even in.

00:53:48.400 --> 00:53:50.580
It doesn't even depend on the.

00:53:51.600 --> 00:53:54.290
The true distribution between the data

00:53:54.290 --> 00:53:56.600
and the thing that we're trying to

00:53:56.600 --> 00:53:57.190
predict.

00:53:57.190 --> 00:53:58.880
So there may be a theoretical

00:53:58.880 --> 00:54:00.730
information gain, which is if you knew

00:54:00.730 --> 00:54:03.360
the true distribution of and Y then

00:54:03.360 --> 00:54:04.570
what would be the probability of Y

00:54:04.570 --> 00:54:05.640
given X?

00:54:05.640 --> 00:54:08.370
But in practice, we never know the true

00:54:08.370 --> 00:54:08.750
distribution.

00:54:09.630 --> 00:54:12.540
It's only the actual information gain

00:54:12.540 --> 00:54:14.695
depends on how we model the data, how

00:54:14.695 --> 00:54:16.430
we're able to squeeze the information

00:54:16.430 --> 00:54:17.770
out and make a prediction.

00:54:17.770 --> 00:54:22.450
For example, if I were like in China or

00:54:22.450 --> 00:54:24.069
something and I stopped somebody and I

00:54:24.070 --> 00:54:27.270
say, how do I get like over how do I

00:54:27.270 --> 00:54:29.110
get to this place and they start

00:54:29.110 --> 00:54:31.490
talking to me in Chinese and I have no

00:54:31.490 --> 00:54:32.430
idea what they're saying.

00:54:33.080 --> 00:54:35.190
They have like all the information is

00:54:35.190 --> 00:54:36.390
in that data.

00:54:36.390 --> 00:54:38.390
Somebody else could use that

00:54:38.390 --> 00:54:40.070
information to get where they want to

00:54:40.070 --> 00:54:42.050
go, but I can't use it because I don't

00:54:42.050 --> 00:54:43.560
have the right model for that data.

00:54:43.560 --> 00:54:45.858
So the information gained to me is 0,

00:54:45.858 --> 00:54:47.502
but the information gain is somebody

00:54:47.502 --> 00:54:49.260
else could be very high because of

00:54:49.260 --> 00:54:49.926
their model.

00:54:49.926 --> 00:54:52.257
And in the same way like we can take

00:54:52.257 --> 00:54:54.870
the same data and that data may have no

00:54:54.870 --> 00:54:57.369
information gain if we don't model it

00:54:57.370 --> 00:54:58.970
correctly, if we're not sure how to

00:54:58.970 --> 00:55:01.520
model it or use the data to extract our

00:55:01.520 --> 00:55:02.490
predictions.

00:55:02.490 --> 00:55:03.070
But.

00:55:03.130 --> 00:55:05.670
As we get better models, we're able to

00:55:05.670 --> 00:55:07.830
improve the information gain that we

00:55:07.830 --> 00:55:09.130
can get from that same data.

00:55:09.130 --> 00:55:10.920
And so that's basically like the goal

00:55:10.920 --> 00:55:13.480
of machine learning is to be able to

00:55:13.480 --> 00:55:14.740
model the data and model the

00:55:14.740 --> 00:55:16.850
relationships in a way that maximizes

00:55:16.850 --> 00:55:19.350
your information gain for predicting

00:55:19.350 --> 00:55:20.470
the thing that you're trying to

00:55:20.470 --> 00:55:20.810
predict.

00:55:23.300 --> 00:55:26.760
So again, we only have an empirical

00:55:26.760 --> 00:55:28.630
estimate based on the observed samples.

00:55:30.680 --> 00:55:31.580
And so.

00:55:32.510 --> 00:55:34.000
So we don't know the true information

00:55:34.000 --> 00:55:36.070
gain, just some estimated information

00:55:36.070 --> 00:55:37.850
gain based on estimated probability

00:55:37.850 --> 00:55:38.560
distributions.

00:55:39.330 --> 00:55:40.930
If we had more data, we could probably

00:55:40.930 --> 00:55:42.200
get a better estimate.

00:55:43.950 --> 00:55:46.870
And when we're trying to estimate

00:55:46.870 --> 00:55:49.090
things based on continuous variables,

00:55:49.090 --> 00:55:50.270
then we have different choices of

00:55:50.270 --> 00:55:50.850
models.

00:55:50.850 --> 00:55:53.753
And so there's a tradeoff between like

00:55:53.753 --> 00:55:55.380
over smoothing or simplifying the

00:55:55.380 --> 00:55:57.770
distribution and making overly

00:55:57.770 --> 00:55:59.740
confident predictions based on small

00:55:59.740 --> 00:56:00.720
data samples.

00:56:00.720 --> 00:56:03.790
So over here, I may have like very good

00:56:03.790 --> 00:56:06.060
estimates for the probability that X

00:56:06.060 --> 00:56:07.840
falls within this broader range.

00:56:09.610 --> 00:56:11.770
But maybe I have, like, smoothed out

00:56:11.770 --> 00:56:13.960
the important information for

00:56:13.960 --> 00:56:15.630
determining whether the Penguin is male

00:56:15.630 --> 00:56:16.230
or female.

00:56:16.980 --> 00:56:19.090
Maybe over here I have much more

00:56:19.090 --> 00:56:20.590
uncertain estimates of each of these

00:56:20.590 --> 00:56:21.360
probabilities.

00:56:21.360 --> 00:56:23.090
Like, is the probability distribution

00:56:23.090 --> 00:56:23.920
really that spiky?

00:56:23.920 --> 00:56:24.990
It's probably not.

00:56:24.990 --> 00:56:26.000
It's probably.

00:56:26.000 --> 00:56:27.710
This is probably a mixture of a few

00:56:27.710 --> 00:56:28.460
Gaussians.

00:56:29.590 --> 00:56:31.490
Which would be a smoother bumpy

00:56:31.490 --> 00:56:34.430
distribution, but on the other hand

00:56:34.430 --> 00:56:35.770
I've like preserved more of the

00:56:35.770 --> 00:56:37.650
information that is needed I would

00:56:37.650 --> 00:56:40.860
think to classify the Penguin as male

00:56:40.860 --> 00:56:41.390
or female.

00:56:42.260 --> 00:56:43.420
So there's this tradeoff.

00:56:44.030 --> 00:56:46.010
And this is just another simple example

00:56:46.010 --> 00:56:47.540
of the bias variance tradeoff.

00:56:47.540 --> 00:56:51.740
So here I have a I have a low variance

00:56:51.740 --> 00:56:53.160
but high bias estimate.

00:56:53.160 --> 00:56:53.960
My distribution.

00:56:53.960 --> 00:56:55.100
It's overly smooth.

00:56:56.000 --> 00:57:00.290
And over there I have a I have a higher

00:57:00.290 --> 00:57:02.575
variance, lower bias estimate of the

00:57:02.575 --> 00:57:02.896
distribution.

00:57:02.896 --> 00:57:04.980
And if I made the step size really

00:57:04.980 --> 00:57:07.175
small so I had that super spiky

00:57:07.175 --> 00:57:08.973
distribution, then that would be a

00:57:08.973 --> 00:57:10.852
really low bias but very high variance

00:57:10.852 --> 00:57:11.135
estimate.

00:57:11.135 --> 00:57:13.250
If I resampled it, I might get spikes

00:57:13.250 --> 00:57:14.987
in totally different places, so a

00:57:14.987 --> 00:57:16.331
totally different estimate of the

00:57:16.331 --> 00:57:16.600
distribution.

00:57:20.910 --> 00:57:22.506
And it's also important to note that

00:57:22.506 --> 00:57:24.040
the that when you're dealing with

00:57:24.040 --> 00:57:25.570
something like the bias variance

00:57:25.570 --> 00:57:28.382
tradeoff, in this case the complexity

00:57:28.382 --> 00:57:29.985
parameter is a step size.

00:57:29.985 --> 00:57:32.200
The optimal parameter depends on how

00:57:32.200 --> 00:57:34.210
much data we have, because the more

00:57:34.210 --> 00:57:36.180
data we have, the lower the variance of

00:57:36.180 --> 00:57:39.870
our estimate and so you the ideal

00:57:39.870 --> 00:57:42.610
complexity changes.

00:57:42.610 --> 00:57:45.256
So if I had lots of data, lots and lots

00:57:45.256 --> 00:57:47.090
and lots of data, then maybe I would

00:57:47.090 --> 00:57:47.360
choose.

00:57:47.430 --> 00:57:49.745
Step size even smaller than one because

00:57:49.745 --> 00:57:51.660
I could estimate those probabilities

00:57:51.660 --> 00:57:53.143
pretty well given all that data.

00:57:53.143 --> 00:57:54.890
I could estimate those little tiny

00:57:54.890 --> 00:57:57.346
ranges where if I'd weigh less data

00:57:57.346 --> 00:57:59.060
than maybe this would become the better

00:57:59.060 --> 00:58:02.470
choice because I otherwise my estimate

00:58:02.470 --> 00:58:03.910
was step size of 1 would just be too

00:58:03.910 --> 00:58:04.580
noisy.

00:58:08.850 --> 00:58:11.050
So the true probability distribution,

00:58:11.050 --> 00:58:13.990
entropy and I mean and information gain

00:58:13.990 --> 00:58:14.880
cannot be known.

00:58:14.880 --> 00:58:16.820
We can only try to make our best

00:58:16.820 --> 00:58:17.420
estimate.

00:58:19.140 --> 00:58:21.550
Alright, so that was all just focusing

00:58:21.550 --> 00:58:22.620
on X.

00:58:22.620 --> 00:58:23.320
Pretty much.

00:58:23.320 --> 00:58:25.716
A little bit of X&Y, but mostly X.

00:58:25.716 --> 00:58:28.130
So let's come back to how this fits

00:58:28.130 --> 00:58:29.760
into the whole machine learning

00:58:29.760 --> 00:58:30.310
framework.

00:58:31.120 --> 00:58:34.240
So we can say that one way that we can

00:58:34.240 --> 00:58:35.100
look at this function.

00:58:35.100 --> 00:58:36.515
Here we're trying to find parameters

00:58:36.515 --> 00:58:39.720
that minimize the loss of our models

00:58:39.720 --> 00:58:41.020
predictions compared to the ground

00:58:41.020 --> 00:58:41.910
truth prediction.

00:58:42.840 --> 00:58:45.126
One way that we can view this is that

00:58:45.126 --> 00:58:48.380
we're we're trying to maximize the

00:58:48.380 --> 00:58:52.550
information gain of Y given X, maybe

00:58:52.550 --> 00:58:54.000
with some additional constraints and

00:58:54.000 --> 00:58:55.850
priors that will improve the robustness

00:58:55.850 --> 00:58:57.940
to limited data that essentially like

00:58:57.940 --> 00:59:00.290
find that trade off for us in the bias

00:59:00.290 --> 00:59:00.720
variance.

00:59:01.920 --> 00:59:02.590
Trade off?

00:59:03.910 --> 00:59:06.960
So I could rewrite this if I'm if my

00:59:06.960 --> 00:59:09.430
loss function is the log probability of

00:59:09.430 --> 00:59:10.090
Y given X.

00:59:11.840 --> 00:59:13.710
Or let's just say for now that I

00:59:13.710 --> 00:59:16.807
rewrite this in terms of the in terms

00:59:16.807 --> 00:59:18.940
of the conditional entropy, or in terms

00:59:18.940 --> 00:59:20.120
of the information gain.

00:59:20.920 --> 00:59:22.610
So let's say I want to find the

00:59:22.610 --> 00:59:23.990
parameters Theta.

00:59:23.990 --> 00:59:25.830
That means that.

00:59:26.770 --> 00:59:29.390
Minimize my negative information gain,

00:59:29.390 --> 00:59:31.730
otherwise maximize my information gain,

00:59:31.730 --> 00:59:32.010
right?

00:59:32.750 --> 00:59:36.690
So that is, I want to maximize the

00:59:36.690 --> 00:59:38.670
difference between the entropy.

00:59:39.690 --> 00:59:43.149
And the entropy of Y the entropy of Y

00:59:43.150 --> 00:59:45.240
given X or equivalently, minimize the

00:59:45.240 --> 00:59:45.920
negative of that.

00:59:46.760 --> 00:59:49.530
Plus some kind of regularization or

00:59:49.530 --> 00:59:52.300
penalty on having unlikely parameters.

00:59:52.300 --> 00:59:54.814
So this would typically be like our

00:59:54.814 --> 00:59:56.380
squared penalty regularization.

00:59:56.380 --> 00:59:57.480
I mean our squared weight

00:59:57.480 --> 00:59:58.290
regularization.

01:00:00.680 --> 01:00:06.810
And if I write down what this entropy

01:00:06.810 --> 01:00:08.810
of Y given X is, then it's just the

01:00:08.810 --> 01:00:12.019
integral over all my data over all

01:00:12.020 --> 01:00:15.839
possible values X of probability of X

01:00:15.840 --> 01:00:18.120
times log probability of Y given X.

01:00:19.490 --> 01:00:22.016
I don't have a continuous distribution

01:00:22.016 --> 01:00:23.685
of XI don't have infinite samples.

01:00:23.685 --> 01:00:25.810
I just have an empirical sample.

01:00:25.810 --> 01:00:27.750
I have a few observations, some limited

01:00:27.750 --> 01:00:30.220
number of observations, and so my

01:00:30.220 --> 01:00:33.040
estimate of this of this integral

01:00:33.040 --> 01:00:35.620
becomes a sum over all the samples I do

01:00:35.620 --> 01:00:36.050
have.

01:00:36.770 --> 01:00:38.700
Assuming that each of these are all

01:00:38.700 --> 01:00:40.850
equally likely, then they'll just be

01:00:40.850 --> 01:00:43.406
some constant for the probability of X.

01:00:43.406 --> 01:00:46.020
So I can kind of like ignore that in

01:00:46.020 --> 01:00:47.470
relative terms, right?

01:00:47.470 --> 01:00:49.830
So I have a over the probability of X

01:00:49.830 --> 01:00:51.170
which would just be like one over

01:00:51.170 --> 01:00:51.420
north.

01:00:52.260 --> 01:00:55.765
Times the negative log probability of

01:00:55.765 --> 01:00:58.510
the label or of the thing that I'm

01:00:58.510 --> 01:01:00.919
trying to predict for the NTH sample

01:01:00.920 --> 01:01:02.900
given the features of the NTH sample.

01:01:03.910 --> 01:01:06.814
And this is exactly the cross entropy.

01:01:06.814 --> 01:01:07.998
This is.

01:01:07.998 --> 01:01:10.180
If Y is a discrete variable, for

01:01:10.180 --> 01:01:11.663
example, this would give us our cross

01:01:11.663 --> 01:01:14.718
entropy, or even if it's not, this is

01:01:14.718 --> 01:01:15.331
the.

01:01:15.331 --> 01:01:18.870
This is the negative log likelihood of

01:01:18.870 --> 01:01:21.430
my labels given the data, and so this

01:01:21.430 --> 01:01:23.420
gives us the loss term that we use

01:01:23.420 --> 01:01:24.610
typically for deep network

01:01:24.610 --> 01:01:26.200
classification or for logistic

01:01:26.200 --> 01:01:26.850
regression.

01:01:27.470 --> 01:01:29.230
And so it's exactly the same as

01:01:29.230 --> 01:01:33.330
maximizing the information gain of the

01:01:33.330 --> 01:01:34.890
variables that we're trying to predict

01:01:34.890 --> 01:01:36.070
given the features that we have

01:01:36.070 --> 01:01:36.560
available.

01:01:39.760 --> 01:01:44.390
So I've been like manually computing

01:01:44.390 --> 01:01:46.207
information gain and probabilities and

01:01:46.207 --> 01:01:48.399
stuff like that using code, but like

01:01:48.400 --> 01:01:50.920
kind of like hand coding lots of stuff.

01:01:50.920 --> 01:01:53.370
But that has its limitations.

01:01:53.370 --> 01:01:56.670
Like I can analyze 11 continuous

01:01:56.670 --> 01:01:59.310
variable or maybe 2 features at once

01:01:59.310 --> 01:02:00.970
and I can come up with some function

01:02:00.970 --> 01:02:03.060
and look at it and use my intuition and

01:02:03.060 --> 01:02:04.570
try to like create a good model based

01:02:04.570 --> 01:02:05.176
on that.

01:02:05.176 --> 01:02:06.910
But if you have thousands of variables,

01:02:06.910 --> 01:02:08.535
it's just like completely impractical

01:02:08.535 --> 01:02:09.430
to do this.

01:02:09.490 --> 01:02:12.246
Right, it would take forever to try to

01:02:12.246 --> 01:02:14.076
like plot all the different features

01:02:14.076 --> 01:02:16.530
and plot combinations and try to like

01:02:16.530 --> 01:02:19.420
manually explore this a big data set.

01:02:19.790 --> 01:02:21.590
And so.

01:02:22.780 --> 01:02:24.370
So we need more like automatic

01:02:24.370 --> 01:02:26.110
approaches to figure out how we can

01:02:26.110 --> 01:02:29.890
maximize the information gain of Y

01:02:29.890 --> 01:02:31.140
given X.

01:02:31.140 --> 01:02:32.810
And so that's basically why we have

01:02:32.810 --> 01:02:33.843
machine learning.

01:02:33.843 --> 01:02:36.560
So in machine learning, we're trying to

01:02:36.560 --> 01:02:39.560
build encoders sometimes to try to

01:02:39.560 --> 01:02:41.740
automatically transform X into some

01:02:41.740 --> 01:02:44.160
representation that makes it easier to

01:02:44.160 --> 01:02:45.850
extract information about why.

01:02:47.110 --> 01:02:49.220
Sometimes, sometimes people do this

01:02:49.220 --> 01:02:49.517
part.

01:02:49.517 --> 01:02:51.326
Sometimes we like hand code the

01:02:51.326 --> 01:02:51.910
features right.

01:02:51.910 --> 01:02:54.270
We create histogram, a gradient

01:02:54.270 --> 01:03:00.120
features for images, or we like I could

01:03:00.120 --> 01:03:01.780
take that common length and split it

01:03:01.780 --> 01:03:03.409
into three different ranges that I

01:03:03.410 --> 01:03:06.185
think represent like the adult male and

01:03:06.185 --> 01:03:08.520
adult female and children for example.

01:03:09.480 --> 01:03:11.770
But sometimes some methods do this

01:03:11.770 --> 01:03:13.925
automatically, and then second we have

01:03:13.925 --> 01:03:15.940
some decoder, something that predicts Y

01:03:15.940 --> 01:03:18.050
from X that automatically extracts the

01:03:18.050 --> 01:03:18.730
information.

01:03:19.530 --> 01:03:22.260
About why from X so our logistic

01:03:22.260 --> 01:03:23.560
regressor for example.

01:03:26.940 --> 01:03:29.460
The most powerful machine learning

01:03:29.460 --> 01:03:32.870
algorithms smoothly combine the feature

01:03:32.870 --> 01:03:34.940
extraction with the decoding, the

01:03:34.940 --> 01:03:37.530
prediction and offer controls or

01:03:37.530 --> 01:03:39.370
protections against overfitting.

01:03:40.860 --> 01:03:43.910
So they both try to make as good

01:03:43.910 --> 01:03:45.190
predictions as possible and the

01:03:45.190 --> 01:03:47.290
training data, and they try to do it in

01:03:47.290 --> 01:03:49.920
a way that is not like overfitting or

01:03:49.920 --> 01:03:51.103
leading to like high variance

01:03:51.103 --> 01:03:52.300
predictions that aren't going to

01:03:52.300 --> 01:03:52.970
generalize well.

01:03:53.800 --> 01:03:55.750
Random forests, for example.

01:03:55.750 --> 01:03:58.070
We have these deep trees that partition

01:03:58.070 --> 01:04:00.830
the feature space, chunk it up, and

01:04:00.830 --> 01:04:03.445
they optimize by optimizing the

01:04:03.445 --> 01:04:04.180
information gain.

01:04:04.180 --> 01:04:04.770
At each step.

01:04:04.770 --> 01:04:06.140
Those trees are trained to try to

01:04:06.140 --> 01:04:07.830
maximize the information gain for the

01:04:07.830 --> 01:04:08.970
variable that you're predicting.

01:04:09.940 --> 01:04:13.300
And until you get some full tree, and

01:04:13.300 --> 01:04:15.910
so individually each of these trees has

01:04:15.910 --> 01:04:16.710
low bias.

01:04:16.710 --> 01:04:18.250
It makes very accurate predictions on

01:04:18.250 --> 01:04:20.480
the training data, but high variance.

01:04:20.480 --> 01:04:22.560
You might get different trees if you

01:04:22.560 --> 01:04:24.479
were to resample the training data.

01:04:25.350 --> 01:04:28.790
And then in a random forest you train a

01:04:28.790 --> 01:04:30.120
whole bunch of these trees with

01:04:30.120 --> 01:04:31.570
different subsets of features.

01:04:32.640 --> 01:04:34.010
And then you average over their

01:04:34.010 --> 01:04:36.550
predictions and that averaging reduces

01:04:36.550 --> 01:04:38.820
the variance and so at the end of the

01:04:38.820 --> 01:04:40.719
day you have like a low variance, low

01:04:40.720 --> 01:04:42.510
bias predictor.

01:04:44.560 --> 01:04:46.350
The boosted trees similarly.

01:04:47.560 --> 01:04:50.020
You have shallow trees this time that

01:04:50.020 --> 01:04:51.860
kind of have low variance individually,

01:04:51.860 --> 01:04:53.170
at least if you have a relatively

01:04:53.170 --> 01:04:54.640
uniform data distribution.

01:04:56.760 --> 01:04:59.000
They again partition the feature space

01:04:59.000 --> 01:05:01.250
by optimizing the information gain, now

01:05:01.250 --> 01:05:02.805
using all the features but on a

01:05:02.805 --> 01:05:04.120
weighted data sample.

01:05:04.120 --> 01:05:05.980
And then each tree is trained on some

01:05:05.980 --> 01:05:07.933
weighted sample that focuses more on

01:05:07.933 --> 01:05:09.560
the examples that previous trees

01:05:09.560 --> 01:05:12.245
misclassified in order to reduce the

01:05:12.245 --> 01:05:12.490
bias.

01:05:12.490 --> 01:05:14.240
So that a sequence of these little

01:05:14.240 --> 01:05:16.640
trees actually has like much lower bias

01:05:16.640 --> 01:05:18.690
than the first tree because they're

01:05:18.690 --> 01:05:20.200
incrementally trying to improve their

01:05:20.200 --> 01:05:21.120
prediction function.

01:05:22.780 --> 01:05:24.690
Now, the downside of the boosted

01:05:24.690 --> 01:05:27.950
decision trees, or the danger of them

01:05:27.950 --> 01:05:30.474
is that they will tend to focus more

01:05:30.474 --> 01:05:32.510
and more on smaller and smaller amounts

01:05:32.510 --> 01:05:33.840
of data that are just really hard to

01:05:33.840 --> 01:05:34.810
misclassify.

01:05:34.810 --> 01:05:36.410
Maybe some of that data was mislabeled

01:05:36.410 --> 01:05:38.040
and so that's why it's so hard to

01:05:38.040 --> 01:05:38.850
classify.

01:05:38.850 --> 01:05:40.626
And maybe it's just very unusual.

01:05:40.626 --> 01:05:43.250
And so as you train lots of these

01:05:43.250 --> 01:05:45.666
boosted trees, eventually they start to

01:05:45.666 --> 01:05:48.326
focus on like a tiny subset of data and

01:05:48.326 --> 01:05:50.080
that can cause high variance

01:05:50.080 --> 01:05:50.640
overfitting.

01:05:51.900 --> 01:05:54.075
And so random forests are very robust

01:05:54.075 --> 01:05:55.476
to overfitting boosted trees.

01:05:55.476 --> 01:05:57.700
You still have to be careful, careful

01:05:57.700 --> 01:06:00.060
about how big those trees are and how

01:06:00.060 --> 01:06:00.990
many of them you train.

01:06:02.650 --> 01:06:03.930
And then deep networks.

01:06:03.930 --> 01:06:05.709
So we have deep networks.

01:06:05.710 --> 01:06:08.066
The mantra of deep networks is end to

01:06:08.066 --> 01:06:11.342
end learning, which means that you just

01:06:11.342 --> 01:06:13.865
give it your simplest features.

01:06:13.865 --> 01:06:17.080
You try not to like, preprocess it too

01:06:17.080 --> 01:06:18.610
much, because then you're just like

01:06:18.610 --> 01:06:20.230
removing some information.

01:06:20.230 --> 01:06:21.856
So you don't compute hog features, you

01:06:21.856 --> 01:06:23.060
just give it pixels.

01:06:24.320 --> 01:06:29.420
And then the optimization is jointly

01:06:29.420 --> 01:06:32.100
trying to process those raw inputs into

01:06:32.100 --> 01:06:35.012
useful features, and then to use those

01:06:35.012 --> 01:06:37.140
useful features to make predictions.

01:06:37.790 --> 01:06:41.040
On your on your for your for your final

01:06:41.040 --> 01:06:41.795
prediction.

01:06:41.795 --> 01:06:44.290
And it's a joint optimization.

01:06:44.290 --> 01:06:47.010
So random forests and boosted trees

01:06:47.010 --> 01:06:50.245
sort of do this, but they're kind of

01:06:50.245 --> 01:06:50.795
like greedy.

01:06:50.795 --> 01:06:52.519
You're trying to you're greedy

01:06:52.520 --> 01:06:54.484
decisions to try to optimize your to

01:06:54.484 --> 01:06:56.070
try to like select your features and

01:06:56.070 --> 01:06:57.420
then use them for predictions.

01:06:58.100 --> 01:07:01.390
While deep networks are like not

01:07:01.390 --> 01:07:02.460
greedy, they're trying to do this

01:07:02.460 --> 01:07:05.460
global optimization to try to maximize

01:07:05.460 --> 01:07:07.750
the information gain of your prediction

01:07:07.750 --> 01:07:08.910
given your features.

01:07:09.670 --> 01:07:11.760
And this end to end learning of

01:07:11.760 --> 01:07:13.220
learning your features and prediction

01:07:13.220 --> 01:07:15.990
at the same time is a big reason why

01:07:15.990 --> 01:07:18.576
people often say that deep learning is

01:07:18.576 --> 01:07:20.869
like the best or it can be the best

01:07:20.870 --> 01:07:22.180
algorithm, at least if you have enough

01:07:22.180 --> 01:07:23.840
data to apply it.

01:07:25.250 --> 01:07:27.210
The intermediate features represent

01:07:27.210 --> 01:07:29.660
transformations of the data that are

01:07:29.660 --> 01:07:31.520
more easily reusable than, like tree

01:07:31.520 --> 01:07:32.609
partitions, for example.

01:07:32.610 --> 01:07:33.925
So this is another big advantage that

01:07:33.925 --> 01:07:36.433
you can take, like the output at some

01:07:36.433 --> 01:07:38.520
intermediate layer, and you can reuse

01:07:38.520 --> 01:07:40.450
it for some other problem, because it

01:07:40.450 --> 01:07:42.200
represents some kind of like

01:07:42.200 --> 01:07:44.446
transformation of image pixels, for

01:07:44.446 --> 01:07:47.510
example, in a way that may be

01:07:47.510 --> 01:07:49.090
semantically meaningful or meaningful

01:07:49.090 --> 01:07:51.250
for a bunch of different tests.

01:07:51.250 --> 01:07:52.870
I'll talk about that more later.

01:07:53.810 --> 01:07:54.660
In another lecture.

01:07:55.470 --> 01:07:57.460
And then the structure of the network,

01:07:57.460 --> 01:07:59.200
for example like the number of nodes

01:07:59.200 --> 01:08:01.290
per layer is something that can be used

01:08:01.290 --> 01:08:02.460
to control the overfitting.

01:08:02.460 --> 01:08:03.840
So you can kind of like squeeze the

01:08:03.840 --> 01:08:07.160
representation into say 512 floating

01:08:07.160 --> 01:08:09.660
point values and that can prevent.

01:08:10.820 --> 01:08:11.810
Prevent overfitting.

01:08:12.770 --> 01:08:15.000
And then often deep learning is used in

01:08:15.000 --> 01:08:17.200
conjunction with massive data sets

01:08:17.200 --> 01:08:18.730
which help to further reduce the

01:08:18.730 --> 01:08:20.210
variance so that you can apply a very

01:08:20.210 --> 01:08:21.250
powerful models.

01:08:22.140 --> 01:08:25.430
Which have low bias and then rely on

01:08:25.430 --> 01:08:27.240
your enormous amount of data to reduce

01:08:27.240 --> 01:08:28.050
the variance.

01:08:31.530 --> 01:08:33.855
So in deep networks, the big challenge,

01:08:33.855 --> 01:08:35.820
the long standing problem with deep

01:08:35.820 --> 01:08:37.400
networks was the optimization.

01:08:37.400 --> 01:08:40.530
So how do we like optimize a many layer

01:08:40.530 --> 01:08:41.070
network?

01:08:41.920 --> 01:08:45.500
And one of the key ideas there was the

01:08:45.500 --> 01:08:47.170
stochastic gradient descent and back

01:08:47.170 --> 01:08:47.723
propagation.

01:08:47.723 --> 01:08:50.720
So we update the weights by summing the

01:08:50.720 --> 01:08:52.875
products of the error gradients from

01:08:52.875 --> 01:08:55.150
the input of the weight to the output

01:08:55.150 --> 01:08:55.730
of the network.

01:08:55.730 --> 01:08:57.710
So we basically trace all the paths

01:08:57.710 --> 01:09:00.050
from some weight into our prediction,

01:09:00.050 --> 01:09:01.810
and then based on that we see how this

01:09:01.810 --> 01:09:03.416
weight contributed to the error.

01:09:03.416 --> 01:09:05.620
And we make a small step to try to

01:09:05.620 --> 01:09:07.850
reduce that error based on a limited

01:09:07.850 --> 01:09:09.510
set of observations.

01:09:11.150 --> 01:09:13.840
And then the back propagation is a kind

01:09:13.840 --> 01:09:16.060
of dynamic program that efficiently

01:09:16.060 --> 01:09:17.970
reuses the weight gradient computations

01:09:17.970 --> 01:09:21.020
that each layer to predict the to do

01:09:21.020 --> 01:09:23.460
the weight updates for the previous

01:09:23.460 --> 01:09:23.890
layer.

01:09:24.670 --> 01:09:27.389
So this step, even though it feels

01:09:27.390 --> 01:09:29.170
backpropagation, feels kind of

01:09:29.170 --> 01:09:31.750
complicated computationally, it's very

01:09:31.750 --> 01:09:32.480
efficient.

01:09:32.480 --> 01:09:33.520
It takes almost.

01:09:33.520 --> 01:09:35.940
It takes about the same amount of time

01:09:35.940 --> 01:09:38.090
to update your weights as to do a

01:09:38.090 --> 01:09:38.700
prediction.

01:09:41.550 --> 01:09:43.160
The deep networks are composed of

01:09:43.160 --> 01:09:44.225
layers and activations.

01:09:44.225 --> 01:09:46.590
So we have these like we talked about

01:09:46.590 --> 01:09:50.350
sigmoid activations, where the downside

01:09:50.350 --> 01:09:52.710
the sigmoids map everything from zero

01:09:52.710 --> 01:09:54.420
to one, and they're downside is that

01:09:54.420 --> 01:09:56.230
the gradient is always less than zero.

01:09:56.230 --> 01:09:57.800
Even at the peak the gradient is only

01:09:57.800 --> 01:10:01.000
.25, and at the gradient is really

01:10:01.000 --> 01:10:01.455
small.

01:10:01.455 --> 01:10:03.099
So if you have a lot of layers.

01:10:03.750 --> 01:10:07.740
The since the gradient update is based

01:10:07.740 --> 01:10:09.900
on a product of these gradients along

01:10:09.900 --> 01:10:11.800
the path, then if you have a whole

01:10:11.800 --> 01:10:13.360
bunch of sigmoids, the gradient keeps

01:10:13.360 --> 01:10:15.209
getting smaller and smaller and smaller

01:10:15.210 --> 01:10:17.320
as you go earlier in the network until

01:10:17.320 --> 01:10:19.226
it's essentially 0 at the beginning of

01:10:19.226 --> 01:10:20.680
the network, which means that you can't

01:10:20.680 --> 01:10:23.050
optimize like the early weights.

01:10:23.050 --> 01:10:25.220
That's the vanishing gradient problem,

01:10:25.220 --> 01:10:27.220
and that was one of the things that got

01:10:27.220 --> 01:10:29.160
like neural networks stuck for many

01:10:29.160 --> 01:10:29.800
years.

01:10:30.950 --> 01:10:31.440
Can you?

01:10:31.440 --> 01:10:32.210
Yeah.

01:10:33.700 --> 01:10:37.490
OK so the OK so first like if you look

01:10:37.490 --> 01:10:40.115
at the gradient of a sigmoid it looks

01:10:40.115 --> 01:10:41.030
like this right?

01:10:41.670 --> 01:10:45.460
And at the peak it's only 25 and then

01:10:45.460 --> 01:10:47.340
at the extreme values it's extremely

01:10:47.340 --> 01:10:48.175
small.

01:10:48.175 --> 01:10:51.290
And So what that means is if you're

01:10:51.290 --> 01:10:52.765
gradient, let's say this is the end of

01:10:52.765 --> 01:10:54.000
the network and this is the beginning.

01:10:54.650 --> 01:10:57.030
Your gradient update for this weight

01:10:57.030 --> 01:10:58.925
will be based on a product of gradients

01:10:58.925 --> 01:11:00.975
for all the weights in between this

01:11:00.975 --> 01:11:02.680
weight and the output.

01:11:03.360 --> 01:11:05.286
And if they're all sigmoid activations,

01:11:05.286 --> 01:11:07.190
all of those gradients are going to be

01:11:07.190 --> 01:11:08.072
less than one.

01:11:08.072 --> 01:11:09.860
And so when you take the product of a

01:11:09.860 --> 01:11:11.330
whole bunch of numbers that are less

01:11:11.330 --> 01:11:12.873
than one, you end up with a really,

01:11:12.873 --> 01:11:14.410
really small number, right?

01:11:14.410 --> 01:11:16.080
And so that's why you can't train a

01:11:16.080 --> 01:11:18.230
deep network using sigmoids, because

01:11:18.230 --> 01:11:20.975
the gradients get they like vanish by

01:11:20.975 --> 01:11:22.525
the time you get to the earlier layers.

01:11:22.525 --> 01:11:24.490
And so the early layers don't train.

01:11:25.120 --> 01:11:26.130
And then you end up with these

01:11:26.130 --> 01:11:27.960
uninformative layers that are sitting

01:11:27.960 --> 01:11:29.170
between the inputs and the final

01:11:29.170 --> 01:11:30.300
layers, so you get really bad

01:11:30.300 --> 01:11:30.910
predictions.

01:11:32.510 --> 01:11:34.390
So that's a sigmoid problem.

01:11:34.390 --> 01:11:36.980
Very loose have a gradient of zero or

01:11:36.980 --> 01:11:40.195
one everywhere, so the relay looks like

01:11:40.195 --> 01:11:40.892
that.

01:11:40.892 --> 01:11:43.996
And in this part the gradient is 1, and

01:11:43.996 --> 01:11:45.869
this part the gradient is zero.

01:11:45.870 --> 01:11:48.470
They helped get networks deeper because

01:11:48.470 --> 01:11:49.880
that gradient of one is perfect.

01:11:49.880 --> 01:11:51.150
It doesn't get bigger, it doesn't get

01:11:51.150 --> 01:11:52.010
smaller as you like.

01:11:52.010 --> 01:11:53.060
Go through a bunch of ones.

01:11:53.930 --> 01:11:56.310
But the problem is that you can have

01:11:56.310 --> 01:11:59.420
these dead Railers where like a

01:11:59.420 --> 01:12:02.140
activation for some node is 0 for most

01:12:02.140 --> 01:12:04.780
of the data and then it has no gradient

01:12:04.780 --> 01:12:07.240
going into the weight and then it never

01:12:07.240 --> 01:12:07.790
changes.

01:12:10.460 --> 01:12:13.690
And so then the final thing that kind

01:12:13.690 --> 01:12:15.179
of fixed this problem was this skip

01:12:15.180 --> 01:12:15.710
connection.

01:12:15.710 --> 01:12:18.000
So the skip connections are a shortcut

01:12:18.000 --> 01:12:19.950
around different layers of the network

01:12:19.950 --> 01:12:22.065
so that the gradients can flow along

01:12:22.065 --> 01:12:23.130
the skip connections.

01:12:23.880 --> 01:12:25.080
All the way to the beginning of the

01:12:25.080 --> 01:12:28.150
network and with a gradient of 1.

01:12:29.330 --> 01:12:30.900
So that was that was coming with the

01:12:30.900 --> 01:12:31.520
Resnet.

01:12:32.980 --> 01:12:33.750
And then?

01:12:35.510 --> 01:12:37.880
And then I also talked about how SGD

01:12:37.880 --> 01:12:39.185
has like a lot of different variants

01:12:39.185 --> 01:12:41.130
and tricks to improve the speed of the

01:12:41.130 --> 01:12:42.960
instability of the optimization.

01:12:42.960 --> 01:12:44.830
For example, we have momentum so that

01:12:44.830 --> 01:12:46.250
if you keep getting weight updates in

01:12:46.250 --> 01:12:47.730
the same direction, those weight

01:12:47.730 --> 01:12:49.394
updates get faster and faster to

01:12:49.394 --> 01:12:50.229
improve the speed.

01:12:51.200 --> 01:12:52.970
You also have these normalizations so

01:12:52.970 --> 01:12:54.690
that you don't focus too much on

01:12:54.690 --> 01:12:56.890
updating weights updating particular

01:12:56.890 --> 01:12:58.620
weights, but you try to minimize the

01:12:58.620 --> 01:13:00.420
overall path of like how much each

01:13:00.420 --> 01:13:01.120
weight changes.

01:13:02.610 --> 01:13:04.173
I didn't talk about it, but another

01:13:04.173 --> 01:13:06.320
another strategy is gradient clipping,

01:13:06.320 --> 01:13:08.990
where you say that a gradient can't be

01:13:08.990 --> 01:13:10.740
too big and that can improve further,

01:13:10.740 --> 01:13:13.515
improve the strategy, the stability of

01:13:13.515 --> 01:13:14.470
the optimization.

01:13:15.670 --> 01:13:18.570
And then most commonly people either

01:13:18.570 --> 01:13:21.410
use SGD plus momentum or atom which is

01:13:21.410 --> 01:13:23.290
one of the last things I talked about.

01:13:23.290 --> 01:13:25.740
But there's more advanced methods range

01:13:25.740 --> 01:13:27.760
or rectified atom with gradient centric

01:13:27.760 --> 01:13:29.860
gradient centering and look ahead which

01:13:29.860 --> 01:13:31.570
have like a whole bunch of complicated

01:13:31.570 --> 01:13:34.160
strategies for doing the same thing but

01:13:34.160 --> 01:13:35.420
just a better search.

01:13:39.250 --> 01:13:40.270
Alright, let me see.

01:13:40.270 --> 01:13:42.280
All right, so I think you probably

01:13:42.280 --> 01:13:44.459
don't want me to skip this, so let me

01:13:44.460 --> 01:13:45.330
talk about.

01:13:46.840 --> 01:13:48.860
Let me just talk about this in the last

01:13:48.860 --> 01:13:49.390
minute.

01:13:49.900 --> 01:13:53.860
And so the so the mid term, so this is

01:13:53.860 --> 01:13:55.703
so the midterm is only going to be on

01:13:55.703 --> 01:13:57.090
things that we've already covered up to

01:13:57.090 --> 01:13:57.280
now.

01:13:57.280 --> 01:13:58.935
It's not going to be on anything that

01:13:58.935 --> 01:14:00.621
we cover in the next couple of days.

01:14:00.621 --> 01:14:02.307
The things that we cover in the next

01:14:02.307 --> 01:14:03.550
couple of days are important for

01:14:03.550 --> 01:14:04.073
homework three.

01:14:04.073 --> 01:14:06.526
So don't skip the lectures or anything,

01:14:06.526 --> 01:14:08.986
but they're not going to be on the

01:14:08.986 --> 01:14:09.251
midterm.

01:14:09.251 --> 01:14:11.750
So the midterms on March 9th and now

01:14:11.750 --> 01:14:12.766
it'll be on Prairie learn.

01:14:12.766 --> 01:14:14.735
So the exam will be open for most of

01:14:14.735 --> 01:14:15.470
the day.

01:14:15.470 --> 01:14:17.600
You don't come here to take it, you

01:14:17.600 --> 01:14:19.650
just take it somewhere else.

01:14:20.070 --> 01:14:23.000
Wherever you are and the exam will be

01:14:23.000 --> 01:14:24.740
75 minutes long or longer.

01:14:24.740 --> 01:14:27.185
If you have dress accommodations and

01:14:27.185 --> 01:14:29.380
you sent them to me, it's mainly going

01:14:29.380 --> 01:14:30.730
to be multiple choice or multiple

01:14:30.730 --> 01:14:31.560
select.

01:14:31.560 --> 01:14:34.950
There's no coding complex calculations

01:14:34.950 --> 01:14:36.920
in it, mainly is like conceptual.

01:14:38.060 --> 01:14:40.350
You can, as I said, take it at home.

01:14:40.350 --> 01:14:42.670
It's open book, so it's not cheating to

01:14:42.670 --> 01:14:43.510
during the exam.

01:14:43.510 --> 01:14:45.630
Consult your notes, look at practice

01:14:45.630 --> 01:14:47.630
questions and answers, look at slides,

01:14:47.630 --> 01:14:48.590
search on the Internet.

01:14:48.590 --> 01:14:49.320
That's all fine.

01:14:50.030 --> 01:14:51.930
It would be cheating if you were to

01:14:51.930 --> 01:14:53.940
talk to a classmate about the exam

01:14:53.940 --> 01:14:55.550
after one, but not both of you have

01:14:55.550 --> 01:14:56.290
taken it.

01:14:56.290 --> 01:14:57.510
So don't try to find out.

01:14:57.510 --> 01:14:59.210
Don't have like one person or I don't

01:14:59.210 --> 01:15:00.120
want to give you ideas.

01:15:02.340 --> 01:15:02.970
I.

01:15:07.170 --> 01:15:09.080
It's also cheating of course to get

01:15:09.080 --> 01:15:10.490
help from another person during the

01:15:10.490 --> 01:15:10.910
exam.

01:15:10.910 --> 01:15:12.510
So like if I found out about either of

01:15:12.510 --> 01:15:13.960
those things, it would be a big deal,

01:15:13.960 --> 01:15:16.150
but I prefer it.

01:15:16.150 --> 01:15:17.260
Just don't do it.

01:15:17.370 --> 01:15:17.880


01:15:19.180 --> 01:15:21.330
And then also it's important to note

01:15:21.330 --> 01:15:22.717
you won't have time to look up all the

01:15:22.717 --> 01:15:22.895
answers.

01:15:22.895 --> 01:15:24.680
So it might sound like multiple choice.

01:15:24.680 --> 01:15:25.855
Open book is like really easy.

01:15:25.855 --> 01:15:27.156
You don't need to study it, just look

01:15:27.156 --> 01:15:28.015
it up when you get there.

01:15:28.015 --> 01:15:28.930
That will not work.

01:15:28.930 --> 01:15:31.879
I can almost guarantee you need to

01:15:31.880 --> 01:15:34.060
learn it ahead of time so that most of

01:15:34.060 --> 01:15:36.380
the answers and you may have time to

01:15:36.380 --> 01:15:37.960
look up one or two, but not more than

01:15:37.960 --> 01:15:38.100
that.

01:15:40.030 --> 01:15:42.600
I've got a list of some of the central

01:15:42.600 --> 01:15:44.210
topics here, and since we're at time,

01:15:44.210 --> 01:15:45.880
I'm not going to walk through it right

01:15:45.880 --> 01:15:46.970
now, but you can review it.

01:15:46.970 --> 01:15:48.040
The slides are posted.

01:15:48.760 --> 01:15:50.540
And then there's just some review

01:15:50.540 --> 01:15:51.230
questions.

01:15:51.230 --> 01:15:53.215
So you can look at these and I think

01:15:53.215 --> 01:15:55.140
the best way to study is to look at the

01:15:55.140 --> 01:15:56.720
practice questions that are posted on

01:15:56.720 --> 01:15:59.744
the website and use that not only to if

01:15:59.744 --> 01:16:01.322
those questions, but also how familiar

01:16:01.322 --> 01:16:02.970
are you with each of those concepts.

01:16:02.970 --> 01:16:04.830
And then go back and review the slides

01:16:04.830 --> 01:16:07.447
if you're like if you feel less

01:16:07.447 --> 01:16:08.660
familiar with the topic.

01:16:09.620 --> 01:16:11.186
Alright, so thank you.

01:16:11.186 --> 01:16:13.330
And on Thursday we're going to resume

01:16:13.330 --> 01:16:15.783
with CNN's and computer vision and

01:16:15.783 --> 01:16:17.320
we're getting into our section on

01:16:17.320 --> 01:16:19.190
applications, so like natural language

01:16:19.190 --> 01:16:20.510
processing and all kinds of other

01:16:20.510 --> 01:16:20.860
things.

01:16:27.120 --> 01:16:30.250
So we are.

01:16:32.010 --> 01:16:34.620
Start a code contains the code from

01:16:34.620 --> 01:16:37.380
homework wise that you normally load

01:16:37.380 --> 01:16:39.650
the data and numbers and yeah Aries,

01:16:39.650 --> 01:16:42.220
but essentially we should transform

01:16:42.220 --> 01:16:44.360
them into like my torch.