WEBVTT Kind: captions; Language: en-US

NOTE
Created on 2024-02-07T20:53:55.0930204Z by ClassTranscribe

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Alright, good morning everybody.

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So I saw in response to the feedback, I

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got some feedback on the course and.

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Overall, there's of course a mix of

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responses, but some on average people

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feel like it's moving a little fast and

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we're and also it's challenging.

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So I wanted to take some time to like

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consolidate and to talk about some of

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the most important points.

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That we've covered so far, and then so

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I'll do that for the first half of the

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lecture, and then I'm also going to go

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through a detailed example using code

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to solve a particular problem.

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So.

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Let me see.

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All right.

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So this is a mostly the same as a slide

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that I showed in the intro.

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This is machine learning in general.

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You've got some raw features and so far

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we've COVID cases where we have

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discrete and continuous values and also

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some simple images in terms of the

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amnesty characters.

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And we have some kind of.

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Sometimes we process those features in

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some way we have like what's called an

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encoder or we have feature transforms.

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We've only gotten into that a little

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bit.

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In terms of the decision trees, which

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you can view as a kind of feature

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transformation.

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And feature selection using one the

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district regression.

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So the job of the encoder is to take

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your raw features and turn them into

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something that's more easily.

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That more easily yields a predictor.

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Then you have decoder, the thing that

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predicts from your encoded features,

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and we've covered pretty much all the

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methods here except for SVM, which

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we're doing next week.

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And so we've got a linear aggressor, a

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logistic regressor, nearest neighbor

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and probabilistic models.

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Now there's lots of different kinds of

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probabilistic models.

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We only talked about a couple of one of

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them nibs.

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But still, we've touched on this.

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And then you have a prediction and

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there's lots of different things you

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can predict.

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You can predict a category or a

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continuous value, which is what we've

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talked about South far.

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You could also be generating clusters

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or pixel labels or poses or other kinds

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of predictions.

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And in training, you've got some data

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and target labels, and you're trying to

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update the models of your parameters to

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get the best prediction possible, where

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you want to really not only maximize

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your prediction on the training data,

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but also to maximize your expected or

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minimize your expected error on the

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test data.

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So one important part of machine

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learning is learning a model.

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So.

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Here this is like this kind of.

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This function, in one form or another

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will be part of every machine learning

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algorithm where you're trying to.

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You have some model F of X Theta.

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Where X is the raw features.

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Beta are the parameters that you're

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trying to optimize that you're going to

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optimize to fit your model.

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And why is the prediction that you're

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trying to make?

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So you're given.

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In supervised learning you're given

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pairs XY of some features and labels.

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And then you're trying to solve for

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parameters that minimizes your loss,

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and your loss is a is like A is a

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objective function that you're trying

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to reduce, and it usually has two

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components.

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1 component is that you want your

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predictions on the training data to be

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as good as possible.

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For example, you might say that you

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want to maximize the probability of

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your labels given your features.

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Or, equivalently, you want to minimize

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the negative sum of log likelihood of

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your labels given your features.

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This is the same as maximizing the

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likelihood of the labels.

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But we often want to minimize things,

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so negative log is.

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Minimizing the negative log is the same

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as maximizing the log and taking the

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log.

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The Max of the log is the same as the

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Max of the value.

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And this form tends to be easier to

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optimize.

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The second term.

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So we want to maximize the likelihood

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of the labels given the data, but we

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also want to have some likely.

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We often want to impose some kinds of

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constraints or some kinds of

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preferences for the parameters of our

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model.

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So.

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And.

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So a common thing is that we want to

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say that the sum of the parameters we

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want to minimize the sum of the

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parameter squared, or we want to

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minimize the sum of the absolute values

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of the parameters.

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So this is called regularization.

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Or if you have a probabilistic model,

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that might be in the form of a prior on

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the statistics that you're estimating.

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So the regularization and priors

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indicate some kind of preference for a

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particular solutions.

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And they tend to improve

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generalization.

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And in some cases they're necessary to

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obtain a unique solution.

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Like there might be many linear models

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that can separate your one class from

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another, and without regularization you

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have no way of choosing among those

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different models.

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The regularization specifies a

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particular solution.

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And this is it's more important the

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less data you have.

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Or the more features or larger your

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problem is.

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Once we've once we've trained a model,

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then we want to do prediction using

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that model.

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So in prediction we're given some new

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set of features.

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It will be the same.

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So in training we might have seen 500

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examples, and for each of those

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examples 10 features and some label

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you're trying to predict.

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So in testing you'll have a set of

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testing examples, and each one will

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also have the same number of features.

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So it might have 10 features as well,

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and you're trying to predict the same

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label.

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But in testing you don't give the model

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your label, you're trying to output the

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label.

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So in testing, we're given some test

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sample with input features XT and if

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we're doing a regression, then we're

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trying to output yet directly.

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So we're trying to say, predict the

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stock price or temperature or something

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like that.

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If we're doing classification, we're

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trying to output the likelihood of a

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particular category or the most likely

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category.

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And.

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So then there's a so if we're trying to

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develop a machine learning algorithm.

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Then we go through this model

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evaluation process.

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So the first step is that we need to

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collect some data.

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So if we're creating a new problem,

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then we might need to capture capture

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images or record observations or

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download information from the Internet,

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or whatever.

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One way or another, you need to get

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some data.

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You need to get labels for that data.

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So it might include.

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You might need to do some manual

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annotation.

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You might need to.

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Crowd source or use platforms to get

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the labels.

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At the end of this you'll have a whole

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set of samples X&Y where X are the are

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the features that you want to use to

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make a prediction and why are the

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predictions that you want to make.

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And then you split that data into a

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training and validation and a test set

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where you're going to use the training

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set to optimize parameters, validation

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set to choose your best model and

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testing for your final evaluation and

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performance.

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So once you have the data, you might

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spend some time inspecting the features

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and trying to understand the problem a

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little bit better.

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Trying to look at do some little test

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to see how like baselines work and how

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certain features predict the label.

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And then you'll decide on some

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candidate models and parameters.

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Then for each candidate you would train

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the parameters using the train set.

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And you'll evaluate your trained model

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on the validation set.

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And then you choose the best model

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based on your validation performance.

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And then you evaluate it on the test

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set.

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And sometimes, very often you have like

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a tree and vowel test set.

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But an alternative is that you could do

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cross validation, which I'll show an

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example of, where you just split your

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whole set into 10 parts and each time

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you train on 9 parts and test on the

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10th part.

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That becomes.

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If you have like a very limited amount

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of data then that can help you make the

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best use of your limited data.

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So typically when you're evaluating the

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performance, you're going to measure

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like the error, the accuracy like root

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mean squared error or accuracy, or the

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amount of variance you can explain.

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Or you could be doing.

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If you're doing like a retrieval task,

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you might do precision recall.

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So there's a variety of metrics that

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depend on the problem.

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So.

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When we're trying to think about like

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these mill algorithms, there's actually

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a lot of different things that we

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should consider.

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One of them is like, what is the model?

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What kinds of things can it represent?

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For example, in a linear model and a

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classifier model, it means that all the

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data that's on one side of the

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hyperplane is going to be assigned to

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one class, and all the data on the

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other side of the hyperplane will be

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assigned to another class, where for

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nearest neighbor you can have much more

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flexible decision boundaries.

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You can also think about.

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Maybe the model implies that some kinds

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of functions are preferred over others.

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You think about like what is your

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objective function?

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So what is it that you're trying to

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minimize, and what kinds of like values

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does that imply?

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So do you prefer?

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Does it mean?

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Does your regularization, for example,

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mean that you prefer that you're using

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a few features or that you have low

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weight on a lot of features?

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Are you trying to minimize a likelihood

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or maximize the likelihood, or are you

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trying to just get high enough

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confidence on each example to get

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things correct?

00:11:49.430 --> 00:11:50.850
And it's important to note that the

00:11:50.850 --> 00:11:53.080
objective function often does not match

00:11:53.080 --> 00:11:54.290
your final evaluation.

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So nobody really trains a model to

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minimize the classification error, even

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though they often evaluate based on

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classification error.

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And there's two reasons for that.

00:12:06.576 --> 00:12:09.388
So one reason is that it's really hard

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to minimize classification error over

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training set, because a small change in

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parameters may not change your

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classification error.

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So it's hard to for an optimization

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algorithm to figure out how it should

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change to minimize that error.

00:12:22.430 --> 00:12:25.823
The second reason is that there might

00:12:25.823 --> 00:12:27.730
be many different models that can have

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similar classification error, the same

00:12:29.620 --> 00:12:31.980
classification error, and so you need

00:12:31.980 --> 00:12:33.560
some way of choosing among them.

00:12:33.560 --> 00:12:35.670
So many algorithms, many times the

00:12:35.670 --> 00:12:37.422
objective function will also say that

00:12:37.422 --> 00:12:39.160
you want to be very confident about

00:12:39.160 --> 00:12:41.274
your examples, not only that, you want

00:12:41.274 --> 00:12:42.010
to be correct.

00:12:45.380 --> 00:12:47.140
The third thing is that you would think

00:12:47.140 --> 00:12:50.070
about how you can optimize the model.

00:12:50.070 --> 00:12:51.610
So does it.

00:12:51.680 --> 00:12:56.200
For example for like logistic

00:12:56.200 --> 00:12:56.880
regression.

00:12:58.760 --> 00:13:01.480
You're able to reach a global optimum.

00:13:01.480 --> 00:13:04.220
It's a convex problem so that you're

00:13:04.220 --> 00:13:06.290
going to find the best solution, where

00:13:06.290 --> 00:13:08.020
for something a neural network it may

00:13:08.020 --> 00:13:09.742
not be possible to get the best

00:13:09.742 --> 00:13:11.000
solution, but you can usually get a

00:13:11.000 --> 00:13:11.860
pretty good solution.

00:13:12.680 --> 00:13:14.430
You also will think about like how long

00:13:14.430 --> 00:13:17.260
does it take to train and how does that

00:13:17.260 --> 00:13:18.709
depend on the number of examples and

00:13:18.709 --> 00:13:19.950
the number of features.

00:13:19.950 --> 00:13:22.010
So if you're later we'll talk about

00:13:22.010 --> 00:13:25.260
SVMS and Kernelized SVM is one of the

00:13:25.260 --> 00:13:27.560
problems, is that it's the training is

00:13:27.560 --> 00:13:29.761
quadratic in the number of examples, so

00:13:29.761 --> 00:13:32.600
it becomes a pretty expensive, at least

00:13:32.600 --> 00:13:34.976
according to the earlier optimization

00:13:34.976 --> 00:13:35.582
algorithms.

00:13:35.582 --> 00:13:38.120
So some algorithms can be used with a

00:13:38.120 --> 00:13:39.710
lot of examples, but some are just too

00:13:39.710 --> 00:13:40.370
expensive.

00:13:40.440 --> 00:13:40.880
Yeah.

00:13:43.520 --> 00:13:47.060
So the objective function is your, it's

00:13:47.060 --> 00:13:48.120
your loss essentially.

00:13:48.120 --> 00:13:50.470
So it usually has that data term where

00:13:50.470 --> 00:13:51.540
you're trying to maximize the

00:13:51.540 --> 00:13:52.910
likelihood of the data or the labels

00:13:52.910 --> 00:13:53.960
given the data.

00:13:53.960 --> 00:13:56.075
And it has some regularization term

00:13:56.075 --> 00:13:58.130
that says that you prefer some models

00:13:58.130 --> 00:13:58.670
over others.

00:14:05.090 --> 00:14:07.890
So yeah, feel free to please do ask as

00:14:07.890 --> 00:14:11.140
many questions as pop into your mind.

00:14:11.140 --> 00:14:13.010
I'm happy to answer them and I want to

00:14:13.010 --> 00:14:14.992
make sure, hopefully at the end of this

00:14:14.992 --> 00:14:17.670
lecture, or if it's or if you like

00:14:17.670 --> 00:14:18.630
further review the lecture.

00:14:18.630 --> 00:14:20.345
Again, I hope that all of this stuff is

00:14:20.345 --> 00:14:22.340
like really clear, and if it's not,

00:14:22.340 --> 00:14:26.847
just don't feel don't be afraid to ask

00:14:26.847 --> 00:14:28.680
questions in office hours or after

00:14:28.680 --> 00:14:29.660
class or whatever.

00:14:31.920 --> 00:14:34.065
So then finally, how does the

00:14:34.065 --> 00:14:34.670
prediction work?

00:14:34.670 --> 00:14:36.340
So then you want to think about like

00:14:36.340 --> 00:14:37.740
can I make a prediction really quickly?

00:14:37.740 --> 00:14:39.730
So like for a nearest neighbor it's not

00:14:39.730 --> 00:14:41.579
necessarily so quick, but for the

00:14:41.580 --> 00:14:43.050
linear models it's pretty fast.

00:14:44.750 --> 00:14:46.580
Can I find the most likely prediction

00:14:46.580 --> 00:14:48.260
according to my model?

00:14:48.260 --> 00:14:50.390
So sometimes even after you've

00:14:50.390 --> 00:14:53.790
optimized your model, you don't have a

00:14:53.790 --> 00:14:55.530
guarantee that you can generate the

00:14:55.530 --> 00:14:57.410
best solution for a new sample.

00:14:57.410 --> 00:14:59.930
So for example with these image

00:14:59.930 --> 00:15:02.090
generation algorithms even though.

00:15:02.890 --> 00:15:05.060
Even after you optimize your model

00:15:05.060 --> 00:15:08.150
given some phrase, you're not

00:15:08.150 --> 00:15:09.720
necessarily going to generate the most

00:15:09.720 --> 00:15:11.630
likely image given that phrase.

00:15:11.630 --> 00:15:13.710
You'll just generate like an image that

00:15:13.710 --> 00:15:16.199
is like consistent with the phrase

00:15:16.200 --> 00:15:18.010
according to some scoring function.

00:15:18.010 --> 00:15:20.810
So not all models can even be perfectly

00:15:20.810 --> 00:15:22.040
optimized for prediction.

00:15:23.100 --> 00:15:25.110
And then finally, does my algorithm

00:15:25.110 --> 00:15:27.180
output confidence as well as

00:15:27.180 --> 00:15:27.710
prediction?

00:15:27.710 --> 00:15:30.770
Usually it's helpful if your model not

00:15:30.770 --> 00:15:32.193
only gives you an answer, but also

00:15:32.193 --> 00:15:33.930
gives you a confidence in how to write

00:15:33.930 --> 00:15:34.790
that answer is.

00:15:35.420 --> 00:15:37.580
And it's nice if that confidence is

00:15:37.580 --> 00:15:38.030
accurate.

00:15:39.240 --> 00:15:41.580
Meaning that if it says that you've got

00:15:41.580 --> 00:15:44.000
like a 99% chance of being correct,

00:15:44.000 --> 00:15:46.250
then hopefully 99 out of 100 times

00:15:46.250 --> 00:15:48.640
you'll be correct in that situation.

00:15:55.440 --> 00:15:57.234
So we looked at.

00:15:57.234 --> 00:15:59.300
We looked at several different

00:15:59.300 --> 00:16:00.870
classification algorithms.

00:16:01.560 --> 00:16:04.440
And so here they're all compared

00:16:04.440 --> 00:16:05.890
side-by-side according to some

00:16:05.890 --> 00:16:06.290
criteria.

00:16:06.290 --> 00:16:08.130
So we can think about like what type of

00:16:08.130 --> 00:16:10.290
algorithm it is it a nearest neighbor

00:16:10.290 --> 00:16:12.480
is instance based, and that the

00:16:12.480 --> 00:16:14.120
parameters are the instances

00:16:14.120 --> 00:16:14.740
themselves.

00:16:14.740 --> 00:16:17.870
There's additional like linear model or

00:16:17.870 --> 00:16:19.450
something that's parametric that you're

00:16:19.450 --> 00:16:20.590
trying to fit to your data.

00:16:22.150 --> 00:16:24.170
Naive Bayes is probabilistic is

00:16:24.170 --> 00:16:26.060
logistic regression, but.

00:16:26.910 --> 00:16:29.090
Naive Bayes, you're maximizing the

00:16:29.090 --> 00:16:31.210
likelihood of your features given the

00:16:31.210 --> 00:16:33.020
data or your features, and I mean

00:16:33.020 --> 00:16:34.270
sorry, you're maximizing likelihood of

00:16:34.270 --> 00:16:35.720
your features and the label.

00:16:36.600 --> 00:16:37.230


00:16:38.790 --> 00:16:40.800
Under the assumption that your features

00:16:40.800 --> 00:16:42.610
are independent given the label.

00:16:43.450 --> 00:16:45.450
Where in logistic regression you're

00:16:45.450 --> 00:16:47.695
directly maximizing the likelihood of

00:16:47.695 --> 00:16:48.970
the label given the data.

00:16:51.820 --> 00:16:53.880
They both often end up being linear

00:16:53.880 --> 00:16:55.750
models, but you're modeling different

00:16:55.750 --> 00:16:57.659
things in these two in these two

00:16:57.660 --> 00:16:58.170
settings.

00:16:58.790 --> 00:17:01.880
And in logistic regression, the model

00:17:01.880 --> 00:17:04.460
the linear part, so it's, I just wrote

00:17:04.460 --> 00:17:05.890
logistic regression, but often we're

00:17:05.890 --> 00:17:07.176
doing linear logistic regression.

00:17:07.176 --> 00:17:09.490
The linear part is that we're seeing

00:17:09.490 --> 00:17:11.993
that this logic function is linear.

00:17:11.993 --> 00:17:15.896
The log ratio of the probability of the

00:17:15.896 --> 00:17:19.830
of label equals one given the features

00:17:19.830 --> 00:17:21.460
over probability of label equals zero

00:17:21.460 --> 00:17:22.319
given the features.

00:17:22.319 --> 00:17:24.323
That thing is the linear thing that

00:17:24.323 --> 00:17:24.970
we're fitting.

00:17:27.290 --> 00:17:28.700
And then we talked about decision

00:17:28.700 --> 00:17:29.350
trees.

00:17:29.350 --> 00:17:31.706
I would also say that's a kind of a

00:17:31.706 --> 00:17:33.040
probabilistic function in the sense

00:17:33.040 --> 00:17:35.555
that we're choosing our splits to

00:17:35.555 --> 00:17:38.700
maximize the mutual information or to,

00:17:38.700 --> 00:17:41.200
sorry, to maximize the information gain

00:17:41.200 --> 00:17:44.870
to minimize the conditional entropy.

00:17:44.870 --> 00:17:47.780
And that's like a probabilistic basis

00:17:47.780 --> 00:17:49.400
for the optimization.

00:17:50.080 --> 00:17:51.810
And then at the end of the prediction,

00:17:51.810 --> 00:17:53.560
you would typically be estimating the

00:17:53.560 --> 00:17:55.330
probability of each label given the

00:17:55.330 --> 00:17:57.170
data that has fallen into some leaf

00:17:57.170 --> 00:17:57.430
node.

00:17:59.490 --> 00:18:01.024
But that has quite different rules than

00:18:01.024 --> 00:18:01.460
the other.

00:18:01.460 --> 00:18:03.260
So nearest neighbor is just going to be

00:18:03.260 --> 00:18:05.189
like finding the sample that has the

00:18:05.190 --> 00:18:06.750
closest distance.

00:18:06.750 --> 00:18:08.422
Naive Bayes and logistic regression

00:18:08.422 --> 00:18:11.363
will be these probability functions

00:18:11.363 --> 00:18:13.540
that will tend to give you like linear

00:18:13.540 --> 00:18:14.485
classifiers.

00:18:14.485 --> 00:18:17.480
And Decision Tree has these conjunctive

00:18:17.480 --> 00:18:19.840
rules that you say if this feature is

00:18:19.840 --> 00:18:22.249
greater than this value then you go

00:18:22.249 --> 00:18:22.615
this way.

00:18:22.615 --> 00:18:23.955
And then if this other thing happens

00:18:23.955 --> 00:18:26.090
then you go another way and then at the

00:18:26.090 --> 00:18:29.350
end you can express that as a series of

00:18:29.350 --> 00:18:29.700
rules.

00:18:29.750 --> 00:18:31.425
Where you have a bunch of and

00:18:31.425 --> 00:18:32.850
conditions, and if all of those

00:18:32.850 --> 00:18:34.220
conditions are met, then you make a

00:18:34.220 --> 00:18:35.290
particular prediction.

00:18:38.370 --> 00:18:40.150
So these algorithms have different

00:18:40.150 --> 00:18:42.480
strengths, like nearest neighbor has

00:18:42.480 --> 00:18:45.547
low bias, so that means that you can

00:18:45.547 --> 00:18:47.340
almost always get perfect training

00:18:47.340 --> 00:18:47.970
accuracy.

00:18:47.970 --> 00:18:49.706
You can fit like almost anything with

00:18:49.706 --> 00:18:50.279
nearest neighbor.

00:18:52.310 --> 00:18:54.725
On the other hand, I guess I didn't put

00:18:54.725 --> 00:18:56.640
it here, but limitation is that it has

00:18:56.640 --> 00:18:57.300
high variance.

00:18:58.000 --> 00:18:59.650
You might get very different prediction

00:18:59.650 --> 00:19:01.590
functions if you resample your data.

00:19:03.390 --> 00:19:05.150
It has no training time.

00:19:06.230 --> 00:19:08.200
It's very widely applicable and it's

00:19:08.200 --> 00:19:08.900
very simple.

00:19:09.690 --> 00:19:12.110
Another limitation is that it can take

00:19:12.110 --> 00:19:13.780
a long time to do inference, but if you

00:19:13.780 --> 00:19:15.642
use approximate nearest neighbor

00:19:15.642 --> 00:19:17.790
inference, which we'll talk about

00:19:17.790 --> 00:19:21.230
later, then it can be like relatively

00:19:21.230 --> 00:19:21.608
fast.

00:19:21.608 --> 00:19:23.881
You can do approximate nearest neighbor

00:19:23.881 --> 00:19:26.600
in log N time, where N is the number of

00:19:26.600 --> 00:19:29.310
training samples, where so far we're

00:19:29.310 --> 00:19:31.470
just doing brute force, which is linear

00:19:31.470 --> 00:19:32.460
in the number of samples.

00:19:34.620 --> 00:19:35.770
Naive bayes.

00:19:35.770 --> 00:19:37.980
The strengths are that you can estimate

00:19:37.980 --> 00:19:39.950
these parameters reasonably well from

00:19:39.950 --> 00:19:40.680
limited data.

00:19:41.690 --> 00:19:43.000
It's also pretty simple.

00:19:43.000 --> 00:19:45.380
It's fast to train, and the downside is

00:19:45.380 --> 00:19:48.030
that as limited modeling power, so even

00:19:48.030 --> 00:19:49.876
on the training set you often won't get

00:19:49.876 --> 00:19:52.049
0 error or even close to 0 error.

00:19:53.520 --> 00:19:55.290
Logistic regression is really powerful

00:19:55.290 --> 00:19:57.250
in high dimensions, so remember that

00:19:57.250 --> 00:19:59.050
even though it's a linear classifier,

00:19:59.050 --> 00:20:01.400
which feels like it can't do much in

00:20:01.400 --> 00:20:04.830
terms of separation in high dimensions,

00:20:04.830 --> 00:20:05.530
you can.

00:20:05.530 --> 00:20:07.330
These classifiers are actually very

00:20:07.330 --> 00:20:07.850
powerful.

00:20:08.510 --> 00:20:10.710
If you have 1000 dimensional feature.

00:20:11.330 --> 00:20:13.930
And you have 1000 data points, then you

00:20:13.930 --> 00:20:16.094
can assign those data points arbitrary

00:20:16.094 --> 00:20:18.210
labels, arbitrary binary labels, and

00:20:18.210 --> 00:20:19.590
still get a perfect classifier.

00:20:19.590 --> 00:20:21.770
You're guaranteed a perfect classifier

00:20:21.770 --> 00:20:23.050
in terms of the training data.

00:20:23.860 --> 00:20:26.740
Now, that power power is always a

00:20:26.740 --> 00:20:27.750
double edged sword.

00:20:27.750 --> 00:20:29.740
You, if you have a powerful classifier,

00:20:29.740 --> 00:20:32.040
means you can fit your training data

00:20:32.040 --> 00:20:34.140
really well, but it also means that

00:20:34.140 --> 00:20:35.850
you're more susceptible to overfitting

00:20:35.850 --> 00:20:37.510
your training data, which means that

00:20:37.510 --> 00:20:38.510
you perform well.

00:20:39.460 --> 00:20:41.160
And the training data, but your test

00:20:41.160 --> 00:20:43.170
performance is not so good, you get

00:20:43.170 --> 00:20:43.940
higher test error.

00:20:45.780 --> 00:20:47.830
It's also widely applicable.

00:20:47.830 --> 00:20:50.480
It produces good confidence estimates,

00:20:50.480 --> 00:20:52.130
so that can be helpful if you want to

00:20:52.130 --> 00:20:54.170
know whether the prediction is correct.

00:20:54.780 --> 00:20:56.640
And it gives you fast prediction

00:20:56.640 --> 00:20:57.840
because it's the linear model.

00:20:59.470 --> 00:21:01.470
Similar to nearest neighbor has a

00:21:01.470 --> 00:21:03.380
limitation that it relies on good input

00:21:03.380 --> 00:21:04.330
features.

00:21:04.330 --> 00:21:05.730
So nearest neighbor if you have a

00:21:05.730 --> 00:21:06.160
simple.

00:21:07.240 --> 00:21:10.040
If you have a simple distance function

00:21:10.040 --> 00:21:13.660
like Euclidian distance, that assumes

00:21:13.660 --> 00:21:15.665
that all your features are scaled so

00:21:15.665 --> 00:21:17.110
that there are like comparable scales

00:21:17.110 --> 00:21:18.930
to each other, and that they're all

00:21:18.930 --> 00:21:19.540
predictive.

00:21:20.400 --> 00:21:22.310
Nearest logistic regression doesn't

00:21:22.310 --> 00:21:23.970
make assumptions that strong.

00:21:23.970 --> 00:21:25.799
It can kind of choose which features to

00:21:25.800 --> 00:21:27.420
use and it can rescale them

00:21:27.420 --> 00:21:29.790
essentially, but it does.

00:21:29.790 --> 00:21:33.230
But it's not able to model like joint

00:21:33.230 --> 00:21:35.425
combinations of features, so the

00:21:35.425 --> 00:21:37.360
features should be individually useful.

00:21:39.270 --> 00:21:41.340
And then finally, decision trees are

00:21:41.340 --> 00:21:42.930
good because they can provide an

00:21:42.930 --> 00:21:44.600
explainable decision function.

00:21:44.600 --> 00:21:47.040
You get these nice rules that are easy

00:21:47.040 --> 00:21:47.750
to communicate.

00:21:48.360 --> 00:21:49.740
It's also widely applicable.

00:21:49.740 --> 00:21:51.400
You can use that on continuous discrete

00:21:51.400 --> 00:21:52.040
data.

00:21:52.040 --> 00:21:54.162
You don't need to scale the features.

00:21:54.162 --> 00:21:55.740
It's like it doesn't really matter if

00:21:55.740 --> 00:21:57.930
you multiply the features by 10, it

00:21:57.930 --> 00:21:59.230
just means that you'd be choosing a

00:21:59.230 --> 00:22:00.790
threshold that's 10 times bigger.

00:22:01.820 --> 00:22:03.510
And you can deal with a mix of discrete

00:22:03.510 --> 00:22:05.720
and continuous variables.

00:22:05.720 --> 00:22:07.380
The downside is that.

00:22:08.330 --> 00:22:11.780
One tree by itself either tends to

00:22:11.780 --> 00:22:14.170
generalize poorly, meaning like you

00:22:14.170 --> 00:22:15.870
train a full tree and you do perfect

00:22:15.870 --> 00:22:18.140
training, but you get bad test error.

00:22:18.770 --> 00:22:20.240
Or you tend to underfit the data.

00:22:20.240 --> 00:22:21.910
If you train a short tree then you

00:22:21.910 --> 00:22:23.510
don't get very good training or test

00:22:23.510 --> 00:22:23.770
error.

00:22:24.650 --> 00:22:26.920
And so a single tree by itself is not

00:22:26.920 --> 00:22:28.160
usually the best predictor.

00:22:31.530 --> 00:22:34.085
So there's just like you can also think

00:22:34.085 --> 00:22:35.530
about these methods, I won't talk

00:22:35.530 --> 00:22:37.366
through this whole slide, but you can

00:22:37.366 --> 00:22:39.290
also think about the methods in terms

00:22:39.290 --> 00:22:42.130
of like the learning objectives, the

00:22:42.130 --> 00:22:44.556
training, like how you optimize those

00:22:44.556 --> 00:22:46.350
learning objectives and then the

00:22:46.350 --> 00:22:47.840
inference, how you make your final

00:22:47.840 --> 00:22:48.430
prediction.

00:22:49.040 --> 00:22:52.460
And so here I also included linear

00:22:52.460 --> 00:22:54.870
SVMS, which we'll talk about next week,

00:22:54.870 --> 00:22:57.590
but you can see for example that.

00:22:59.260 --> 00:23:01.730
That these in terms of inference,

00:23:01.730 --> 00:23:04.200
linear SVM, logistic regression, Naive

00:23:04.200 --> 00:23:06.790
Bayes are all linear models, at least

00:23:06.790 --> 00:23:08.230
in the case where you're dealing with

00:23:08.230 --> 00:23:11.190
discrete variables or Gaussians for 9

00:23:11.190 --> 00:23:11.630
days.

00:23:11.630 --> 00:23:13.948
But they have different ways, they have

00:23:13.948 --> 00:23:15.695
different learning objectives and then

00:23:15.695 --> 00:23:17.000
different ways of doing the training.

00:23:22.330 --> 00:23:24.790
And then question go ahead.

00:23:36.030 --> 00:23:37.450
Yeah.

00:23:37.450 --> 00:23:39.810
Thank you for the clarification, so.

00:23:40.710 --> 00:23:42.850
So what I mean by that it doesn't

00:23:42.850 --> 00:23:46.110
require feature scaling is that if you

00:23:46.110 --> 00:23:47.909
could have one feature that ranges from

00:23:47.910 --> 00:23:50.495
like zero to 1000 and another feature

00:23:50.495 --> 00:23:52.160
that ranges from zero to 1.

00:23:52.960 --> 00:23:56.090
And decision trees are perfectly fine

00:23:56.090 --> 00:23:57.770
with that, because it can like freely

00:23:57.770 --> 00:23:59.390
choose the threshold and stuff.

00:23:59.390 --> 00:24:01.450
And if you multiply 1 feature value by

00:24:01.450 --> 00:24:03.700
50, it doesn't really change the

00:24:03.700 --> 00:24:05.643
function, it can still choose like

00:24:05.643 --> 00:24:07.300
threshold that's 50 times larger.

00:24:08.050 --> 00:24:10.220
Where nearest neighbor, for example, if

00:24:10.220 --> 00:24:13.084
one feature ranges from zero to 1001

00:24:13.084 --> 00:24:15.880
ranges from zero to 1, then it's not

00:24:15.880 --> 00:24:17.673
going to care at all about the zero to

00:24:17.673 --> 00:24:19.270
1 feature because like that difference

00:24:19.270 --> 00:24:21.790
of like 200 on the scale of zero to

00:24:21.790 --> 00:24:23.738
1000 is going to overwhelm completely a

00:24:23.738 --> 00:24:26.290
difference of 1 on the 0 to one

00:24:26.290 --> 00:24:26.609
feature.

00:24:35.130 --> 00:24:36.275
Right, it doesn't.

00:24:36.275 --> 00:24:37.910
It's not influenced.

00:24:37.910 --> 00:24:40.040
I guess it's not influenced by the

00:24:40.040 --> 00:24:41.370
variance of the features, yeah.

00:24:46.320 --> 00:24:49.130
So I don't need to read talk through

00:24:49.130 --> 00:24:51.260
all of this because even for

00:24:51.260 --> 00:24:53.480
aggression, most of these algorithms

00:24:53.480 --> 00:24:55.219
are the same and they have the same

00:24:55.220 --> 00:24:56.710
strengths and the same weaknesses.

00:24:57.500 --> 00:24:59.630
The only difference between regression

00:24:59.630 --> 00:25:01.310
and classification is that you tend to

00:25:01.310 --> 00:25:03.235
have a different loss function where

00:25:03.235 --> 00:25:04.820
you because you're trying to predict a

00:25:04.820 --> 00:25:06.790
continuous value instead of predicting

00:25:06.790 --> 00:25:09.590
a likelihood of a categorical value, or

00:25:09.590 --> 00:25:11.240
trying to just output the categorical

00:25:11.240 --> 00:25:12.000
value directly.

00:25:14.330 --> 00:25:17.450
Linear regression though is A1 new

00:25:17.450 --> 00:25:18.290
algorithm here.

00:25:18.980 --> 00:25:21.923
So in linear regression, you're trying

00:25:21.923 --> 00:25:24.585
to fit the data, so you're not trying

00:25:24.585 --> 00:25:24.940
to.

00:25:26.480 --> 00:25:28.396
Fit like a probability model like

00:25:28.396 --> 00:25:29.590
linear logistic regression.

00:25:29.590 --> 00:25:31.860
You're just trying to directly fit the

00:25:31.860 --> 00:25:33.680
prediction given the data, and so you

00:25:33.680 --> 00:25:35.575
have like a linear function like W

00:25:35.575 --> 00:25:37.960
transpose X or West transpose X + B.

00:25:37.960 --> 00:25:41.120
That should ideally output output Y

00:25:41.120 --> 00:25:41.710
directly.

00:25:43.830 --> 00:25:45.670
Similar to linear to logistic

00:25:45.670 --> 00:25:47.030
regression, though it's powerful and

00:25:47.030 --> 00:25:48.220
high dimensions, it's widely

00:25:48.220 --> 00:25:48.820
applicable.

00:25:48.820 --> 00:25:50.650
You get fast prediction.

00:25:50.650 --> 00:25:52.770
Also, it can be useful to interpret the

00:25:52.770 --> 00:25:54.300
coefficients to say like what the

00:25:54.300 --> 00:25:56.040
correlations are of the features with

00:25:56.040 --> 00:25:58.110
your prediction, or to see which

00:25:58.110 --> 00:25:59.900
features are more predictive than

00:25:59.900 --> 00:26:00.300
others.

00:26:01.410 --> 00:26:03.440
And similar to logistic regression, it

00:26:03.440 --> 00:26:06.140
relies to some extent on good features.

00:26:06.140 --> 00:26:07.720
In fact, I would say even more.

00:26:08.320 --> 00:26:12.220
Because this is assuming that Y is

00:26:12.220 --> 00:26:15.040
going to be a linear function of X and

00:26:15.040 --> 00:26:17.130
West, which is in a way a stronger

00:26:17.130 --> 00:26:18.140
assumption than that.

00:26:18.140 --> 00:26:20.670
Like a binary classification will be a

00:26:20.670 --> 00:26:21.870
linear function of the features.

00:26:23.360 --> 00:26:24.940
So you often have to do some kind of

00:26:24.940 --> 00:26:26.950
feature transformations to make it work

00:26:26.950 --> 00:26:27.220
well.

00:26:28.520 --> 00:26:28.960
Question.

00:26:40.800 --> 00:26:43.402
So naive bayes.

00:26:43.402 --> 00:26:46.295
The example I gave was a semi semi

00:26:46.295 --> 00:26:48.850
Naive Bayes algorithm for classifying

00:26:48.850 --> 00:26:50.650
faces and cars.

00:26:50.650 --> 00:26:52.618
So there they took groups of features

00:26:52.618 --> 00:26:54.190
and modeled the probabilities of small

00:26:54.190 --> 00:26:55.720
groups of features and then took the

00:26:55.720 --> 00:26:57.090
product of those to give you your

00:26:57.090 --> 00:26:58.190
probabilistic model.

00:26:58.190 --> 00:27:01.770
I also would use like Naive Bayes if

00:27:01.770 --> 00:27:03.719
I'm trying to do like color like

00:27:03.720 --> 00:27:05.600
segmentation based on color and I need

00:27:05.600 --> 00:27:08.000
to estimate the probability of color

00:27:08.000 --> 00:27:09.490
given that it's in one region versus

00:27:09.490 --> 00:27:11.470
another, I might assume that.

00:27:11.530 --> 00:27:15.320
By that, my color features like the hue

00:27:15.320 --> 00:27:17.920
versus intensity for example, are

00:27:17.920 --> 00:27:19.380
independent given the region that it

00:27:19.380 --> 00:27:22.260
came from and so use that as part of my

00:27:22.260 --> 00:27:23.760
probabilistic model for doing the

00:27:23.760 --> 00:27:24.670
segmentation.

00:27:25.880 --> 00:27:30.940
Logistic regression you would like any

00:27:30.940 --> 00:27:32.610
neural network is doing logistic

00:27:32.610 --> 00:27:35.807
regression in the last layer.

00:27:35.807 --> 00:27:38.703
So most things are using logistic

00:27:38.703 --> 00:27:40.770
regression now as part of it.

00:27:40.770 --> 00:27:42.775
So you can view like the early layers

00:27:42.775 --> 00:27:44.674
as feature learning and the last layer

00:27:44.674 --> 00:27:45.519
is logistic regression.

00:27:46.490 --> 00:27:49.250
And then decision trees are.

00:27:50.660 --> 00:27:52.200
We'll see an example.

00:27:52.200 --> 00:27:53.670
It's used in the example I'm going to

00:27:53.670 --> 00:27:55.723
give, but like medical analysis is a is

00:27:55.723 --> 00:27:57.680
a good one because you often want some

00:27:57.680 --> 00:28:00.631
interpretable function as well as some

00:28:00.631 --> 00:28:01.620
good prediction.

00:28:03.820 --> 00:28:04.090
Yep.

00:28:09.200 --> 00:28:11.450
All right, so one of the one of the key

00:28:11.450 --> 00:28:15.360
concepts is like how performance varies

00:28:15.360 --> 00:28:17.230
with the number of training samples.

00:28:17.230 --> 00:28:20.080
So as you get more training data, you

00:28:20.080 --> 00:28:21.670
should be able to fit a more accurate

00:28:21.670 --> 00:28:22.120
model.

00:28:23.310 --> 00:28:25.600
And so you would expect that your test

00:28:25.600 --> 00:28:27.746
error should decrease as you get more

00:28:27.746 --> 00:28:29.760
training samples, because if you have

00:28:29.760 --> 00:28:33.640
only like 1 training sample, then you

00:28:33.640 --> 00:28:34.700
don't know if that's like really

00:28:34.700 --> 00:28:36.420
representative, if it's covering all

00:28:36.420 --> 00:28:37.195
the different cases.

00:28:37.195 --> 00:28:39.263
As you get more and more training

00:28:39.263 --> 00:28:41.020
samples, you can fit more complex

00:28:41.020 --> 00:28:43.858
models and you can be more assured that

00:28:43.858 --> 00:28:46.110
the training samples that you've seen

00:28:46.110 --> 00:28:47.850
fully represent the distribution that

00:28:47.850 --> 00:28:48.710
you'll see in testing.

00:28:50.040 --> 00:28:52.040
But as you get more training, it

00:28:52.040 --> 00:28:53.700
becomes harder to fit the training

00:28:53.700 --> 00:28:54.060
data.

00:28:54.920 --> 00:28:57.655
So maybe a linear model can perfectly

00:28:57.655 --> 00:29:00.340
classify like 500 examples, but it

00:29:00.340 --> 00:29:02.350
can't perfectly classify 500 million

00:29:02.350 --> 00:29:04.900
examples, even if they're even in the

00:29:04.900 --> 00:29:05.430
training set.

00:29:07.110 --> 00:29:10.420
As you get more data, these will test

00:29:10.420 --> 00:29:12.630
and the training error will converge.

00:29:13.380 --> 00:29:15.100
And if they're coming from exactly the

00:29:15.100 --> 00:29:16.540
same distribution, then they'll

00:29:16.540 --> 00:29:18.500
converge to exactly the same value.

00:29:19.680 --> 00:29:21.030
Only if they come from different

00:29:21.030 --> 00:29:22.790
distributions would you possibly have a

00:29:22.790 --> 00:29:24.250
gap if you have infinite training

00:29:24.250 --> 00:29:24.720
samples.

00:29:25.330 --> 00:29:27.133
So we have these concepts of the test

00:29:27.133 --> 00:29:27.411
error.

00:29:27.411 --> 00:29:29.253
So that's the error on some samples

00:29:29.253 --> 00:29:31.420
that are not used for training that are

00:29:31.420 --> 00:29:34.360
randomly sampled from your distribution

00:29:34.360 --> 00:29:35.020
of data.

00:29:35.020 --> 00:29:38.744
The training error is the error on your

00:29:38.744 --> 00:29:41.240
training set that is used to optimize

00:29:41.240 --> 00:29:43.458
your model, and the generalization

00:29:43.458 --> 00:29:46.803
error is the gap between the test and

00:29:46.803 --> 00:29:49.237
the training error, so that the

00:29:49.237 --> 00:29:51.672
generalization error is your error due

00:29:51.672 --> 00:29:55.386
to due to like an imperfect model due

00:29:55.386 --> 00:29:55.679
to.

00:29:55.750 --> 00:29:57.280
To limited training samples.

00:30:04.950 --> 00:30:05.650
Question.

00:30:07.940 --> 00:30:09.675
So there's test error.

00:30:09.675 --> 00:30:12.620
So that's the I'll start with training.

00:30:12.620 --> 00:30:14.070
OK, so first there's training error.

00:30:14.810 --> 00:30:17.610
So training error is you fit, you fit a

00:30:17.610 --> 00:30:19.010
model on a training set, and then

00:30:19.010 --> 00:30:20.540
you're evaluating the error on the same

00:30:20.540 --> 00:30:21.230
training set.

00:30:22.490 --> 00:30:24.620
So if your model is really powerful,

00:30:24.620 --> 00:30:27.282
that training error might be 0, But if

00:30:27.282 --> 00:30:29.220
it's if it's more limited, like Naive

00:30:29.220 --> 00:30:32.090
Bayes, you'll often have nonzero error.

00:30:32.950 --> 00:30:35.652
And you since your loss is, since you

00:30:35.652 --> 00:30:36.384
have some.

00:30:36.384 --> 00:30:38.580
If you're optimizing a loss like the

00:30:38.580 --> 00:30:41.160
probability, then there's always room

00:30:41.160 --> 00:30:42.870
to improve that loss, so you'll always

00:30:42.870 --> 00:30:45.430
have like non like some loss on your

00:30:45.430 --> 00:30:45.890
training set.

00:30:47.970 --> 00:30:50.120
The test error is if you take that same

00:30:50.120 --> 00:30:52.770
model, but now you evaluate it on other

00:30:52.770 --> 00:30:54.516
samples from the distribution, other

00:30:54.516 --> 00:30:56.040
test samples, and you compute an

00:30:56.040 --> 00:30:56.835
expected error.

00:30:56.835 --> 00:30:59.264
The average error over those test

00:30:59.264 --> 00:31:01.172
samples, your test error.

00:31:01.172 --> 00:31:03.330
You always expect your test error to be

00:31:03.330 --> 00:31:04.480
higher than your training error.

00:31:05.130 --> 00:31:06.400
Because you're.

00:31:06.490 --> 00:31:07.000
Time.

00:31:07.860 --> 00:31:10.140
Because your test error was not used to

00:31:10.140 --> 00:31:11.530
optimize your model, but your training

00:31:11.530 --> 00:31:12.000
error was.

00:31:13.140 --> 00:31:15.260
In that gap between the test air and

00:31:15.260 --> 00:31:16.260
the training error is the

00:31:16.260 --> 00:31:17.320
generalization error.

00:31:18.050 --> 00:31:20.560
So that's how that's the error due to

00:31:20.560 --> 00:31:23.680
the challenge of making predictions

00:31:23.680 --> 00:31:25.330
about new samples that were not made in

00:31:25.330 --> 00:31:25.710
training.

00:31:26.340 --> 00:31:27.510
That were not seen in training.

00:31:29.880 --> 00:31:30.260
Question.

00:31:33.240 --> 00:31:35.950
So overfit means that.

00:31:35.950 --> 00:31:37.920
So this isn't the ideal plot for

00:31:37.920 --> 00:31:38.610
overfitting, but.

00:31:39.500 --> 00:31:41.520
Overfitting is that as your model gets

00:31:41.520 --> 00:31:43.600
more complicated, your training error

00:31:43.600 --> 00:31:45.115
will always should always go down.

00:31:45.115 --> 00:31:48.510
You would expect it to go down if you.

00:31:49.070 --> 00:31:52.200
If you, for example were to keep adding

00:31:52.200 --> 00:31:55.040
features to your model, then the same

00:31:55.040 --> 00:31:57.030
model should keep getting better on

00:31:57.030 --> 00:31:58.550
your training set because you've got

00:31:58.550 --> 00:32:00.235
more features with which to fit your

00:32:00.235 --> 00:32:00.810
training data.

00:32:02.050 --> 00:32:04.430
And maybe for a while your test error

00:32:04.430 --> 00:32:06.320
will also go down because you genuinely

00:32:06.320 --> 00:32:07.350
get a better predictor.

00:32:08.190 --> 00:32:10.200
But then at some point, as you continue

00:32:10.200 --> 00:32:12.500
to increase the complexity, the test

00:32:12.500 --> 00:32:13.880
error will start going up.

00:32:13.880 --> 00:32:15.260
Even though the training error keeps

00:32:15.260 --> 00:32:17.540
going down, the test error goes up, and

00:32:17.540 --> 00:32:18.690
that's the point at which you've

00:32:18.690 --> 00:32:19.180
overfit.

00:32:19.920 --> 00:32:21.604
So you can't.

00:32:21.604 --> 00:32:22.165
Really.

00:32:22.165 --> 00:32:24.600
Common, really common conceptual

00:32:24.600 --> 00:32:27.500
mistake that people make is to think

00:32:27.500 --> 00:32:29.670
that once you're training error is 0,

00:32:29.670 --> 00:32:30.890
then you've overfit.

00:32:30.890 --> 00:32:32.060
That's not overfitting.

00:32:32.060 --> 00:32:32.515
You can't.

00:32:32.515 --> 00:32:33.930
You can't look at your training error

00:32:33.930 --> 00:32:35.789
by itself to say that you've overfit.

00:32:36.560 --> 00:32:38.430
Overfitting is when your test error

00:32:38.430 --> 00:32:40.480
starts to go up after increasing the

00:32:40.480 --> 00:32:41.190
complexity.

00:32:43.380 --> 00:32:44.950
So in your homework 2.

00:32:45.850 --> 00:32:47.778
Trees are like a really good way to

00:32:47.778 --> 00:32:49.235
look at overfitting because the

00:32:49.235 --> 00:32:51.280
complexity is like the depth of the

00:32:51.280 --> 00:32:52.983
tree or the number of nodes in the

00:32:52.983 --> 00:32:53.329
tree.

00:32:53.330 --> 00:32:56.530
So in your in your homework two, you're

00:32:56.530 --> 00:32:58.930
going to look at overfitting and how

00:32:58.930 --> 00:33:01.170
the training and test error varies as

00:33:01.170 --> 00:33:02.510
you increase the complexity of your

00:33:02.510 --> 00:33:03.080
classifiers.

00:33:04.230 --> 00:33:04.550
Question.

00:33:09.440 --> 00:33:09.880
Right.

00:33:09.880 --> 00:33:10.820
Yeah, that's a good point.

00:33:10.820 --> 00:33:13.380
So increasing the sample size does not

00:33:13.380 --> 00:33:15.610
Causeway overfitting, but you will

00:33:15.610 --> 00:33:21.280
always get, you should expect to get a

00:33:21.280 --> 00:33:24.070
better fit to the true model, a closer

00:33:24.070 --> 00:33:25.450
fit to the true model as you increase

00:33:25.450 --> 00:33:26.340
the training size.

00:33:26.340 --> 00:33:28.550
The reason that I say I keep on saying

00:33:28.550 --> 00:33:31.860
expect and what that means is that if

00:33:31.860 --> 00:33:34.416
you were to resample this problem, like

00:33:34.416 --> 00:33:36.430
resample your data over and over again.

00:33:36.590 --> 00:33:39.152
Than on average this will happen, but

00:33:39.152 --> 00:33:41.289
in any particular scenario you can get

00:33:41.290 --> 00:33:41.840
unlucky.

00:33:41.840 --> 00:33:44.270
You could add like 5 training examples

00:33:44.270 --> 00:33:46.490
and they're really non representative

00:33:46.490 --> 00:33:48.620
by chance and they cause your model to

00:33:48.620 --> 00:33:49.500
get worse.

00:33:49.500 --> 00:33:51.080
So there's no guarantees.

00:33:51.080 --> 00:33:53.365
But you can say more easily what will

00:33:53.365 --> 00:33:55.980
happen in expectation, which means on

00:33:55.980 --> 00:33:58.420
average under the same kinds of

00:33:58.420 --> 00:33:59.100
situations.

00:34:06.160 --> 00:34:10.527
Alright, so I want to so a lot of a lot

00:34:10.527 --> 00:34:13.120
of people said that these a lot of

00:34:13.120 --> 00:34:14.729
respondents to the survey said that.

00:34:16.090 --> 00:34:17.850
Even when these concepts feel like they

00:34:17.850 --> 00:34:20.910
make sense abstractly or theoretically,

00:34:20.910 --> 00:34:22.540
it's not that easy to understand.

00:34:22.540 --> 00:34:23.749
How do you actually put it into

00:34:23.750 --> 00:34:25.660
practice and turn it into code?

00:34:25.660 --> 00:34:27.750
So I want to work through a particular

00:34:27.750 --> 00:34:29.200
example in some detail.

00:34:30.090 --> 00:34:33.490
And the example I choose is this

00:34:33.490 --> 00:34:35.550
Wisconsin breast cancer data set.

00:34:36.450 --> 00:34:38.290
So this data set was collected in the

00:34:38.290 --> 00:34:39.360
early 90s.

00:34:40.440 --> 00:34:44.650
The motivation is that is that doctors

00:34:44.650 --> 00:34:46.800
wanted to use this tool, called fine

00:34:46.800 --> 00:34:50.410
needle aspirates to diagnose whether a

00:34:50.410 --> 00:34:52.660
tumor is malignant or benign.

00:34:53.900 --> 00:34:54.900
And doctors.

00:34:54.900 --> 00:34:57.040
In some medical papers, doctors

00:34:57.040 --> 00:35:01.360
reported a 94% accuracy in making this

00:35:01.360 --> 00:35:02.540
diagnosis.

00:35:02.540 --> 00:35:06.560
But the authors of this study, the

00:35:06.560 --> 00:35:08.520
first author, is a medical doctor

00:35:08.520 --> 00:35:08.980
himself.

00:35:11.150 --> 00:35:12.490
Have like 2 concerns.

00:35:12.490 --> 00:35:14.210
One is that they want to see if you can

00:35:14.210 --> 00:35:15.327
get a better accuracy.

00:35:15.327 --> 00:35:17.983
They want two or three, maybe they want

00:35:17.983 --> 00:35:19.560
to reduce the amount of expertise

00:35:19.560 --> 00:35:21.160
that's needed in order to make a good

00:35:21.160 --> 00:35:21.925
diagnosis.

00:35:21.925 --> 00:35:24.080
And third, they suspect that these

00:35:24.080 --> 00:35:26.620
reports may be biased because there's a

00:35:26.620 --> 00:35:29.065
they note that there tends to be like a

00:35:29.065 --> 00:35:30.900
bias towards positive results that are.

00:35:30.900 --> 00:35:34.638
I mean, yeah, there tends to be a bias

00:35:34.638 --> 00:35:36.879
towards positive results and reports,

00:35:36.880 --> 00:35:37.130
right?

00:35:37.990 --> 00:35:40.140
People are more likely to report

00:35:40.140 --> 00:35:41.436
something if they think it's good, then

00:35:41.436 --> 00:35:43.240
if they get a disappointing outcome.

00:35:44.810 --> 00:35:47.190
So they want to create computer based

00:35:47.190 --> 00:35:49.250
tests that are less objective and

00:35:49.250 --> 00:35:51.270
provide an effective diagnostic tool.

00:35:52.830 --> 00:35:55.350
So they collected data from 569

00:35:55.350 --> 00:35:58.660
patients and then for developing the

00:35:58.660 --> 00:36:00.584
algorithm and doing their first tests

00:36:00.584 --> 00:36:02.525
and then they collected an additional

00:36:02.525 --> 00:36:03.250
54.

00:36:03.960 --> 00:36:06.570
Data from another 54 patients for their

00:36:06.570 --> 00:36:07.290
final tests.

00:36:08.850 --> 00:36:13.080
And so you can it's like important to

00:36:13.080 --> 00:36:16.090
understand like how painstaking this

00:36:16.090 --> 00:36:18.340
process is of collecting data.

00:36:18.340 --> 00:36:18.740
So.

00:36:19.470 --> 00:36:21.620
These are these are real people who

00:36:21.620 --> 00:36:24.350
have tumors and they take medical

00:36:24.350 --> 00:36:26.660
images of them and then they have some

00:36:26.660 --> 00:36:28.730
interface where somebody can go in and

00:36:28.730 --> 00:36:31.176
outline several of the cells, many of

00:36:31.176 --> 00:36:32.530
the cells that were detected.

00:36:33.930 --> 00:36:35.836
And then they have a.

00:36:35.836 --> 00:36:38.220
Then they do like an automated analysis

00:36:38.220 --> 00:36:40.060
of those outlines to compute different

00:36:40.060 --> 00:36:42.100
features, like how what is the radius

00:36:42.100 --> 00:36:43.853
of the cells and what's the area of the

00:36:43.853 --> 00:36:45.250
cells and what's the compactness.

00:36:46.420 --> 00:36:47.350
And then?

00:36:47.450 --> 00:36:48.110


00:36:48.860 --> 00:36:51.460
As the final features, they look at

00:36:51.460 --> 00:36:53.790
these characteristics of the cells.

00:36:53.790 --> 00:36:54.810
They look at the average

00:36:54.810 --> 00:36:57.162
characteristic, the characteristic of

00:36:57.162 --> 00:36:59.620
the largest cell, the worst cell.

00:37:00.340 --> 00:37:04.030
And the and then the standard deviation

00:37:04.030 --> 00:37:05.340
of these characteristics.

00:37:05.340 --> 00:37:06.730
So they're looking at trying to look at

00:37:06.730 --> 00:37:09.250
like the distribution of these shape

00:37:09.250 --> 00:37:11.680
properties of the cells in order to

00:37:11.680 --> 00:37:13.410
determine if the cancerous cells are

00:37:13.410 --> 00:37:14.390
malignant or benign.

00:37:15.880 --> 00:37:18.820
So it's a pretty involved process to

00:37:18.820 --> 00:37:19.620
collect that data.

00:37:22.080 --> 00:37:22.420


00:38:00.720 --> 00:38:01.480
Right.

00:38:01.480 --> 00:38:04.120
So what you would do?

00:38:04.120 --> 00:38:08.160
And if you go for any kinds of tests,

00:38:08.160 --> 00:38:10.000
you'll probably experience this to some

00:38:10.000 --> 00:38:10.320
extent.

00:38:11.820 --> 00:38:13.870
Like often, somebody will go, a

00:38:13.870 --> 00:38:16.093
technician will go in, they see some

00:38:16.093 --> 00:38:17.710
image, they take different measurements

00:38:17.710 --> 00:38:18.350
on the image.

00:38:19.090 --> 00:38:22.410
And then they can say then they may run

00:38:22.410 --> 00:38:24.765
this like through some data analysis,

00:38:24.765 --> 00:38:27.650
and either either they have rules in

00:38:27.650 --> 00:38:29.640
their head for like what are acceptable

00:38:29.640 --> 00:38:32.715
variations, or they run it through some

00:38:32.715 --> 00:38:36.760
analysis and they'll say, they might

00:38:36.760 --> 00:38:39.110
tell you have no cause for concern, or

00:38:39.110 --> 00:38:41.474
there's like some cause for concern, or

00:38:41.474 --> 00:38:43.350
like there's great cause for concern.

00:38:44.140 --> 00:38:45.510
But if you have an algorithm that it

00:38:45.510 --> 00:38:47.100
might tell you, in this case, for

00:38:47.100 --> 00:38:49.630
example, what's the probability that

00:38:49.630 --> 00:38:51.850
these cells are malignant versus

00:38:51.850 --> 00:38:52.980
benign?

00:38:52.980 --> 00:38:55.595
And then you might say, if there's a

00:38:55.595 --> 00:38:57.730
30% chance that it's malignant, then

00:38:57.730 --> 00:38:59.210
I'm going to recommend a biopsy.

00:38:59.210 --> 00:39:02.160
So you want to have some confidence

00:39:02.160 --> 00:39:03.140
with your prediction.

00:39:04.210 --> 00:39:05.360
So in this.

00:39:06.760 --> 00:39:08.392
In our analysis, we're not going to

00:39:08.392 --> 00:39:11.020
look at the confidences too much for

00:39:11.020 --> 00:39:12.010
simplicity.

00:39:12.010 --> 00:39:15.457
But in the study they also will look,

00:39:15.457 --> 00:39:18.340
they also look at the like specificity,

00:39:18.340 --> 00:39:20.560
like how often can you do you

00:39:20.560 --> 00:39:22.406
misdiagnose one way or the other and

00:39:22.406 --> 00:39:24.155
they can use the confidence as part of

00:39:24.155 --> 00:39:24.860
the recommendation.

00:39:30.410 --> 00:39:35.273
Alright, so I'm going to go into this

00:39:35.273 --> 00:39:37.140
and I think now is a good time to take

00:39:37.140 --> 00:39:38.050
a minute or two.

00:39:38.050 --> 00:39:39.515
You can think about this problem, how

00:39:39.515 --> 00:39:40.250
you would solve it.

00:39:40.250 --> 00:39:42.130
You've got 30 features, continuous

00:39:42.130 --> 00:39:43.510
features, and you're trying to predict

00:39:43.510 --> 00:39:44.450
malignant or benign.

00:39:45.150 --> 00:39:48.480
And also feel free to stretch your it.

00:39:48.480 --> 00:39:51.920
You need to prepare your mind for the

00:39:51.920 --> 00:39:52.410
next half.

00:40:20.140 --> 00:40:20.570
Question.

00:40:36.560 --> 00:40:39.556
Decision trees for example does that

00:40:39.556 --> 00:40:42.250
and neural networks will also do that.

00:40:42.250 --> 00:40:44.940
Or kernelized SVMS and nearest

00:40:44.940 --> 00:40:45.374
neighbor.

00:40:45.374 --> 00:40:47.950
They all they all depend jointly on the

00:40:47.950 --> 00:40:48.560
features.

00:40:51.930 --> 00:40:52.700
How does what?

00:40:56.030 --> 00:40:58.985
I guess because the distance is.

00:40:58.985 --> 00:41:01.517
That's a good point, yeah.

00:41:01.517 --> 00:41:04.160
The K&NI guess, it depends jointly on

00:41:04.160 --> 00:41:05.790
them, but it's independently

00:41:05.790 --> 00:41:07.020
considering those features.

00:41:07.020 --> 00:41:08.180
That's right, yeah.

00:41:20.030 --> 00:41:23.680
But it's nice if it's often hard to

00:41:23.680 --> 00:41:25.810
know what's relevant, and so it's nice.

00:41:25.810 --> 00:41:27.510
The ideal is that you can just collect

00:41:27.510 --> 00:41:28.840
a lot of things that you think might be

00:41:28.840 --> 00:41:30.950
relevant and feed it into the algorithm

00:41:30.950 --> 00:41:34.578
and not have to manually like manually

00:41:34.578 --> 00:41:36.640
like prune it and out.

00:41:42.050 --> 00:41:45.256
Yeah, so one is robust to irrelevant

00:41:45.256 --> 00:41:47.780
features, but if you do L2, it's not so

00:41:47.780 --> 00:41:49.340
robust to irrelevant features.

00:41:49.340 --> 00:41:50.900
So that's like another property of the

00:41:50.900 --> 00:41:52.160
algorithm is whether it has that

00:41:52.160 --> 00:41:52.660
robustness.

00:41:57.120 --> 00:41:59.780
Alright, so let me zoom in a little

00:41:59.780 --> 00:42:00.280
bit.

00:42:03.050 --> 00:42:04.260
I guess over here.

00:42:10.690 --> 00:42:13.660
So we've got this data set.

00:42:13.660 --> 00:42:15.710
Fortunately, in this case, I can load

00:42:15.710 --> 00:42:17.900
the data set from sklearn datasets.

00:42:19.720 --> 00:42:22.300
So here I have the initialization code

00:42:22.300 --> 00:42:22.965
and your homework.

00:42:22.965 --> 00:42:24.790
I provided this code to you as well

00:42:24.790 --> 00:42:26.670
that initially like loads the data and

00:42:26.670 --> 00:42:28.480
splits it up into different datasets.

00:42:29.440 --> 00:42:32.010
But here I've just got my libraries

00:42:32.010 --> 00:42:33.470
that I'm going to use.

00:42:33.470 --> 00:42:37.960
I load the data I this data comes in

00:42:37.960 --> 00:42:39.260
like a particular structure.

00:42:39.260 --> 00:42:40.930
So I take out the features which are

00:42:40.930 --> 00:42:43.740
capital X, the predictions which are Y.

00:42:44.490 --> 00:42:45.940
And it also gives me names of the

00:42:45.940 --> 00:42:49.120
features and names of the predictions

00:42:49.120 --> 00:42:50.690
which are good for visualization.

00:42:51.740 --> 00:42:53.330
So if I run this, it's going to start

00:42:53.330 --> 00:42:55.328
an instance on collabs and then it's

00:42:55.328 --> 00:42:57.366
going to download the data and print

00:42:57.366 --> 00:42:59.900
out the shape and the shape of Y.

00:42:59.900 --> 00:43:02.950
So I often like I print a lot of shapes

00:43:02.950 --> 00:43:05.130
of variables when I'm doing stuff

00:43:05.130 --> 00:43:07.880
because it helps me to make sure I

00:43:07.880 --> 00:43:09.230
understand exactly what I loaded.

00:43:09.230 --> 00:43:11.679
Like if I print out the shape and it's

00:43:11.679 --> 00:43:14.006
if the shape of X is 1 by something

00:43:14.006 --> 00:43:15.660
then I would be like maybe I took the

00:43:15.660 --> 00:43:18.160
wrong like values from this data

00:43:18.160 --> 00:43:18.630
structure.

00:43:19.760 --> 00:43:23.580
Alright, so I've got 569 data points.

00:43:23.580 --> 00:43:26.950
So remember that there were 569 samples

00:43:26.950 --> 00:43:28.790
that were drawn at first that were used

00:43:28.790 --> 00:43:30.350
for their training and algorithm

00:43:30.350 --> 00:43:32.680
development, and then another like 56

00:43:32.680 --> 00:43:34.340
or something that we use for testing.

00:43:34.340 --> 00:43:36.380
The 56 are not released, they're not

00:43:36.380 --> 00:43:37.170
part of this data set.

00:43:38.230 --> 00:43:40.150
And then there's 30 features, there's

00:43:40.150 --> 00:43:41.300
10 characteristics.

00:43:41.970 --> 00:43:44.560
That correspond to the like the worst

00:43:44.560 --> 00:43:46.230
case, the average case and the steering

00:43:46.230 --> 00:43:46.760
deviation.

00:43:47.470 --> 00:43:50.034
And I've got 569 labels, so number of

00:43:50.034 --> 00:43:52.010
labels equals number of data points, so

00:43:52.010 --> 00:43:52.500
that's good.

00:43:54.430 --> 00:43:56.433
Now I can print out.

00:43:56.433 --> 00:43:58.960
I usually will also like print out some

00:43:58.960 --> 00:44:00.940
examples just to make sure that there's

00:44:00.940 --> 00:44:01.585
nothing weird here.

00:44:01.585 --> 00:44:04.125
I don't have any nins or anything like

00:44:04.125 --> 00:44:04.330
that.

00:44:05.190 --> 00:44:06.620
So here are the different feature

00:44:06.620 --> 00:44:08.060
names.

00:44:08.060 --> 00:44:11.080
Here's I chose a few random example

00:44:11.080 --> 00:44:11.760
indices.

00:44:12.430 --> 00:44:14.980
And I can see, I can see some of the

00:44:14.980 --> 00:44:15.740
feature values.

00:44:15.740 --> 00:44:18.530
So there's no NANS or Memphis or

00:44:18.530 --> 00:44:19.570
anything like that in there.

00:44:19.570 --> 00:44:20.400
That's good.

00:44:20.400 --> 00:44:22.320
Also I can notice like.

00:44:23.030 --> 00:44:25.974
Some of some of their values are like

00:44:25.974 --> 00:44:30.416
1.2 E 2 or 11 E 3, so this is like

00:44:30.416 --> 00:44:32.080
1000, while some other ones are really

00:44:32.080 --> 00:44:36.134
small, like 1188 E -, 1.

00:44:36.134 --> 00:44:37.910
So that's something to consider.

00:44:37.910 --> 00:44:39.340
There's a pretty big range of the

00:44:39.340 --> 00:44:40.230
feature values here.

00:44:43.520 --> 00:44:45.600
So then another thing I'll do early is

00:44:45.600 --> 00:44:48.050
say how common is each class, because

00:44:48.050 --> 00:44:50.120
if like 99% of the examples are in one

00:44:50.120 --> 00:44:51.745
class, that's something I need to keep

00:44:51.745 --> 00:44:53.840
in mind versus a 5050 split.

00:44:55.290 --> 00:44:56.650
So in this case.

00:44:56.750 --> 00:44:57.360


00:44:58.700 --> 00:45:02.810
37% of the examples have Class 0 and

00:45:02.810 --> 00:45:04.600
63% have Class 1.

00:45:05.630 --> 00:45:10.190
And if I think I printed the label

00:45:10.190 --> 00:45:12.105
names, yeah, so the label names.

00:45:12.105 --> 00:45:14.750
So 0 means malignant and one means

00:45:14.750 --> 00:45:15.260
benign.

00:45:15.940 --> 00:45:20.190
So in this sample, 37% are malignant

00:45:20.190 --> 00:45:21.940
and 63% are benign.

00:45:24.410 --> 00:45:26.060
Now I'm going to create a training and

00:45:26.060 --> 00:45:27.160
validation set.

00:45:27.160 --> 00:45:29.410
So I define the number of training

00:45:29.410 --> 00:45:31.720
samples 469.

00:45:32.650 --> 00:45:35.845
I use a random seed and that's because

00:45:35.845 --> 00:45:38.360
it might be that the training samples

00:45:38.360 --> 00:45:40.141
are stored in some structured way.

00:45:40.141 --> 00:45:42.125
Maybe they put all the examples with

00:45:42.125 --> 00:45:44.260
zero first, label zero first and then

00:45:44.260 --> 00:45:45.280
label one.

00:45:45.280 --> 00:45:47.629
Or maybe they were structured in some

00:45:47.630 --> 00:45:49.910
other way and I want it to be random,

00:45:49.910 --> 00:45:51.800
so randomness is not something you can

00:45:51.800 --> 00:45:52.720
leave to chance.

00:45:52.720 --> 00:45:56.250
You need to use some permutation to

00:45:56.250 --> 00:45:58.450
make sure that you get a random sample

00:45:58.450 --> 00:45:59.040
of the data.

00:46:00.580 --> 00:46:03.319
So I do a random permutation of the

00:46:03.320 --> 00:46:05.840
same length as the number of indices.

00:46:05.840 --> 00:46:08.280
I set a seed here because I just wanted

00:46:08.280 --> 00:46:10.010
this to be repeatable for the purpose

00:46:10.010 --> 00:46:11.890
of the class, and actually it's a good

00:46:11.890 --> 00:46:14.310
idea to set a seed anyway so that.

00:46:16.450 --> 00:46:18.540
Because takes out one source of

00:46:18.540 --> 00:46:20.210
variance for your debugging.

00:46:21.980 --> 00:46:24.145
So I split it into a training set.

00:46:24.145 --> 00:46:25.770
I took the first untrained.

00:46:26.750 --> 00:46:29.290
It's my X train and Y train and then I

00:46:29.290 --> 00:46:32.420
took all the rest as my X value, Y Val

00:46:32.420 --> 00:46:34.410
and by the 1st examples I mean the

00:46:34.410 --> 00:46:36.060
first ones that in this random

00:46:36.060 --> 00:46:37.130
permutation list.

00:46:38.330 --> 00:46:41.580
Now X train and Y train have.

00:46:42.020 --> 00:46:47.790
I have 469 examples so 469 by 30.

00:46:48.680 --> 00:46:51.575
And X value Y Val which is the second

00:46:51.575 --> 00:46:53.310
one has 100 examples.

00:46:55.420 --> 00:46:58.375
Sometimes the first thing I'll do is

00:46:58.375 --> 00:47:01.360
like a simple classifier just to see is

00:47:01.360 --> 00:47:02.390
this problem trivial.

00:47:02.390 --> 00:47:04.125
If I get like 0 error right away, then

00:47:04.125 --> 00:47:06.780
I can just like stop spend time on it.

00:47:07.630 --> 00:47:10.909
So I made a nearest neighbor

00:47:10.910 --> 00:47:11.620
classifier.

00:47:11.620 --> 00:47:13.390
So I have nearest neighbor.

00:47:13.390 --> 00:47:15.600
X train and Y train are fed in as well

00:47:15.600 --> 00:47:16.340
as X test.

00:47:17.640 --> 00:47:21.470
Pre initialize my predictions, so I do

00:47:21.470 --> 00:47:23.560
initialize it with zeros.

00:47:23.560 --> 00:47:25.990
For each test sample, I take the

00:47:25.990 --> 00:47:27.540
difference from the test sample and all

00:47:27.540 --> 00:47:29.140
the training samples.

00:47:29.140 --> 00:47:30.940
Under the hood, Numpy we'll do like

00:47:30.940 --> 00:47:32.800
broadcasting, which means it will copy

00:47:32.800 --> 00:47:36.085
this as necessary so that the X test

00:47:36.085 --> 00:47:38.669
will be a 1 by 30 and it will copy it

00:47:38.669 --> 00:47:42.560
so that it becomes a 469 by 30.

00:47:43.860 --> 00:47:45.139
Then I take the difference.

00:47:45.140 --> 00:47:46.330
It will be the difference of each

00:47:46.330 --> 00:47:49.270
element of the features and samples.

00:47:49.960 --> 00:47:51.840
Square it will be the square of each

00:47:51.840 --> 00:47:54.660
element and then I sum over axis one

00:47:54.660 --> 00:47:55.920
which is the 2nd axis.

00:47:55.920 --> 00:47:57.210
Zero is the first axis.

00:47:58.110 --> 00:47:59.790
So this will be the sum squared

00:47:59.790 --> 00:48:00.830
distance of the features.

00:48:01.890 --> 00:48:02.770
Euclidean distance.

00:48:02.770 --> 00:48:04.390
You would also take the square root,

00:48:04.390 --> 00:48:05.857
but I don't need to take the square

00:48:05.857 --> 00:48:09.008
root because the minimum of the square

00:48:09.008 --> 00:48:11.104
of a value is the same as the minimum

00:48:11.104 --> 00:48:13.251
of the square of the square of the

00:48:13.251 --> 00:48:13.519
value.

00:48:13.680 --> 00:48:13.890
Right.

00:48:16.060 --> 00:48:19.780
J is the argument distance, so I say J

00:48:19.780 --> 00:48:21.495
equals the argument and this distance.

00:48:21.495 --> 00:48:23.130
So this will give me the index that had

00:48:23.130 --> 00:48:24.010
the minimum distance.

00:48:24.700 --> 00:48:26.420
If I needed more than one, I could use

00:48:26.420 --> 00:48:29.500
argsort and then take like the first K

00:48:29.500 --> 00:48:30.050
indices.

00:48:31.000 --> 00:48:33.386
I assign the test to the training to

00:48:33.386 --> 00:48:34.720
the training sample that had the

00:48:34.720 --> 00:48:36.500
minimum distance and I returned it.

00:48:36.500 --> 00:48:39.240
So nearest neighbor is pretty simple.

00:48:40.800 --> 00:48:43.980
This like if you're a proficient coder,

00:48:43.980 --> 00:48:46.410
it's like a two minutes or whatever to

00:48:46.410 --> 00:48:46.790
decode it.

00:48:48.690 --> 00:48:52.140
Then I'm going to test it, so I then do

00:48:52.140 --> 00:48:54.050
the prediction on the validation set.

00:48:54.050 --> 00:48:55.230
Remember, nearest neighbor has no

00:48:55.230 --> 00:48:56.870
training, so I have no training code

00:48:56.870 --> 00:48:58.105
here, it's just really a prediction

00:48:58.105 --> 00:48:58.430
code.

00:48:59.450 --> 00:49:02.320
And now compute my average accuracy,

00:49:02.320 --> 00:49:05.309
which is why is the number of times the

00:49:05.310 --> 00:49:08.500
mean times that the validation label is

00:49:08.500 --> 00:49:09.760
equal to the prediction label.

00:49:10.710 --> 00:49:12.230
And then the error is 1 minus the

00:49:12.230 --> 00:49:13.490
accuracy, right?

00:49:13.490 --> 00:49:14.040
So let's run it.

00:49:16.480 --> 00:49:21.550
All right, so I got an error of 8% now.

00:49:23.090 --> 00:49:24.060
I could quit here.

00:49:24.060 --> 00:49:26.840
I could be like, OK, I'm done 8%, but I

00:49:26.840 --> 00:49:28.150
shouldn't really be satisfied with

00:49:28.150 --> 00:49:29.080
this, right?

00:49:29.080 --> 00:49:32.400
So the remember that in the study they

00:49:32.400 --> 00:49:34.105
said that doctors were reporting that

00:49:34.105 --> 00:49:37.380
they can get like 6% error, they had

00:49:37.380 --> 00:49:38.810
94% accuracy.

00:49:39.530 --> 00:49:41.906
And since I'm a machine learning

00:49:41.906 --> 00:49:43.940
machine learning engineer, I'm armed

00:49:43.940 --> 00:49:44.800
with data.

00:49:44.800 --> 00:49:47.250
I should be able to outperform a

00:49:47.250 --> 00:49:49.190
medical Doctor Who has years of

00:49:49.190 --> 00:49:51.960
experience on the same problem.

00:49:54.860 --> 00:49:56.800
Right, so all of his wits and

00:49:56.800 --> 00:49:58.420
experience is just bringing a knife to

00:49:58.420 --> 00:49:59.300
a gunfight.

00:50:01.760 --> 00:50:02.410
I'm just kidding.

00:50:03.810 --> 00:50:05.670
But seriously, like, I can probably do

00:50:05.670 --> 00:50:06.130
better, right?

00:50:06.130 --> 00:50:07.190
It's just my first attempt.

00:50:07.900 --> 00:50:09.530
So let's look at the data a little bit

00:50:09.530 --> 00:50:11.440
better, a little more in depth.

00:50:12.340 --> 00:50:13.610
So remember that one thing we noticed

00:50:13.610 --> 00:50:15.145
is that it looked like some feature

00:50:15.145 --> 00:50:16.895
values were a lot larger than other

00:50:16.895 --> 00:50:18.540
values, and nearest neighbor is not

00:50:18.540 --> 00:50:19.716
very robust to that.

00:50:19.716 --> 00:50:22.830
It might be like emphasizing the large

00:50:22.830 --> 00:50:24.620
values much more, which might not be

00:50:24.620 --> 00:50:25.840
the most important features.

00:50:26.490 --> 00:50:28.390
So here I have a print statement.

00:50:28.390 --> 00:50:30.210
The only thing fancy is that I use some

00:50:30.210 --> 00:50:32.900
spacing thing to make it like evenly

00:50:32.900 --> 00:50:33.420
spaced.

00:50:34.040 --> 00:50:35.828
And I'm printing the means of the

00:50:35.828 --> 00:50:37.330
features, the standard deviations of

00:50:37.330 --> 00:50:39.710
the features, the means of the features

00:50:39.710 --> 00:50:42.413
where y = 1 zero, and the means of the

00:50:42.413 --> 00:50:43.599
features were y = 1.

00:50:44.340 --> 00:50:46.250
So that can kind of tell me a couple

00:50:46.250 --> 00:50:46.580
things.

00:50:46.580 --> 00:50:48.100
One is like what is the scale that

00:50:48.100 --> 00:50:49.530
features by looking at the steering

00:50:49.530 --> 00:50:50.310
deviation and the mean.

00:50:51.170 --> 00:50:54.050
Also, are the features like predictive

00:50:54.050 --> 00:50:54.338
or not?

00:50:54.338 --> 00:50:56.315
If I have a good spread of the means of

00:50:56.315 --> 00:50:59.095
the two features, I mean of the of y =

00:50:59.095 --> 00:51:01.749
0 and y = 1, then it's predictive.

00:51:01.750 --> 00:51:03.600
But if I have a small spread compared

00:51:03.600 --> 00:51:05.530
to the steering deviation then it's not

00:51:05.530 --> 00:51:06.240
very predictive.

00:51:07.350 --> 00:51:10.150
Right, so for example, this feature

00:51:10.150 --> 00:51:11.824
here means smoothness.

00:51:11.824 --> 00:51:15.584
Mean is 1, standard deviation is 01,

00:51:15.584 --> 00:51:19.947
the mean of zero is 1, the mean of one

00:51:19.947 --> 00:51:20.690
is 09.

00:51:20.690 --> 00:51:22.770
And you know with three digits there

00:51:22.770 --> 00:51:24.305
might be look even closer.

00:51:24.305 --> 00:51:26.092
So obviously smoothness means

00:51:26.092 --> 00:51:28.430
smoothness is not a very good feature,

00:51:28.430 --> 00:51:31.340
it's not very predictive of the label.

00:51:32.120 --> 00:51:35.050
Where if I look at something like.

00:51:35.140 --> 00:51:35.930


00:51:37.780 --> 00:51:40.240
If I look at something like this, just

00:51:40.240 --> 00:51:42.125
take the first one, the difference of

00:51:42.125 --> 00:51:43.730
the means is more than one steering

00:51:43.730 --> 00:51:47.620
deviation of the feature, and so mean

00:51:47.620 --> 00:51:49.420
radius is like fairly predictive.

00:51:51.210 --> 00:51:53.395
But the thing my take home from this is

00:51:53.395 --> 00:51:56.480
that some features have means and

00:51:56.480 --> 00:51:58.950
standard deviations that are sub one

00:51:58.950 --> 00:51:59.730
less than one.

00:52:00.400 --> 00:52:03.340
And others are in the hundreds, so not

00:52:03.340 --> 00:52:04.540
that's not good.

00:52:04.540 --> 00:52:05.700
So I want to do some kind of

00:52:05.700 --> 00:52:06.590
normalization.

00:52:09.520 --> 00:52:11.857
So I'm going to normalize by the mean

00:52:11.857 --> 00:52:13.820
and steering deviation, which means

00:52:13.820 --> 00:52:16.537
that I subtract the mean and divide by

00:52:16.537 --> 00:52:17.880
the standard deviation.

00:52:17.880 --> 00:52:20.040
Importantly, you want to compute the

00:52:20.040 --> 00:52:22.138
mean and the standard deviation once on

00:52:22.138 --> 00:52:23.880
the training set and then apply the

00:52:23.880 --> 00:52:25.531
same normalization to the training and

00:52:25.531 --> 00:52:26.566
the validation set.

00:52:26.566 --> 00:52:28.580
So you can't provide different

00:52:28.580 --> 00:52:31.620
normalizations to different sets, or

00:52:31.620 --> 00:52:33.080
else you're going to your features will

00:52:33.080 --> 00:52:35.030
not be comparable and you'll it's a

00:52:35.030 --> 00:52:35.640
bug.

00:52:35.640 --> 00:52:37.360
It's so it won't work.

00:52:38.650 --> 00:52:40.240
OK, so I compute the mean compute

00:52:40.240 --> 00:52:41.720
steering, aviation take the difference,

00:52:41.720 --> 00:52:43.160
divide by zero and aviation do the same

00:52:43.160 --> 00:52:44.220
thing on my valve set.

00:52:44.990 --> 00:52:46.430
And there's nothing to print here, but

00:52:46.430 --> 00:52:47.430
I need to run it.

00:52:47.430 --> 00:52:48.000
Whoops.

00:52:51.250 --> 00:52:52.380
All right, so now I'm going to repeat

00:52:52.380 --> 00:52:53.150
my nearest neighbor.

00:52:53.920 --> 00:52:54.866
OK, 4%.

00:52:54.866 --> 00:52:57.336
So there was a lot better before I got

00:52:57.336 --> 00:53:01.206
12%, I think 8%, yeah, so before I got

00:53:01.206 --> 00:53:01.500
8%.

00:53:02.130 --> 00:53:03.200
Now it's 4%.

00:53:04.050 --> 00:53:04.720
So that's good.

00:53:05.380 --> 00:53:07.040
But I still don't know if like nearest

00:53:07.040 --> 00:53:07.850
neighbor is the best.

00:53:07.850 --> 00:53:09.240
So I shouldn't just try like 1

00:53:09.240 --> 00:53:11.140
algorithm and then assume that's the

00:53:11.140 --> 00:53:11.910
best I should get.

00:53:11.910 --> 00:53:14.620
I should try other algorithms and try

00:53:14.620 --> 00:53:16.280
to see if I can improve things further.

00:53:17.510 --> 00:53:18.110
Question.

00:53:24.670 --> 00:53:25.550
So the yes.

00:53:25.550 --> 00:53:26.940
So the question is why did the error

00:53:26.940 --> 00:53:28.170
rate get better?

00:53:28.170 --> 00:53:30.950
And I think it's because under the

00:53:30.950 --> 00:53:33.920
original features, these features like

00:53:33.920 --> 00:53:38.000
mean area that have a huge range are

00:53:38.000 --> 00:53:40.690
going to dominate the distances.

00:53:40.690 --> 00:53:42.420
All of these features concavity,

00:53:42.420 --> 00:53:45.470
compactness, concave point, symmetry at

00:53:45.470 --> 00:53:48.730
mostly we'll add a distance of .1 or

00:53:48.730 --> 00:53:51.010
something like that where this mean

00:53:51.010 --> 00:53:53.887
area is going to tend to add distances

00:53:53.887 --> 00:53:54.430
of.

00:53:54.490 --> 00:53:54.960
Hundreds.

00:53:55.580 --> 00:53:58.620
And so if I don't normalize it, that

00:53:58.620 --> 00:54:00.100
means that essentially I'm seeing the

00:54:00.100 --> 00:54:01.728
bigger the feature values, the more

00:54:01.728 --> 00:54:02.990
important they are, or the more

00:54:02.990 --> 00:54:04.307
variants and the feature values, the

00:54:04.307 --> 00:54:05.049
more important they are.

00:54:05.670 --> 00:54:07.340
And that's not based on any like

00:54:07.340 --> 00:54:08.480
knowledge of the problem.

00:54:08.480 --> 00:54:09.970
That was just because that's how the

00:54:09.970 --> 00:54:10.720
data turned out.

00:54:10.720 --> 00:54:12.560
And so I don't really trust that kind

00:54:12.560 --> 00:54:14.210
of decision.

00:54:16.270 --> 00:54:16.650
Go ahead.

00:54:18.070 --> 00:54:18.350
OK.

00:54:19.290 --> 00:54:20.240
You had a question?

00:54:29.700 --> 00:54:32.490
So I compute the mean and this is

00:54:32.490 --> 00:54:34.615
computing the mean over the first axis.

00:54:34.615 --> 00:54:36.640
So it means that for every feature

00:54:36.640 --> 00:54:38.700
value I compute the mean over all the

00:54:38.700 --> 00:54:39.320
examples.

00:54:40.110 --> 00:54:42.680
Of the training features XTR.

00:54:43.450 --> 00:54:45.560
So I computed the mean, the expectation

00:54:45.560 --> 00:54:49.370
or the arithmetic average of each

00:54:49.370 --> 00:54:50.010
feature.

00:54:50.990 --> 00:54:53.330
Over all the training samples, and then

00:54:53.330 --> 00:54:56.500
I compute this stern deviation of each

00:54:56.500 --> 00:54:58.140
feature over all the examples.

00:54:58.140 --> 00:54:58.960
So that's the.

00:55:00.570 --> 00:55:00.940
Right.

00:55:03.150 --> 00:55:07.200
So remember that X train has this shape

00:55:07.200 --> 00:55:11.920
469 by 30, so if I go down the first

00:55:11.920 --> 00:55:14.480
axis then I'm changing the example.

00:55:14.480 --> 00:55:17.330
So 0123 et cetera are different

00:55:17.330 --> 00:55:18.100
examples.

00:55:18.100 --> 00:55:20.363
And if I go down the second axis then

00:55:20.363 --> 00:55:22.470
I'm going into different feature

00:55:22.470 --> 00:55:22.960
columns.

00:55:23.680 --> 00:55:25.760
And so I want to take the mean over the

00:55:25.760 --> 00:55:27.524
examples for each feature.

00:55:27.524 --> 00:55:30.113
And so I say access equals zero for the

00:55:30.113 --> 00:55:31.870
mean to take the mean over samples.

00:55:31.870 --> 00:55:34.774
Otherwise I'll end up with a 1 by 30

00:55:34.774 --> 00:55:38.480
where I mean with a 469 by 1 where I've

00:55:38.480 --> 00:55:39.850
taken the average feature for each

00:55:39.850 --> 00:55:40.380
example.

00:55:46.980 --> 00:55:49.390
So if I say X is equals zero, it means

00:55:49.390 --> 00:55:51.000
it will take the mean over all the

00:55:51.000 --> 00:55:52.400
remaining dimensions.

00:55:52.750 --> 00:55:53.320
And.

00:55:54.040 --> 00:55:55.590
Averaging over the first dimension.

00:56:02.380 --> 00:56:04.870
So then this will be a 30 dimensional

00:56:04.870 --> 00:56:06.080
vector X MU.

00:56:07.050 --> 00:56:11.230
It will be the mean of each feature

00:56:11.230 --> 00:56:12.060
over the samples.

00:56:12.930 --> 00:56:14.540
And this is also a 30 dimensional

00:56:14.540 --> 00:56:15.880
vector standard deviation.

00:56:17.170 --> 00:56:19.300
And then I'm subtracting off the mean

00:56:19.300 --> 00:56:21.185
and dividing by the standard deviation.

00:56:21.185 --> 00:56:24.150
And Numpy is nice that even though X

00:56:24.150 --> 00:56:28.355
train is 469 by 30 and X mu is 30, is

00:56:28.355 --> 00:56:28.840
30.

00:56:29.030 --> 00:56:32.370
Numpy is smart, and it says you're

00:56:32.370 --> 00:56:35.390
doing a 469 by 30 -, A thirty.

00:56:35.390 --> 00:56:39.060
So I need to copy that 3469 times to

00:56:39.060 --> 00:56:39.810
take the difference.

00:56:41.550 --> 00:56:42.790
And same for the divide.

00:56:42.790 --> 00:56:44.990
This is an element wise divide so it's

00:56:44.990 --> 00:56:45.800
important to know.

00:56:46.500 --> 00:56:48.340
There you can have like a matrix

00:56:48.340 --> 00:56:50.710
multiplication or matrix inverse or you

00:56:50.710 --> 00:56:53.006
can have an element wise multiplication

00:56:53.006 --> 00:56:53.759
or inverse.

00:56:54.570 --> 00:56:57.070
Usually like the simple operators are

00:56:57.070 --> 00:56:58.320
element wise in Python.

00:56:58.970 --> 00:57:01.485
So this means that for every element of

00:57:01.485 --> 00:57:04.796
this matrix, I'm going to divide by the

00:57:04.796 --> 00:57:06.940
standard deviation the corresponding

00:57:06.940 --> 00:57:07.680
standard deviation.

00:57:09.390 --> 00:57:10.690
And then I do the same thing for the

00:57:10.690 --> 00:57:11.640
validation set.

00:57:11.640 --> 00:57:12.960
And what was your question?

00:57:22.780 --> 00:57:23.490
Yeah.

00:57:32.420 --> 00:57:37.550
So L1 used L1 regularization for linear

00:57:37.550 --> 00:57:40.183
logistic regression and that will that

00:57:40.183 --> 00:57:43.110
will like put that will like select

00:57:43.110 --> 00:57:44.030
features for.

00:57:44.030 --> 00:57:46.110
You could also use L1 nearest neighbor

00:57:46.110 --> 00:57:47.720
distance which would be less sensitive

00:57:47.720 --> 00:57:48.110
to this.

00:57:49.700 --> 00:57:52.150
But with this range of like .1 versus

00:57:52.150 --> 00:57:54.590
like 500, it will still be that the

00:57:54.590 --> 00:57:55.820
larger features will dominate.

00:57:57.180 --> 00:57:57.430
Yep.

00:57:59.850 --> 00:58:03.560
All right, so after I normalized, now

00:58:03.560 --> 00:58:06.550
note that I'm passing in X train N,

00:58:06.550 --> 00:58:08.670
which is for stands for norm for me.

00:58:09.450 --> 00:58:10.380
In X Val north.

00:58:10.380 --> 00:58:12.240
Now I get lower error.

00:58:12.830 --> 00:58:14.220
Alright, so now let's try a different

00:58:14.220 --> 00:58:14.885
classifier.

00:58:14.885 --> 00:58:17.340
Let's do Naive Bayes, and I'm going to

00:58:17.340 --> 00:58:21.055
assume that each feature value given

00:58:21.055 --> 00:58:23.399
the class is a Gaussian.

00:58:23.399 --> 00:58:27.480
So given that y = 0, Y equals one.

00:58:27.480 --> 00:58:30.232
Then my probability of the feature is a

00:58:30.232 --> 00:58:31.770
Gaussian with some mean and some

00:58:31.770 --> 00:58:32.680
standard deviation.

00:58:33.410 --> 00:58:35.640
Now for nibs I need a training and

00:58:35.640 --> 00:58:36.610
prediction function.

00:58:37.590 --> 00:58:40.560
So I'm going to pass in my training

00:58:40.560 --> 00:58:41.430
data X&Y.

00:58:42.300 --> 00:58:44.760
App says some like I'm going to use

00:58:44.760 --> 00:58:46.864
that as like a prior to add it to the

00:58:46.864 --> 00:58:48.390
variance so that even if my feature

00:58:48.390 --> 00:58:50.340
value has no variance in training, I'm

00:58:50.340 --> 00:58:52.175
going to have some minimal variance so

00:58:52.175 --> 00:58:54.450
that I don't have like a divide by zero

00:58:54.450 --> 00:58:56.610
essentially where I'm not like over

00:58:56.610 --> 00:59:00.600
relying on the variance that I observe.

00:59:02.080 --> 00:59:03.960
All right, so initialize my MU and my

00:59:03.960 --> 00:59:06.988
Sigma to be the number of features by

00:59:06.988 --> 00:59:08.880
two, and the two is because there's two

00:59:08.880 --> 00:59:10.360
classes, so I'm going to estimate this

00:59:10.360 --> 00:59:10.960
for each class.

00:59:12.250 --> 00:59:14.988
I compute my probability of the label

00:59:14.988 --> 00:59:17.870
to be just the mean of y = 0.

00:59:17.870 --> 00:59:19.180
So this is a probability that the label

00:59:19.180 --> 00:59:20.000
is equal to 0.

00:59:21.530 --> 00:59:23.820
And then for each feature so range,

00:59:23.820 --> 00:59:25.650
you'll be 0 to the number of features.

00:59:26.510 --> 00:59:30.100
I compute the mean over the cases where

00:59:30.100 --> 00:59:31.330
the label equals 0.

00:59:32.660 --> 00:59:34.770
And the mean over the case where the

00:59:34.770 --> 00:59:36.450
labels equals one.

00:59:36.450 --> 00:59:37.990
And I could do this as like a

00:59:37.990 --> 00:59:40.260
vectorized operation like over an axis,

00:59:40.260 --> 00:59:41.970
but for clarity I did it this way.

00:59:42.700 --> 00:59:43.350
With the four loop.

00:59:45.040 --> 00:59:47.990
Compute their stern deviation where y =

00:59:47.990 --> 00:59:50.827
0 and the stereo deviation where y = 1

00:59:50.827 --> 00:59:52.520
and again like this epsilon will be

00:59:52.520 --> 00:59:55.600
some small number that will just like

00:59:55.600 --> 00:59:57.260
make sure that my variance isn't zero.

00:59:57.260 --> 00:59:59.810
Or like says that like I think there

00:59:59.810 --> 01:00:01.030
might be a little bit more variance

01:00:01.030 --> 01:00:01.740
than I observe.

01:00:03.080 --> 01:00:03.600
And.

01:00:04.420 --> 01:00:05.090
That's it.

01:00:05.090 --> 01:00:07.570
So then I'll return my mean steering

01:00:07.570 --> 01:00:09.150
deviation and the probability of the

01:00:09.150 --> 01:00:10.010
label question.

01:00:12.500 --> 01:00:12.760
Sorry.

01:00:21.950 --> 01:00:24.952
Because X shape one, so X shape zero is

01:00:24.952 --> 01:00:26.505
the number of samples and X shape one

01:00:26.505 --> 01:00:27.840
is the number of features.

01:00:27.840 --> 01:00:30.810
And there's a mean for every mean

01:00:30.810 --> 01:00:33.273
estimate for every feature, not for

01:00:33.273 --> 01:00:34.050
every sample.

01:00:35.780 --> 01:00:37.840
So this will be a number of features by

01:00:37.840 --> 01:00:38.230
two.

01:00:43.510 --> 01:00:44.720
Alright, and then I'm going to do

01:00:44.720 --> 01:00:45.380
prediction.

01:00:45.380 --> 01:00:48.200
So now I'll write my prediction code.

01:00:48.200 --> 01:00:50.080
I now need to pass in the thing that I

01:00:50.080 --> 01:00:50.930
want to predict for.

01:00:51.620 --> 01:00:53.720
That means in the steering deviations

01:00:53.720 --> 01:00:55.840
and the P0 that I estimated from my

01:00:55.840 --> 01:00:56.670
training function.

01:00:57.640 --> 01:01:00.450
And I'm going to compute the log

01:01:00.450 --> 01:01:04.460
probability of X given of X&Y, not the

01:01:04.460 --> 01:01:05.390
probability of X&Y.

01:01:06.130 --> 01:01:07.889
And the reason for that is that if I

01:01:07.890 --> 01:01:09.960
multiply a lot of small probabilities

01:01:09.960 --> 01:01:11.706
together then I get a really small

01:01:11.706 --> 01:01:11.972
number.

01:01:11.972 --> 01:01:13.955
And if I have a lot of features like

01:01:13.955 --> 01:01:16.418
you do for MNIST for example, then that

01:01:16.418 --> 01:01:18.470
small number will eventually become

01:01:18.470 --> 01:01:21.820
zero and like in terms of floating

01:01:21.820 --> 01:01:23.889
point operations or it will become like

01:01:23.890 --> 01:01:26.470
unwieldly small.

01:01:26.470 --> 01:01:28.160
So you want to compute the log

01:01:28.160 --> 01:01:29.460
probability, not the probability.

01:01:30.460 --> 01:01:33.100
And minimizing the OR maximizing the

01:01:33.100 --> 01:01:34.602
log probability is the same as

01:01:34.602 --> 01:01:35.660
maximizing the probability.

01:01:36.860 --> 01:01:38.560
So for each feature.

01:01:39.350 --> 01:01:43.388
I add the log probability of the

01:01:43.388 --> 01:01:46.726
feature given y = 0 or the feature

01:01:46.726 --> 01:01:47.739
given y = 1.

01:01:48.960 --> 01:01:53.265
And this is this is the log of the

01:01:53.265 --> 01:01:54.000
Gaussian function.

01:01:54.000 --> 01:01:56.340
Just ignoring the constant multiplier

01:01:56.340 --> 01:01:58.540
in the Gaussian function because that

01:01:58.540 --> 01:02:01.300
won't be any different whether y = 0

01:02:01.300 --> 01:02:03.059
one there one over square root, square

01:02:03.059 --> 01:02:04.310
root 2π is Sigma.

01:02:06.200 --> 01:02:12.750
So this minus mean minus X ^2 divided

01:02:12.750 --> 01:02:14.140
by Sigma squared.

01:02:14.140 --> 01:02:15.930
That's like in the exponent of the

01:02:15.930 --> 01:02:16.490
Gaussian.

01:02:16.490 --> 01:02:18.530
So when I take the log of it, I've just

01:02:18.530 --> 01:02:19.860
got that exponent there.

01:02:20.820 --> 01:02:25.040
So I'm adding that to my score of log

01:02:25.040 --> 01:02:29.630
PX y = 0 and log pxy equals one.

01:02:32.780 --> 01:02:35.721
Then I'm adding my prior so to my 0

01:02:35.721 --> 01:02:38.204
score I add the log probability of y =

01:02:38.204 --> 01:02:38.479
0.

01:02:38.480 --> 01:02:41.440
Into my one score, I add the log

01:02:41.440 --> 01:02:44.230
probability of y = 1, which is just one

01:02:44.230 --> 01:02:45.729
minus the probability of y = 0.

01:02:46.780 --> 01:02:48.540
And then I take the argmax to get my

01:02:48.540 --> 01:02:50.899
prediction and I'm taking the argmax

01:02:50.900 --> 01:02:53.910
over axis one because that was my label

01:02:53.910 --> 01:02:54.380
axis.

01:02:55.170 --> 01:02:55.720
So.

01:02:56.860 --> 01:02:58.875
So here the first axis is the number of

01:02:58.875 --> 01:03:00.915
test samples, the second axis is the

01:03:00.915 --> 01:03:01.860
number of labels.

01:03:01.860 --> 01:03:04.470
I take the argmax over the labels to

01:03:04.470 --> 01:03:07.820
get my maximum my most likely

01:03:07.820 --> 01:03:09.510
prediction for every test sample.

01:03:13.750 --> 01:03:15.930
And then finally the code to call this

01:03:15.930 --> 01:03:18.334
so I call Gaussian train NI Bayes

01:03:18.334 --> 01:03:21.650
Gaussian train and I use this as my as

01:03:21.650 --> 01:03:23.800
like my prior on the variance my

01:03:23.800 --> 01:03:24.290
epsilon.

01:03:25.400 --> 01:03:29.310
And then I'd call predict and I pass in

01:03:29.310 --> 01:03:30.240
the validation data.

01:03:31.200 --> 01:03:32.510
And then I measure my error.

01:03:33.400 --> 01:03:35.130
And I'm going to do this.

01:03:35.130 --> 01:03:36.970
So here's a question.

01:03:36.970 --> 01:03:39.338
Do you think that here I'm doing it on

01:03:39.338 --> 01:03:41.219
the non normalized features and here

01:03:41.219 --> 01:03:43.182
I'm doing it on the normalized

01:03:43.182 --> 01:03:43.509
features?

01:03:44.380 --> 01:03:47.160
Do you think that those results will be

01:03:47.160 --> 01:03:48.800
different or the same?

01:03:48.800 --> 01:03:50.510
So how many people think that these

01:03:50.510 --> 01:03:52.260
will be the same if I?

01:03:52.960 --> 01:03:56.930
Do not have bays on rescaled and mean

01:03:56.930 --> 01:04:00.130
normalized features versus normalized.

01:04:01.370 --> 01:04:02.790
So how many people think it will be the

01:04:02.790 --> 01:04:03.640
same result?

01:04:05.470 --> 01:04:07.060
OK, how many people think it will be a

01:04:07.060 --> 01:04:07.610
different result?

01:04:10.570 --> 01:04:12.250
About 5050.

01:04:12.250 --> 01:04:13.510
Alright, so let's see.

01:04:13.510 --> 01:04:14.820
Let's see how it turns out.

01:04:18.860 --> 01:04:20.980
So it's exactly the same, and it's

01:04:20.980 --> 01:04:22.855
actually guaranteed to be exactly the

01:04:22.855 --> 01:04:25.350
same in this case because.

01:04:27.190 --> 01:04:28.790
Because if I scale or shift the

01:04:28.790 --> 01:04:30.910
features, all it's going to do is

01:04:30.910 --> 01:04:32.320
change my mean invariance.

01:04:32.960 --> 01:04:34.420
But it will change it the same way for

01:04:34.420 --> 01:04:36.500
each class, so the probability of the

01:04:36.500 --> 01:04:38.450
features given the data given the label

01:04:38.450 --> 01:04:40.540
doesn't change at all when I shift them

01:04:40.540 --> 01:04:42.050
or scale them according to a Gaussian

01:04:42.050 --> 01:04:42.990
distribution.

01:04:42.990 --> 01:04:45.080
So that's why the feature normalization

01:04:45.080 --> 01:04:46.790
isn't really necessary here for Naive

01:04:46.790 --> 01:04:47.060
Bayes.

01:04:48.890 --> 01:04:50.605
But it wasn't didn't do great.

01:04:50.605 --> 01:04:51.790
It doesn't usually.

01:04:51.790 --> 01:04:52.870
So not a big surprise.

01:04:54.240 --> 01:04:56.697
So then finally, let's do.

01:04:56.697 --> 01:04:58.500
Let's put in a logistic there.

01:04:58.500 --> 01:05:00.100
Let's do linear and logistic

01:05:00.100 --> 01:05:03.060
regression, and I'm going to use the

01:05:03.060 --> 01:05:03.770
model here.

01:05:04.510 --> 01:05:06.700
So C = 1 is the default that's Lambda

01:05:06.700 --> 01:05:07.650
equals one.

01:05:07.650 --> 01:05:09.410
I'll give it plenty of iterations, just

01:05:09.410 --> 01:05:10.750
make sure it can converge.

01:05:10.750 --> 01:05:12.350
I fit it on the training data.

01:05:13.230 --> 01:05:15.310
Test it on the validation data.

01:05:15.310 --> 01:05:17.270
And here I'm going to compare for if I

01:05:17.270 --> 01:05:19.230
don't normalize versus I normalize.

01:05:23.690 --> 01:05:27.037
And so in this case I got 3% error when

01:05:27.037 --> 01:05:29.907
I didn't normalize and I got 0% error

01:05:29.907 --> 01:05:31.350
when I normalized.

01:05:33.670 --> 01:05:34.990
So the normalization.

01:05:34.990 --> 01:05:36.470
The reason it makes a difference in

01:05:36.470 --> 01:05:39.070
this linear model is that I have some

01:05:39.070 --> 01:05:40.100
regularization weight.

01:05:40.770 --> 01:05:43.420
So if I set this to something really

01:05:43.420 --> 01:05:46.780
big, SK learn is a little awkward and

01:05:46.780 --> 01:05:48.620
that C is the inverse of Lambda.

01:05:48.620 --> 01:05:50.970
So the higher this value is, the less

01:05:50.970 --> 01:05:51.970
the regularization.

01:05:58.010 --> 01:06:00.710
I thought they would do something, but

01:06:00.710 --> 01:06:01.240
it didn't.

01:06:03.440 --> 01:06:05.290
That's not going to make a difference.

01:06:06.730 --> 01:06:07.790
That's interesting actually.

01:06:07.790 --> 01:06:08.970
I don't know why.

01:06:09.730 --> 01:06:11.180
Maybe I maybe I got.

01:06:11.180 --> 01:06:13.510
Let's see, let's make it really small

01:06:13.510 --> 01:06:13.980
instead.

01:06:24.460 --> 01:06:24.920
What's what?

01:06:29.290 --> 01:06:32.130
So that definitely changed things, but

01:06:32.130 --> 01:06:33.620
it made the normalization worse.

01:06:33.620 --> 01:06:34.500
That's interesting.

01:06:34.500 --> 01:06:36.420
OK, I cannot explain that off the dot

01:06:36.420 --> 01:06:37.200
my head.

01:06:38.070 --> 01:06:41.200
But another thing is that if I do 0.

01:06:42.740 --> 01:06:44.095
Wait, actually zero.

01:06:44.095 --> 01:06:46.425
I don't remember again if which way?

01:06:46.425 --> 01:06:47.710
I have to, yeah.

01:06:48.470 --> 01:06:48.990
So.

01:06:50.650 --> 01:06:52.340
You need like you need some

01:06:52.340 --> 01:06:53.280
regularization.

01:06:54.220 --> 01:06:55.780
Or else you get errors like that.

01:06:58.220 --> 01:07:01.460
They're not regularizing is not info.

01:07:02.560 --> 01:07:05.650
Not regularizing is usually not an

01:07:05.650 --> 01:07:05.980
option.

01:07:05.980 --> 01:07:07.070
OK, never mind, all right.

01:07:08.140 --> 01:07:10.723
Yeah, you guys can play with it if you

01:07:10.723 --> 01:07:10.859
want.

01:07:10.860 --> 01:07:11.323
I'm going to.

01:07:11.323 --> 01:07:12.910
I just, I don't want to get stuck there

01:07:12.910 --> 01:07:15.340
as getting too much into the weeds.

01:07:16.530 --> 01:07:20.235
The normalization helped in the case of

01:07:20.235 --> 01:07:22.370
the default regularization.

01:07:24.010 --> 01:07:27.120
I can also plot a.

01:07:27.790 --> 01:07:29.590
I can also do like other ways of

01:07:29.590 --> 01:07:31.360
looking at the data.

01:07:31.360 --> 01:07:32.550
Let's look at.

01:07:32.550 --> 01:07:34.390
I'm going to change this since it was

01:07:34.390 --> 01:07:35.520
kind of boring.

01:07:37.500 --> 01:07:38.410
Let me just.

01:07:38.500 --> 01:07:39.190


01:07:41.150 --> 01:07:41.510
Whoops.

01:07:42.630 --> 01:07:44.430
I don't it's not very interesting to

01:07:44.430 --> 01:07:46.340
look at an Roc curve if you get perfect

01:07:46.340 --> 01:07:46.910
prediction.

01:07:48.670 --> 01:07:50.290
So let me just change this a little

01:07:50.290 --> 01:07:50.640
bit.

01:07:52.040 --> 01:07:54.870
So I'm going to look at the one where I

01:07:54.870 --> 01:07:56.380
did not perfect prediction.

01:07:57.840 --> 01:07:58.650


01:08:00.300 --> 01:08:00.830
Mexican.

01:08:03.700 --> 01:08:07.390
Right, so this arc curve shows me given

01:08:07.390 --> 01:08:09.320
if I choose different thresholds on my

01:08:09.320 --> 01:08:10.000
confidence.

01:08:10.870 --> 01:08:13.535
By default, you choose a confidence at

01:08:13.535 --> 01:08:14.050
5:00.

01:08:14.050 --> 01:08:15.810
If probability is greater than five,

01:08:15.810 --> 01:08:17.810
then you assign it to the class that

01:08:17.810 --> 01:08:19.069
had that greater probability.

01:08:19.700 --> 01:08:21.440
But you can say for example if the

01:08:21.440 --> 01:08:23.820
probability is greater than .3 then I'm

01:08:23.820 --> 01:08:27.030
going to say it's like malignant and

01:08:27.030 --> 01:08:28.150
otherwise it's benign.

01:08:28.150 --> 01:08:29.740
So you can choose different thresholds.

01:08:30.450 --> 01:08:31.990
Especially if there's a different

01:08:31.990 --> 01:08:33.440
consequence to getting either one

01:08:33.440 --> 01:08:36.100
wrong, like which there is for

01:08:36.100 --> 01:08:37.260
malignant versus benign.

01:08:38.080 --> 01:08:40.530
So you can look at this arc curve which

01:08:40.530 --> 01:08:42.260
shows you the true positive rate and

01:08:42.260 --> 01:08:43.990
the false positive rate for different

01:08:43.990 --> 01:08:44.700
thresholds.

01:08:45.460 --> 01:08:48.710
So I can choose a value such that L

01:08:48.710 --> 01:08:50.170
never have a.

01:08:50.940 --> 01:08:52.910
Where here I define true positive as y

01:08:52.910 --> 01:08:53.510
= 0.

01:08:54.220 --> 01:08:56.190
So I can choose a threshold where.

01:08:57.010 --> 01:08:59.930
I will get every single malign case

01:08:59.930 --> 01:09:02.380
correct, but I'll have like 20% false

01:09:02.380 --> 01:09:03.450
positives.

01:09:03.450 --> 01:09:05.870
Or I can choose a case where I'll

01:09:05.870 --> 01:09:07.360
sometimes make mistakes.

01:09:07.360 --> 01:09:10.110
Thinking I'm malignant is not

01:09:10.110 --> 01:09:11.040
malignant.

01:09:11.040 --> 01:09:15.360
But when it's benign, like 9099% of the

01:09:15.360 --> 01:09:16.570
time I'll think it's benign.

01:09:16.570 --> 01:09:18.815
So you can choose like you can kind of

01:09:18.815 --> 01:09:19.450
choose your errors.

01:09:25.800 --> 01:09:30.690
So this is so this like given some

01:09:30.690 --> 01:09:33.080
point on this curve, it tells me the

01:09:33.080 --> 01:09:35.120
true positive rate is the percent of

01:09:35.120 --> 01:09:37.775
times that I correctly classify equals

01:09:37.775 --> 01:09:39.379
zero as y = 0.

01:09:40.330 --> 01:09:42.020
And the false positive rate is the

01:09:42.020 --> 01:09:43.660
percent of times that I.

01:09:45.460 --> 01:09:46.790
Classify.

01:09:48.160 --> 01:09:50.400
Y = 1 as y = 0.

01:09:54.870 --> 01:09:57.410
Alright, so I can also look at the

01:09:57.410 --> 01:09:58.350
feature importance.

01:09:58.350 --> 01:10:01.450
So if I do L1, so here I trained one

01:10:01.450 --> 01:10:04.230
model with L1 logistic regression or

01:10:04.230 --> 01:10:06.586
this is L2 and one with L1 logistic

01:10:06.586 --> 01:10:06.930
regression?

01:10:07.740 --> 01:10:08.860
And that makes me use a different

01:10:08.860 --> 01:10:10.000
solver if it's L1.

01:10:11.270 --> 01:10:13.980
So I can see the errors.

01:10:14.070 --> 01:10:14.730


01:10:18.090 --> 01:10:19.505
A little weird but that error.

01:10:19.505 --> 01:10:24.588
But OK, I can see the errors and I can

01:10:24.588 --> 01:10:26.780
see the feature values.

01:10:29.290 --> 01:10:32.870
So with L2 I get lots of low weights,

01:10:32.870 --> 01:10:34.222
but none of them are zero.

01:10:34.222 --> 01:10:37.750
With L1 I get lots of 0 weights in a

01:10:37.750 --> 01:10:39.160
few larger weights.

01:10:43.420 --> 01:10:44.910
And then I can also do some further

01:10:44.910 --> 01:10:46.400
analysis looking at the tree.

01:10:48.090 --> 01:10:50.090
So first I'll train a full tree.

01:10:51.060 --> 01:10:53.010
And then next I'll train a tree with

01:10:53.010 --> 01:10:54.370
Max depth equals 2.

01:10:56.680 --> 01:11:00.006
So with the full tree I got error of

01:11:00.006 --> 01:11:00.403
4%.

01:11:00.403 --> 01:11:05.106
So it was as good as the OR was not as

01:11:05.106 --> 01:11:06.590
good as logistic regressor but pretty

01:11:06.590 --> 01:11:06.930
decent.

01:11:08.220 --> 01:11:09.500
But this tree is kind of hard to

01:11:09.500 --> 01:11:09.940
interpret.

01:11:09.940 --> 01:11:11.410
You wouldn't be able to give it to a

01:11:11.410 --> 01:11:13.415
technician and say like use this tree

01:11:13.415 --> 01:11:14.330
to make your decision.

01:11:15.050 --> 01:11:17.020
The short tree had higher error, but

01:11:17.020 --> 01:11:18.730
it's a lot simpler, so I can see its

01:11:18.730 --> 01:11:20.530
first splitting on the perimeter of the

01:11:20.530 --> 01:11:21.240
largest cells.

01:11:25.000 --> 01:11:27.510
And then finally, after doing all this

01:11:27.510 --> 01:11:30.010
analysis, I'm going to do tenfold cross

01:11:30.010 --> 01:11:32.780
validation using my best model.

01:11:33.370 --> 01:11:35.590
So here I'll just compare L1 logistic

01:11:35.590 --> 01:11:38.240
regression and nearest neighbor.

01:11:39.160 --> 01:11:41.345
I am doing tenfold, so I'm going to do

01:11:41.345 --> 01:11:45.126
10 estimates I do for each split.

01:11:45.126 --> 01:11:48.490
So the split will be after permutation.

01:11:48.490 --> 01:11:53.120
The first split will take indices 01020

01:11:53.120 --> 01:11:56.414
or yeah, 0102030, et cetera.

01:11:56.414 --> 01:12:00.540
The second split will take 11121, the

01:12:00.540 --> 01:12:03.840
third will take 21222, et cetera.

01:12:04.830 --> 01:12:07.050
Every time I use 90% of the data to

01:12:07.050 --> 01:12:09.400
train and the remaining data to test.

01:12:10.520 --> 01:12:12.510
And I'm doing that by just specifying

01:12:12.510 --> 01:12:13.990
the data that I'm using to test and

01:12:13.990 --> 01:12:15.930
then subtracting those indices to get

01:12:15.930 --> 01:12:17.100
the data that I used to train.

01:12:18.080 --> 01:12:21.396
Every time I normalize based on the

01:12:21.396 --> 01:12:23.140
training data, normalize both my

01:12:23.140 --> 01:12:24.554
training and validation data based on

01:12:24.554 --> 01:12:26.180
the same training data for the current

01:12:26.180 --> 01:12:26.540
split.

01:12:27.600 --> 01:12:29.340
Then I train and evaluate my nearest

01:12:29.340 --> 01:12:31.870
neighbor and logistic regressor.

01:12:38.000 --> 01:12:39.230
So that was fast.

01:12:40.850 --> 01:12:41.103
Right.

01:12:41.103 --> 01:12:43.950
And so then I have my errors.

01:12:43.950 --> 01:12:46.970
So one thing to note is that my even

01:12:46.970 --> 01:12:48.250
though in that one case I was

01:12:48.250 --> 01:12:50.310
evaluating before that one split, my

01:12:50.310 --> 01:12:52.190
logistic regression error was zero,

01:12:52.190 --> 01:12:53.670
it's not 0 every time.

01:12:53.670 --> 01:12:56.984
It ranges from zero to 5.3.

01:12:56.984 --> 01:12:59.906
And my nearest neighbor accuracy ranges

01:12:59.906 --> 01:13:02.980
from zero to 8 or 8.7 depending on the

01:13:02.980 --> 01:13:03.330
split.

01:13:04.300 --> 01:13:06.085
So different samples of your training

01:13:06.085 --> 01:13:08.592
and test data will give you different

01:13:08.592 --> 01:13:09.866
error measurement errors.

01:13:09.866 --> 01:13:11.950
And so that's why like cross validation

01:13:11.950 --> 01:13:14.300
can be a nice tool to give you not only

01:13:14.300 --> 01:13:16.870
an expected error, but some variance on

01:13:16.870 --> 01:13:18.140
the estimate of that error.

01:13:19.000 --> 01:13:19.500
So.

01:13:20.410 --> 01:13:23.330
My standard error of my estimate of the

01:13:23.330 --> 01:13:26.195
mean, which is the stair deviation of

01:13:26.195 --> 01:13:28.390
my error estimates divided by the

01:13:28.390 --> 01:13:29.720
square of the number of samples.

01:13:30.680 --> 01:13:35.420
Is 09 for nearest neighbor and six for

01:13:35.420 --> 01:13:36.500
logistic regression.

01:13:37.500 --> 01:13:39.270
And I can also use that to compute a

01:13:39.270 --> 01:13:41.540
confidence interval by multiplying that

01:13:41.540 --> 01:13:45.410
standard error by I forgot 1.96.

01:13:46.280 --> 01:13:49.330
So I can say like I'm 95% confident

01:13:49.330 --> 01:13:51.930
that my logistic regression error is

01:13:51.930 --> 01:13:56.440
somewhere between 12 and 34 or three.

01:13:56.440 --> 01:14:00.040
Sorry, 1.2% and 34%.

01:14:02.360 --> 01:14:04.615
And my nearest neighbor error is higher

01:14:04.615 --> 01:14:06.620
and I have like a bigger confidence

01:14:06.620 --> 01:14:07.020
interval.

01:14:09.360 --> 01:14:14.360
Now let's just compare very briefly how

01:14:14.360 --> 01:14:14.860
that.

01:14:15.610 --> 01:14:19.660
How the original paper did on this same

01:14:19.660 --> 01:14:20.110
problem?

01:14:23.320 --> 01:14:25.480
I just have one more slide, so don't

01:14:25.480 --> 01:14:27.950
worry, we will finish.

01:14:28.690 --> 01:14:30.360
Within a minute or so of runtime.

01:14:31.200 --> 01:14:33.610
Alright, so in the paper they use an

01:14:33.610 --> 01:14:36.300
MSM tree, which is that you have a

01:14:36.300 --> 01:14:37.820
linear classifier.

01:14:37.820 --> 01:14:39.240
Essentially that's used to do each

01:14:39.240 --> 01:14:40.140
split of the tree.

01:14:41.090 --> 01:14:42.720
But at the end of the day they choose

01:14:42.720 --> 01:14:44.550
only one split, so it ends up being a

01:14:44.550 --> 01:14:45.380
linear classifier.

01:14:46.300 --> 01:14:49.633
There they are trying to minimize the

01:14:49.633 --> 01:14:51.520
number of features as well as the

01:14:51.520 --> 01:14:53.900
number of splitting planes in order to

01:14:53.900 --> 01:14:55.550
improve generalization and make a

01:14:55.550 --> 01:14:57.090
simple interpretable function.

01:14:57.800 --> 01:14:59.370
So at the end of the day, they choose

01:14:59.370 --> 01:15:01.105
just three features, mean texture,

01:15:01.105 --> 01:15:02.780
worst area and worst smoothness.

01:15:03.520 --> 01:15:04.420
And.

01:15:05.930 --> 01:15:08.610
They used tenfold cross validation and

01:15:08.610 --> 01:15:11.770
they got an error of 3% within a

01:15:11.770 --> 01:15:15.570
confidence interval or minus 15%.

01:15:15.570 --> 01:15:17.120
So pretty similar to what we got.

01:15:17.120 --> 01:15:18.960
We got slightly lower error but we were

01:15:18.960 --> 01:15:20.560
using more features in the logistic

01:15:20.560 --> 01:15:21.090
regressor.

01:15:21.910 --> 01:15:23.694
And then they tested it on their held

01:15:23.694 --> 01:15:26.475
out set and they got a perfect accuracy

01:15:26.475 --> 01:15:27.730
on the held out set.

01:15:28.550 --> 01:15:29.849
Now that doesn't mean that their

01:15:29.850 --> 01:15:31.670
accuracy is perfect because they're

01:15:31.670 --> 01:15:34.350
cross validation if anything, is a

01:15:34.350 --> 01:15:37.315
biased towards a underestimating the

01:15:37.315 --> 01:15:37.570
error.

01:15:37.570 --> 01:15:40.440
So I would say their error is like

01:15:40.440 --> 01:15:43.870
roughly 15 to 45%, which is what they

01:15:43.870 --> 01:15:45.180
correctly report in the paper.

01:15:46.950 --> 01:15:47.290
Right.

01:15:47.290 --> 01:15:51.030
So we performed fairly similarly to the

01:15:51.030 --> 01:15:51.705
analysis.

01:15:51.705 --> 01:15:53.670
The nice thing is that now I can do

01:15:53.670 --> 01:15:56.900
this like in under an hour if I want.

01:15:56.900 --> 01:15:59.140
Well at that time it would be a lot

01:15:59.140 --> 01:16:01.380
more work to do that kind of analysis.

01:16:02.330 --> 01:16:04.490
But they also need to obviously want to

01:16:04.490 --> 01:16:06.410
be a lot more careful and do careful

01:16:06.410 --> 01:16:07.780
analysis and make sure that this is

01:16:07.780 --> 01:16:10.240
going to be like a useful tool for.

01:16:10.320 --> 01:16:12.180
That guy's diagnosis.

01:16:14.130 --> 01:16:14.870
Hey.

01:16:14.870 --> 01:16:16.400
So hopefully that was helpful.

01:16:16.400 --> 01:16:19.700
And next week I am going to talk about

01:16:19.700 --> 01:16:20.150
or not.

01:16:20.150 --> 01:16:21.750
Next week it's only Tuesday.

01:16:21.750 --> 01:16:23.550
On Thursday I'm going to talk about.

01:16:23.550 --> 01:16:24.962
No, wait, what day is it?

01:16:24.962 --> 01:16:25.250
Thursday.

01:16:25.250 --> 01:16:25.868
OK, good.

01:16:25.868 --> 01:16:27.020
It is next week.

01:16:27.020 --> 01:16:28.810
Yeah, at least chat with time.

01:16:30.520 --> 01:16:33.300
Next week I'll talk about ensembles and

01:16:33.300 --> 01:16:35.310
SVM and stochastic gradient descent.

01:16:35.310 --> 01:16:35.780
Thanks.

01:16:35.780 --> 01:16:36.690
Have a good weekend.

01:16:38.360 --> 01:16:40.130
And remember that homework one is due

01:16:40.130 --> 01:16:40.830
Monday.

01:16:41.650 --> 01:16:42.760
For those asking question.