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+WEBVTT Kind: captions; Language: en-US
+
+NOTE
+Created on 2024-02-07T20:59:36.8732843Z by ClassTranscribe
+
+00:01:39.900 --> 00:01:41.600
+Alright, good morning everybody.
+
+00:01:43.340 --> 00:01:45.450
+So we're going to do another
+
+00:01:45.450 --> 00:01:47.490
+consolidation and review session.
+
+00:01:47.870 --> 00:01:50.320
+I'm going, it's going to be sort of
+
+00:01:50.320 --> 00:01:51.790
+like just a different perspective on
+
+00:01:51.790 --> 00:01:54.145
+some of the things we've seen and then
+
+00:01:54.145 --> 00:01:56.260
+and then I'll talk about the exam a
+
+00:01:56.260 --> 00:01:57.130
+little bit as well.
+
+00:01:59.970 --> 00:02:04.120
+So far we've been talking about this
+
+00:02:04.120 --> 00:02:05.800
+whole function quite a lot.
+
+00:02:05.800 --> 00:02:09.309
+That we have some data, we have some
+
+00:02:09.310 --> 00:02:11.700
+model F, we have some parameters Theta.
+
+00:02:11.700 --> 00:02:13.580
+We have something that we're trying to
+
+00:02:13.580 --> 00:02:15.530
+predict why we have some loss that
+
+00:02:15.530 --> 00:02:17.680
+defines how good our prediction is.
+
+00:02:18.500 --> 00:02:20.720
+And we're trying to solve for some
+
+00:02:20.720 --> 00:02:23.370
+parameters that minimize the loss.
+
+00:02:24.770 --> 00:02:26.630
+Given our model and our data and our
+
+00:02:26.630 --> 00:02:29.500
+parameters and our labels.
+
+00:02:30.410 --> 00:02:33.700
+And so it's all, it's pretty
+
+00:02:33.700 --> 00:02:34.230
+complicated.
+
+00:02:34.230 --> 00:02:35.195
+There's a lot there.
+
+00:02:35.195 --> 00:02:37.700
+And if I were going to reteach the
+
+00:02:37.700 --> 00:02:39.610
+class, I would probably start more
+
+00:02:39.610 --> 00:02:42.460
+simply by just talking about X.
+
+00:02:42.460 --> 00:02:45.190
+So let's just talk about X for now.
+
+00:02:46.900 --> 00:02:48.970
+So for example, when you have one bit
+
+00:02:48.970 --> 00:02:50.900
+and another bit and they like each
+
+00:02:50.900 --> 00:02:52.860
+other very much and they come together,
+
+00:02:52.860 --> 00:02:53.710
+it makes 3.
+
+00:02:54.390 --> 00:02:55.030
+I'm just kidding.
+
+00:02:55.030 --> 00:02:56.250
+That's how integers are made.
+
+00:02:59.170 --> 00:03:03.190
+So let's talk about the data for a bit.
+
+00:03:03.190 --> 00:03:05.590
+So first, like, what is data?
+
+00:03:05.590 --> 00:03:08.140
+This sounds like kind of elementary,
+
+00:03:08.140 --> 00:03:09.890
+but it's actually not a very easy
+
+00:03:09.890 --> 00:03:11.000
+question to answer, right?
+
+00:03:11.860 --> 00:03:15.113
+So if we talk about one way that we can
+
+00:03:15.113 --> 00:03:17.041
+think about it is that we can think
+
+00:03:17.041 --> 00:03:19.510
+about data is information that helps us
+
+00:03:19.510 --> 00:03:20.740
+make decisions.
+
+00:03:22.320 --> 00:03:23.930
+Another way that we can think about it
+
+00:03:23.930 --> 00:03:25.850
+is data is just numbers, right?
+
+00:03:25.850 --> 00:03:27.457
+Like if it's stored on.
+
+00:03:27.457 --> 00:03:30.390
+If you have data stored on a computer,
+
+00:03:30.390 --> 00:03:33.050
+it's just like a big sequence of bits.
+
+00:03:33.050 --> 00:03:35.976
+And that's all that's really all data
+
+00:03:35.976 --> 00:03:36.159
+is.
+
+00:03:36.159 --> 00:03:37.590
+It's just a bunch of numbers.
+
+00:03:40.250 --> 00:03:43.495
+So for people, if we think about how do
+
+00:03:43.495 --> 00:03:46.030
+we represent data, we store it in terms
+
+00:03:46.030 --> 00:03:49.200
+of media that we can see, read or hear.
+
+00:03:49.200 --> 00:03:51.190
+So we might have images.
+
+00:03:51.820 --> 00:03:54.513
+We might have like text documents, we
+
+00:03:54.513 --> 00:03:57.240
+might have audio files, we could have
+
+00:03:57.240 --> 00:03:58.450
+plots and tables.
+
+00:03:58.450 --> 00:04:00.090
+So there are things that we perceive
+
+00:04:00.090 --> 00:04:01.920
+and then we make sense of it based on
+
+00:04:01.920 --> 00:04:02.810
+our perception.
+
+00:04:04.900 --> 00:04:05.989
+And we can.
+
+00:04:05.989 --> 00:04:07.980
+The data can take different forms
+
+00:04:07.980 --> 00:04:09.450
+without really changing its meaning.
+
+00:04:09.450 --> 00:04:11.900
+So we can resize an image, we can
+
+00:04:11.900 --> 00:04:16.045
+refreeze a paragraph, we can speed up
+
+00:04:16.045 --> 00:04:18.770
+an audio book, and all of that changes
+
+00:04:18.770 --> 00:04:20.860
+the form of the data a bit, but it
+
+00:04:20.860 --> 00:04:22.809
+doesn't really change much of the
+
+00:04:22.810 --> 00:04:26.470
+information that data contained.
+
+00:04:29.200 --> 00:04:31.890
+And sometimes we can change the data so
+
+00:04:31.890 --> 00:04:33.750
+that it becomes more informative to us.
+
+00:04:33.750 --> 00:04:36.940
+So we can denoise an image, we can
+
+00:04:36.940 --> 00:04:37.590
+clean it up.
+
+00:04:37.590 --> 00:04:39.825
+We can try to identify the key points
+
+00:04:39.825 --> 00:04:42.460
+and insights in a document.
+
+00:04:42.460 --> 00:04:43.186
+Cliff notes.
+
+00:04:43.186 --> 00:04:45.280
+We can remove background noise from
+
+00:04:45.280 --> 00:04:45.900
+audio.
+
+00:04:47.030 --> 00:04:50.945
+And none of these operations really add
+
+00:04:50.945 --> 00:04:52.040
+information to the data.
+
+00:04:52.040 --> 00:04:53.530
+If anything, they take away
+
+00:04:53.530 --> 00:04:55.230
+information, they prune it.
+
+00:04:56.170 --> 00:04:58.890
+But they reorganize it, and they
+
+00:04:58.890 --> 00:05:01.390
+removed distracting information so that
+
+00:05:01.390 --> 00:05:03.276
+it's easier for us to extract
+
+00:05:03.276 --> 00:05:05.550
+information that we want from that
+
+00:05:05.550 --> 00:05:05.970
+data.
+
+00:05:08.040 --> 00:05:09.570
+So that's from the, that's from our
+
+00:05:09.570 --> 00:05:10.790
+perspective as people.
+
+00:05:11.930 --> 00:05:15.510
+For computers, data are just numbers,
+
+00:05:15.510 --> 00:05:17.060
+so the numbers don't really mean
+
+00:05:17.060 --> 00:05:18.730
+anything by themselves.
+
+00:05:18.730 --> 00:05:20.090
+They're just bits, right?
+
+00:05:20.780 --> 00:05:22.505
+The meaning comes from the way the
+
+00:05:22.505 --> 00:05:24.169
+numbers were produced and how they can
+
+00:05:24.170 --> 00:05:25.620
+inform what they can tell us about
+
+00:05:25.620 --> 00:05:26.930
+other numbers, essentially.
+
+00:05:28.090 --> 00:05:28.820
+So.
+
+00:05:29.490 --> 00:05:32.400
+There you could have like each.
+
+00:05:32.400 --> 00:05:34.490
+Each number could be informative on its
+
+00:05:34.490 --> 00:05:37.160
+own, or it could only be informative if
+
+00:05:37.160 --> 00:05:39.175
+you view it in patterns of other groups
+
+00:05:39.175 --> 00:05:39.860
+of numbers.
+
+00:05:41.530 --> 00:05:43.410
+So one bit.
+
+00:05:43.410 --> 00:05:44.975
+If you have a whole bit string, the
+
+00:05:44.975 --> 00:05:46.320
+bits individually may not mean
+
+00:05:46.320 --> 00:05:48.624
+anything, but those bits may form
+
+00:05:48.624 --> 00:05:50.208
+characters, and those characters may
+
+00:05:50.208 --> 00:05:52.410
+form words, and those words may tell us
+
+00:05:52.410 --> 00:05:53.420
+something useful.
+
+00:05:55.980 --> 00:05:59.479
+So just like just like just like we can
+
+00:05:59.480 --> 00:06:02.160
+resize images and speed up audio and
+
+00:06:02.160 --> 00:06:04.494
+things like that to change the form of
+
+00:06:04.494 --> 00:06:06.114
+the data without changing the
+
+00:06:06.114 --> 00:06:08.390
+information and the data, we can also
+
+00:06:08.390 --> 00:06:11.090
+transform data without changing its
+
+00:06:11.090 --> 00:06:13.250
+information and computer programs.
+
+00:06:13.830 --> 00:06:16.290
+So, for example, we can add or multiply
+
+00:06:16.290 --> 00:06:19.607
+a vector by a constant value, and as
+
+00:06:19.607 --> 00:06:21.220
+long as we do that consistently, it
+
+00:06:21.220 --> 00:06:22.740
+doesn't really change the information
+
+00:06:22.740 --> 00:06:24.160
+that's contained in that data.
+
+00:06:24.160 --> 00:06:27.230
+So there's nothing inherently different
+
+00:06:27.230 --> 00:06:29.136
+about, for example, if I represent a
+
+00:06:29.136 --> 00:06:31.000
+vector or I represent the negative
+
+00:06:31.000 --> 00:06:33.140
+vector, as long as I'm consistent.
+
+00:06:34.810 --> 00:06:36.726
+We can represent the data in different
+
+00:06:36.726 --> 00:06:39.130
+ways, As for example 16 or 32 bit
+
+00:06:39.130 --> 00:06:40.360
+floats or integers.
+
+00:06:40.360 --> 00:06:41.750
+We might lose a little bit, but not
+
+00:06:41.750 --> 00:06:42.503
+very much.
+
+00:06:42.503 --> 00:06:45.000
+We can compress the document or store
+
+00:06:45.000 --> 00:06:47.070
+it in a different file format, so
+
+00:06:47.070 --> 00:06:48.400
+there's lots of different ways to
+
+00:06:48.400 --> 00:06:50.630
+represent the same data without
+
+00:06:50.630 --> 00:06:52.060
+changing the information.
+
+00:06:52.680 --> 00:06:54.590
+That is stored in that data or that's
+
+00:06:54.590 --> 00:06:55.820
+represented by that data?
+
+00:06:57.980 --> 00:07:00.860
+And justice like sometimes we can
+
+00:07:00.860 --> 00:07:02.984
+create summaries or ways to make data
+
+00:07:02.984 --> 00:07:04.490
+more informative for people.
+
+00:07:04.490 --> 00:07:06.597
+We can also sometimes transform the
+
+00:07:06.597 --> 00:07:08.639
+data to make it more informative for
+
+00:07:08.640 --> 00:07:09.230
+computers.
+
+00:07:10.070 --> 00:07:12.400
+So we can center and rescale the images
+
+00:07:12.400 --> 00:07:13.890
+of digits so that they're easier to
+
+00:07:13.890 --> 00:07:15.850
+compare each other to each other.
+
+00:07:15.850 --> 00:07:18.240
+For example, we can normalize the data,
+
+00:07:18.240 --> 00:07:19.910
+for example, subtract the means and
+
+00:07:19.910 --> 00:07:21.944
+divide by a stern deviations of the
+
+00:07:21.944 --> 00:07:24.023
+features of like cancer cell
+
+00:07:24.023 --> 00:07:26.025
+measurements that make similarity
+
+00:07:26.025 --> 00:07:28.740
+measurements better reflect malignancy.
+
+00:07:28.740 --> 00:07:31.430
+And we can do feature selection or
+
+00:07:31.430 --> 00:07:33.780
+create new features out of combinations
+
+00:07:33.780 --> 00:07:34.590
+of inputs.
+
+00:07:34.590 --> 00:07:38.330
+So this is kind of like analogous to
+
+00:07:38.330 --> 00:07:40.230
+creating a summary of a document.
+
+00:07:40.280 --> 00:07:42.370
+Or denoising the image so that we can
+
+00:07:42.370 --> 00:07:44.580
+see it better, or enhancing or things
+
+00:07:44.580 --> 00:07:45.290
+like that, right?
+
+00:07:46.210 --> 00:07:48.880
+Makes it easier to extract information
+
+00:07:48.880 --> 00:07:50.240
+from the same data.
+
+00:07:53.320 --> 00:07:55.000
+And sometimes they also change the
+
+00:07:55.000 --> 00:07:57.370
+structure of the data to make it easier
+
+00:07:57.370 --> 00:07:58.250
+to process.
+
+00:07:58.960 --> 00:08:01.610
+So we might naturally think of the
+
+00:08:01.610 --> 00:08:05.505
+image as a matrix because we where each
+
+00:08:05.505 --> 00:08:09.260
+of these grid cells represent some
+
+00:08:09.260 --> 00:08:12.356
+intensity at some position in the
+
+00:08:12.356 --> 00:08:12.619
+image.
+
+00:08:13.430 --> 00:08:16.350
+And this feels natural because the
+
+00:08:16.350 --> 00:08:18.640
+image is like takes up some area.
+
+00:08:18.640 --> 00:08:20.219
+It's like it makes sense to think of it
+
+00:08:20.220 --> 00:08:22.530
+in terms of rows and columns, but we
+
+00:08:22.530 --> 00:08:24.780
+can equivalently represent it as a
+
+00:08:24.780 --> 00:08:27.340
+vector, which is what we did for the
+
+00:08:27.340 --> 00:08:28.580
+homework and what we often do.
+
+00:08:29.300 --> 00:08:32.610
+And you just reshape it, and this is
+
+00:08:32.610 --> 00:08:33.510
+more convenient.
+
+00:08:33.510 --> 00:08:35.432
+So the matrix form is more convenient
+
+00:08:35.432 --> 00:08:37.900
+for local pattern analysis if we're
+
+00:08:37.900 --> 00:08:39.550
+trying to look for edges and things
+
+00:08:39.550 --> 00:08:40.370
+like that.
+
+00:08:40.370 --> 00:08:42.416
+The vector form is more convenient if
+
+00:08:42.416 --> 00:08:44.360
+we're trying to apply a linear model to
+
+00:08:44.360 --> 00:08:46.552
+it, because we can just do that as a as
+
+00:08:46.552 --> 00:08:48.090
+a dot product operation.
+
+00:08:50.040 --> 00:08:52.010
+So either way, it doesn't change the
+
+00:08:52.010 --> 00:08:53.510
+information and the data.
+
+00:08:53.510 --> 00:08:56.310
+But this form like makes no sense to us
+
+00:08:56.310 --> 00:08:57.110
+as people.
+
+00:08:57.110 --> 00:08:59.790
+But for computers it's more convenient
+
+00:08:59.790 --> 00:09:01.360
+to do certain kinds of operations if
+
+00:09:01.360 --> 00:09:03.020
+you represent it as a vector versus a
+
+00:09:03.020 --> 00:09:03.540
+matrix.
+
+00:09:06.210 --> 00:09:08.270
+So let's talk about how some different
+
+00:09:08.270 --> 00:09:10.120
+forms of information are represented.
+
+00:09:10.120 --> 00:09:13.390
+So as I mentioned a little bit in the
+
+00:09:13.390 --> 00:09:16.580
+last class, we can represent images as
+
+00:09:16.580 --> 00:09:17.920
+3D matrices.
+
+00:09:18.660 --> 00:09:20.930
+Where the three dimensions are the row,
+
+00:09:20.930 --> 00:09:22.190
+the column and the color.
+
+00:09:22.820 --> 00:09:24.565
+So if we have some intensity pattern
+
+00:09:24.565 --> 00:09:29.290
+like this, then the bright values are
+
+00:09:29.290 --> 00:09:31.640
+typically one or 255 depending on your
+
+00:09:31.640 --> 00:09:32.410
+representation.
+
+00:09:33.090 --> 00:09:35.580
+The dark values will be very low, like
+
+00:09:35.580 --> 00:09:37.990
+0 or in this case the darkest values
+
+00:09:37.990 --> 00:09:39.210
+are only about .3.
+
+00:09:40.190 --> 00:09:43.140
+And you represent that for the entire
+
+00:09:43.140 --> 00:09:45.140
+image area, and that gives you.
+
+00:09:45.140 --> 00:09:47.880
+If you're representing a grayscale
+
+00:09:47.880 --> 00:09:49.410
+image, you would just have one color
+
+00:09:49.410 --> 00:09:51.130
+dimension, so you'd have a number of
+
+00:09:51.130 --> 00:09:52.808
+rows by number of columns by one.
+
+00:09:52.808 --> 00:09:55.425
+If you have an RGB image, then you
+
+00:09:55.425 --> 00:09:57.933
+would have one matrix for each of the
+
+00:09:57.933 --> 00:09:59.040
+color dimensions.
+
+00:09:59.040 --> 00:10:01.912
+So you'd have a 2D matrix for R2D
+
+00:10:01.912 --> 00:10:04.260
+matrix for G and a 2D matrix for B.
+
+00:10:08.340 --> 00:10:12.180
+Text can be represented as a sequence
+
+00:10:12.180 --> 00:10:13.090
+of integers.
+
+00:10:14.020 --> 00:10:15.890
+And it's actually, I'm going to talk
+
+00:10:15.890 --> 00:10:18.010
+we'll learn a lot more about word
+
+00:10:18.010 --> 00:10:21.210
+representations next week and how to
+
+00:10:21.210 --> 00:10:24.025
+process language, but it's actually a
+
+00:10:24.025 --> 00:10:25.976
+more subtle problem than you might
+
+00:10:25.976 --> 00:10:27.010
+think at first.
+
+00:10:27.010 --> 00:10:29.745
+So you might think well represent each
+
+00:10:29.745 --> 00:10:31.240
+word as an integer.
+
+00:10:31.240 --> 00:10:34.420
+But then that becomes kind of tricky
+
+00:10:34.420 --> 00:10:35.880
+because you can have lots of similar
+
+00:10:35.880 --> 00:10:39.075
+words swims and swim and swim, and
+
+00:10:39.075 --> 00:10:40.752
+those will all be different integers.
+
+00:10:40.752 --> 00:10:42.930
+And those integers are kind of like
+
+00:10:42.930 --> 00:10:43.990
+arbitrary tokens.
+
+00:10:44.100 --> 00:10:45.940
+Don't necessarily have any similarity
+
+00:10:45.940 --> 00:10:46.800
+to each other.
+
+00:10:48.530 --> 00:10:50.170
+And then if you try to represent things
+
+00:10:50.170 --> 00:10:51.680
+as integers, and then you run into
+
+00:10:51.680 --> 00:10:53.525
+names and lots of different varieties
+
+00:10:53.525 --> 00:10:55.020
+of ways that we put characters
+
+00:10:55.020 --> 00:10:56.250
+together, then you have difficulty
+
+00:10:56.250 --> 00:10:57.140
+representing all of those.
+
+00:10:57.140 --> 00:10:58.459
+You need an awful lot of integers.
+
+00:10:59.860 --> 00:11:01.665
+So you can go to another extreme and
+
+00:11:01.665 --> 00:11:03.016
+represent the characters as.
+
+00:11:03.016 --> 00:11:05.042
+You can just represent the characters
+
+00:11:05.042 --> 00:11:05.984
+as byte values.
+
+00:11:05.984 --> 00:11:09.430
+So you can represent dog eat as like
+
+00:11:09.430 --> 00:11:13.490
+four 15727 using 27 as space 125.
+
+00:11:13.490 --> 00:11:16.164
+So you could just represent the
+
+00:11:16.164 --> 00:11:18.920
+characters as a bite stream and process
+
+00:11:18.920 --> 00:11:19.550
+it that way.
+
+00:11:19.550 --> 00:11:21.335
+That's one extreme.
+
+00:11:21.335 --> 00:11:23.579
+The other extreme is that you represent
+
+00:11:23.580 --> 00:11:26.170
+each complete word as an integer value
+
+00:11:26.170 --> 00:11:28.630
+and so you pre assign you have some.
+
+00:11:28.690 --> 00:11:30.480
+Vocabulary where you have like all the
+
+00:11:30.480 --> 00:11:31.490
+words that you think you might
+
+00:11:31.490 --> 00:11:32.146
+encounter.
+
+00:11:32.146 --> 00:11:34.974
+You assign each word to some integer,
+
+00:11:34.974 --> 00:11:36.820
+and then you have an integer sequence
+
+00:11:36.820 --> 00:11:38.270
+that you're going to process.
+
+00:11:38.270 --> 00:11:41.660
+And if you see some new set of
+
+00:11:41.660 --> 00:11:43.953
+characters that is not any rockabilly,
+
+00:11:43.953 --> 00:11:46.490
+you assign it to an unknown token, a
+
+00:11:46.490 --> 00:11:49.930
+token called Unknown or UNK typically.
+
+00:11:51.080 --> 00:11:54.410
+And then there's also like intermediate
+
+00:11:54.410 --> 00:11:55.920
+things, which I'll talk about more when
+
+00:11:55.920 --> 00:11:57.419
+I talk about language, where you can
+
+00:11:57.420 --> 00:12:00.560
+group common groups of letters into
+
+00:12:00.560 --> 00:12:02.589
+their own little groups and represent
+
+00:12:02.590 --> 00:12:03.530
+each of those.
+
+00:12:03.530 --> 00:12:05.270
+So you can represent, for example,
+
+00:12:05.270 --> 00:12:10.020
+bedroom 1521 as bed, one token for bed,
+
+00:12:10.020 --> 00:12:12.279
+or one integer for bed, one integer for
+
+00:12:12.280 --> 00:12:15.446
+room, and then four more integers for
+
+00:12:15.446 --> 00:12:16.013
+1521.
+
+00:12:16.013 --> 00:12:18.090
+And with this kind of representation
+
+00:12:18.090 --> 00:12:19.960
+you can model any kind of like
+
+00:12:19.960 --> 00:12:20.370
+sequence.
+
+00:12:20.420 --> 00:12:22.610
+The characters just really weird
+
+00:12:22.610 --> 00:12:24.590
+sequences like random letters will take
+
+00:12:24.590 --> 00:12:26.590
+a lot of different integers to
+
+00:12:26.590 --> 00:12:29.870
+represent, while something, well,
+
+00:12:29.870 --> 00:12:32.310
+common words will only take one integer
+
+00:12:32.310 --> 00:12:32.650
+each.
+
+00:12:37.160 --> 00:12:39.623
+And then we also may want to represent
+
+00:12:39.623 --> 00:12:40.039
+audio.
+
+00:12:40.040 --> 00:12:43.270
+So audio we can represent in different
+
+00:12:43.270 --> 00:12:45.839
+ways, we can represent it as amplitude
+
+00:12:45.839 --> 00:12:46.606
+versus time.
+
+00:12:46.606 --> 00:12:48.870
+The wave form, and this is usually the
+
+00:12:48.870 --> 00:12:50.590
+way that it's stored is just you have
+
+00:12:50.590 --> 00:12:54.930
+an amplitude at some high frequency or
+
+00:12:54.930 --> 00:12:58.530
+you can represent it as a spectrogram
+
+00:12:58.530 --> 00:13:00.660
+as like a frequency, amplitude versus
+
+00:13:00.660 --> 00:13:02.970
+time like what's the power and the.
+
+00:13:03.060 --> 00:13:04.900
+And the low notes versus the high notes
+
+00:13:04.900 --> 00:13:06.530
+at each time step.
+
+00:13:10.280 --> 00:13:11.720
+And then there's lots of other kinds of
+
+00:13:11.720 --> 00:13:12.030
+data.
+
+00:13:12.030 --> 00:13:14.610
+So we can represent measurements and
+
+00:13:14.610 --> 00:13:16.420
+continuous values as floating point
+
+00:13:16.420 --> 00:13:18.760
+numbers, temperature length, area,
+
+00:13:18.760 --> 00:13:21.970
+dollars, categorical values like color,
+
+00:13:21.970 --> 00:13:24.930
+like whether something's happy or sad
+
+00:13:24.930 --> 00:13:27.430
+or big or small, those can be
+
+00:13:27.430 --> 00:13:29.537
+represented as integers.
+
+00:13:29.537 --> 00:13:32.450
+And here the distinction is that when
+
+00:13:32.450 --> 00:13:34.052
+you're representing categorical values
+
+00:13:34.052 --> 00:13:36.210
+as integers, these integers.
+
+00:13:36.840 --> 00:13:38.620
+The distance between integers doesn't
+
+00:13:38.620 --> 00:13:40.920
+imply similarity usually, so you don't
+
+00:13:40.920 --> 00:13:42.790
+necessarily say that zero is more
+
+00:13:42.790 --> 00:13:45.150
+similar to one than it is to two when
+
+00:13:45.150 --> 00:13:46.910
+you're representing categorical values.
+
+00:13:47.960 --> 00:13:49.530
+But if you're representing continuous
+
+00:13:49.530 --> 00:13:51.110
+values, then you see that some
+
+00:13:51.110 --> 00:13:52.820
+Euclidean distance between those values
+
+00:13:52.820 --> 00:13:53.710
+is meaningful.
+
+00:13:55.920 --> 00:13:57.820
+And all of these different types of
+
+00:13:57.820 --> 00:14:00.120
+values, the text, the images and the
+
+00:14:00.120 --> 00:14:02.560
+measurements can be reshaped and
+
+00:14:02.560 --> 00:14:04.670
+concatenated into a long feature
+
+00:14:04.670 --> 00:14:05.050
+vector.
+
+00:14:05.050 --> 00:14:06.610
+And that's often what we do.
+
+00:14:06.610 --> 00:14:09.240
+We take everything, every kind of
+
+00:14:09.240 --> 00:14:11.300
+information that we think can be
+
+00:14:11.300 --> 00:14:13.900
+applicable to solve some problem or
+
+00:14:13.900 --> 00:14:15.500
+predict some why that we're interested
+
+00:14:15.500 --> 00:14:15.730
+in.
+
+00:14:16.440 --> 00:14:20.190
+At some point we take that information,
+
+00:14:20.190 --> 00:14:22.640
+we reshape it into a big vector, and
+
+00:14:22.640 --> 00:14:24.970
+then we do a prediction based on that
+
+00:14:24.970 --> 00:14:25.410
+vector.
+
+00:14:33.060 --> 00:14:34.640
+Weird screeching sound.
+
+00:14:35.270 --> 00:14:35.840
+
+
+00:14:37.010 --> 00:14:39.780
+So this is the same information.
+
+00:14:39.780 --> 00:14:41.440
+Content can be represented in many
+
+00:14:41.440 --> 00:14:41.910
+ways.
+
+00:14:43.150 --> 00:14:45.930
+Essentially, if the original numbers
+
+00:14:45.930 --> 00:14:47.502
+can be recovered, then it means that
+
+00:14:47.502 --> 00:14:49.475
+the change in representation doesn't
+
+00:14:49.475 --> 00:14:50.980
+change the information content.
+
+00:14:50.980 --> 00:14:52.729
+So any kind of transformation that we
+
+00:14:52.730 --> 00:14:54.419
+apply that we can invert, that we can
+
+00:14:54.420 --> 00:14:56.350
+get back to the original is not
+
+00:14:56.350 --> 00:14:57.720
+changing the information, it's just
+
+00:14:57.720 --> 00:14:59.510
+reshaping the data in some way that
+
+00:14:59.510 --> 00:15:01.550
+might make it easier or maybe harder to
+
+00:15:01.550 --> 00:15:02.210
+process.
+
+00:15:03.570 --> 00:15:05.795
+And we can store all types of data as
+
+00:15:05.795 --> 00:15:07.100
+1D vectors and arrays.
+
+00:15:07.850 --> 00:15:10.800
+And so we'll typically have like as our
+
+00:15:10.800 --> 00:15:15.480
+data set will have some set of vectors,
+
+00:15:15.480 --> 00:15:17.630
+a matrix where the columns are
+
+00:15:17.630 --> 00:15:20.320
+individual data samples and the rows
+
+00:15:20.320 --> 00:15:22.570
+correspond to different features as
+
+00:15:22.570 --> 00:15:24.340
+representing a set of data.
+
+00:15:25.500 --> 00:15:27.820
+And you don't, really.
+
+00:15:27.820 --> 00:15:30.060
+You never really need to use matrices
+
+00:15:30.060 --> 00:15:31.680
+or other data structures, but they just
+
+00:15:31.680 --> 00:15:33.690
+make it easier for us to code, and so
+
+00:15:33.690 --> 00:15:34.170
+it doesn't.
+
+00:15:34.170 --> 00:15:36.080
+Again, like there's nothing inherent
+
+00:15:36.080 --> 00:15:37.740
+about those structures that adds
+
+00:15:37.740 --> 00:15:39.800
+information to the data, it's just for
+
+00:15:39.800 --> 00:15:40.570
+convenience.
+
+00:15:42.980 --> 00:15:45.000
+So all of that so far is kind of
+
+00:15:45.000 --> 00:15:49.019
+describing a data .1 piece of data that
+
+00:15:49.020 --> 00:15:51.460
+we might use to make a prediction to
+
+00:15:51.460 --> 00:15:52.980
+gather some information from.
+
+00:15:53.750 --> 00:15:55.660
+But in machine learning, we're usually
+
+00:15:55.660 --> 00:15:56.035
+dealing.
+
+00:15:56.035 --> 00:15:58.385
+We're often dealing with data sets, so
+
+00:15:58.385 --> 00:16:01.340
+we want to learn from some set of data
+
+00:16:01.340 --> 00:16:03.676
+so that when we get some new data
+
+00:16:03.676 --> 00:16:05.540
+point, we can make some useful
+
+00:16:05.540 --> 00:16:07.060
+prediction from that data point.
+
+00:16:08.850 --> 00:16:12.144
+So we can write this as that we have
+
+00:16:12.144 --> 00:16:14.436
+some where X is a set of data.
+
+00:16:14.436 --> 00:16:17.607
+The little X here, or actually I have X
+
+00:16:17.607 --> 00:16:18.670
+is not a set of data, sorry.
+
+00:16:18.670 --> 00:16:21.190
+The little X is a data point with M
+
+00:16:21.190 --> 00:16:24.120
+features, so it has some M scalar
+
+00:16:24.120 --> 00:16:27.304
+values and it's drawn from some
+
+00:16:27.304 --> 00:16:29.720
+distribution D so for example, your
+
+00:16:29.720 --> 00:16:32.114
+distribution D could be all the images
+
+00:16:32.114 --> 00:16:34.650
+that are on the Internet and you're
+
+00:16:34.650 --> 00:16:36.207
+just like downloading random images
+
+00:16:36.207 --> 00:16:37.070
+from the Internet.
+
+00:16:37.120 --> 00:16:38.820
+And then one of those random images is
+
+00:16:38.820 --> 00:16:39.820
+a little X.
+
+00:16:41.330 --> 00:16:43.650
+We can sample many of these X's so we
+
+00:16:43.650 --> 00:16:45.040
+could download different documents from
+
+00:16:45.040 --> 00:16:45.442
+the Internet.
+
+00:16:45.442 --> 00:16:47.170
+We could download like emails to
+
+00:16:47.170 --> 00:16:49.000
+classify spam or not spam.
+
+00:16:49.000 --> 00:16:51.769
+We could take pictures, we could take
+
+00:16:51.770 --> 00:16:54.830
+measurements, and then we get a
+
+00:16:54.830 --> 00:16:57.180
+collection of those data points and
+
+00:16:57.180 --> 00:16:59.830
+that gives us some big X.
+
+00:16:59.830 --> 00:17:03.610
+It's a set of these X little X vectors
+
+00:17:03.610 --> 00:17:06.890
+from one to N, from zero to N guess it
+
+00:17:06.890 --> 00:17:08.290
+should be 0 to minus one.
+
+00:17:09.170 --> 00:17:11.830
+And that's John.
+
+00:17:11.830 --> 00:17:13.790
+It's all drawn from some distribution D
+
+00:17:13.790 --> 00:17:15.260
+so there's always some implicit
+
+00:17:15.260 --> 00:17:16.865
+distribution even if we don't know what
+
+00:17:16.865 --> 00:17:19.190
+it is, some source of the data that
+
+00:17:19.190 --> 00:17:19.950
+we're sampling.
+
+00:17:19.950 --> 00:17:21.936
+And typically we assume that we don't
+
+00:17:21.936 --> 00:17:23.332
+have all the data, we just have like
+
+00:17:23.332 --> 00:17:25.020
+some of it, we have some representative
+
+00:17:25.020 --> 00:17:26.200
+sample of that data.
+
+00:17:27.380 --> 00:17:28.940
+So we can repeat the collection many
+
+00:17:28.940 --> 00:17:30.980
+times, or we can collect one big data
+
+00:17:30.980 --> 00:17:33.670
+set and split it, and then we'll often
+
+00:17:33.670 --> 00:17:36.173
+split it into some X train, which are
+
+00:17:36.173 --> 00:17:37.950
+the samples that we're going to learn
+
+00:17:37.950 --> 00:17:40.935
+from an ex test, which are the samples
+
+00:17:40.935 --> 00:17:42.820
+that we're going to use to see how we
+
+00:17:42.820 --> 00:17:43.350
+learned.
+
+00:17:44.950 --> 00:17:47.210
+And usually we assume that all the data
+
+00:17:47.210 --> 00:17:49.518
+samples within X train and X test come
+
+00:17:49.518 --> 00:17:51.240
+from the same distribution and are
+
+00:17:51.240 --> 00:17:52.505
+independent of each other.
+
+00:17:52.505 --> 00:17:54.620
+So that term is called IID or
+
+00:17:54.620 --> 00:17:56.470
+independent identically distributed.
+
+00:17:56.470 --> 00:17:59.760
+And essentially that just means that no
+
+00:17:59.760 --> 00:18:01.510
+data point tells you anything about
+
+00:18:01.510 --> 00:18:03.590
+another data point if you the sampling
+
+00:18:03.590 --> 00:18:04.027
+distribution.
+
+00:18:04.027 --> 00:18:06.654
+So they come from the same
+
+00:18:06.654 --> 00:18:07.092
+distribution.
+
+00:18:07.092 --> 00:18:09.865
+So maybe they have they may have
+
+00:18:09.865 --> 00:18:12.077
+similar values to each other, but if
+
+00:18:12.077 --> 00:18:13.466
+know that distribution then they're
+
+00:18:13.466 --> 00:18:14.299
+then they're independent.
+
+00:18:14.360 --> 00:18:16.050
+If you randomly download images from
+
+00:18:16.050 --> 00:18:16.660
+the Internet.
+
+00:18:17.410 --> 00:18:19.105
+Each image tells you something about
+
+00:18:19.105 --> 00:18:20.460
+images, but they don't really tell you
+
+00:18:20.460 --> 00:18:22.336
+directly anything about the other
+
+00:18:22.336 --> 00:18:24.149
+images about a specific other image.
+
+00:18:27.230 --> 00:18:29.540
+So let's look at an example from this
+
+00:18:29.540 --> 00:18:33.550
+Penguins data set that we use in the
+
+00:18:33.550 --> 00:18:34.000
+homework.
+
+00:18:34.820 --> 00:18:36.640
+And I'm not actually going to analyze
+
+00:18:36.640 --> 00:18:38.120
+it in a way that directly helps you
+
+00:18:38.120 --> 00:18:38.720
+with your homework.
+
+00:18:38.720 --> 00:18:40.220
+It's just an example that you may be
+
+00:18:40.220 --> 00:18:40.760
+familiar with.
+
+00:18:41.830 --> 00:18:43.010
+But let's look at this.
+
+00:18:43.010 --> 00:18:44.670
+So we have this.
+
+00:18:44.670 --> 00:18:46.970
+It's represented in this like Panda
+
+00:18:46.970 --> 00:18:49.370
+framework, but basically just a tabular
+
+00:18:49.370 --> 00:18:49.820
+framework.
+
+00:18:50.490 --> 00:18:53.020
+So we have a whole bunch of data points
+
+00:18:53.020 --> 00:18:55.360
+where we know the species, the island,
+
+00:18:55.360 --> 00:18:56.600
+the.
+
+00:18:57.400 --> 00:18:58.810
+I don't even know what a Coleman is.
+
+00:18:58.810 --> 00:18:59.950
+Maybe the beak or something.
+
+00:19:01.270 --> 00:19:03.130
+Cullman length and depth probably not
+
+00:19:03.130 --> 00:19:05.290
+to be, I don't know, flipper length,
+
+00:19:05.290 --> 00:19:07.700
+body mass and the sets of the Penguin
+
+00:19:07.700 --> 00:19:08.700
+which may be unknown.
+
+00:19:10.120 --> 00:19:11.920
+And so the first thing we do, which is
+
+00:19:11.920 --> 00:19:14.158
+in the starter code, is we try to
+
+00:19:14.158 --> 00:19:17.830
+process the process the data into a
+
+00:19:17.830 --> 00:19:19.830
+format that is more convenient for
+
+00:19:19.830 --> 00:19:20.510
+machine learning.
+
+00:19:21.570 --> 00:19:24.270
+And so for example like the.
+
+00:19:25.220 --> 00:19:29.770
+The SK learn learn methods for training
+
+00:19:29.770 --> 00:19:32.790
+trees does not deal with like multi
+
+00:19:32.790 --> 00:19:34.450
+valued categorical variables.
+
+00:19:34.450 --> 00:19:35.850
+So it can't deal with that.
+
+00:19:35.850 --> 00:19:37.325
+There are like 3 different islands.
+
+00:19:37.325 --> 00:19:39.065
+It means you to turn it into binary
+
+00:19:39.065 --> 00:19:39.540
+variables.
+
+00:19:40.340 --> 00:19:42.430
+And so the first thing that you often
+
+00:19:42.430 --> 00:19:44.340
+do when you're trying to analyze a
+
+00:19:44.340 --> 00:19:48.020
+problem is you, like, reformat the data
+
+00:19:48.020 --> 00:19:51.250
+in a way that allows you to process the
+
+00:19:51.250 --> 00:19:53.370
+data or learn from the data more
+
+00:19:53.370 --> 00:19:54.130
+conveniently.
+
+00:19:54.980 --> 00:19:58.900
+So in this code we read the CSV that
+
+00:19:58.900 --> 00:20:02.280
+gives us some tabular format for the
+
+00:20:02.280 --> 00:20:03.190
+Penguin data.
+
+00:20:04.230 --> 00:20:08.290
+And then I just form this into an array
+
+00:20:08.290 --> 00:20:10.490
+so I get extracted features.
+
+00:20:10.490 --> 00:20:12.160
+These are all the different columns of
+
+00:20:12.160 --> 00:20:13.253
+that Penguin data.
+
+00:20:13.253 --> 00:20:15.072
+I put it in a Numpy array.
+
+00:20:15.072 --> 00:20:18.435
+I get the species because that's what
+
+00:20:18.435 --> 00:20:20.100
+the problem was to predict.
+
+00:20:20.100 --> 00:20:22.389
+And then I get the unique values of the
+
+00:20:22.390 --> 00:20:23.300
+island.
+
+00:20:23.300 --> 00:20:26.840
+I get the unique values of the sex
+
+00:20:26.840 --> 00:20:28.880
+which will be male, female and unknown.
+
+00:20:28.880 --> 00:20:32.760
+And I initialize some array where I'm
+
+00:20:32.760 --> 00:20:34.000
+going to store my data.
+
+00:20:34.430 --> 00:20:36.722
+Then I loop through all the elements or
+
+00:20:36.722 --> 00:20:38.250
+all the data points, and I know that
+
+00:20:38.250 --> 00:20:39.830
+there's one data point for each Y
+
+00:20:39.830 --> 00:20:41.440
+value, so I looked through the length
+
+00:20:41.440 --> 00:20:41.800
+of Y.
+
+00:20:42.950 --> 00:20:44.770
+And then I just replace the island
+
+00:20:44.770 --> 00:20:46.890
+names with an indicator variable with
+
+00:20:46.890 --> 00:20:48.960
+three indicator variables so I forget
+
+00:20:48.960 --> 00:20:49.353
+what the.
+
+00:20:49.353 --> 00:20:50.720
+I guess they're down here so if the
+
+00:20:50.720 --> 00:20:51.930
+island is Biscoe.
+
+00:20:52.690 --> 00:20:54.830
+Then the first value will be zero, I
+
+00:20:54.830 --> 00:20:55.560
+mean will be one.
+
+00:20:56.460 --> 00:20:58.292
+F and otherwise it will be 0.
+
+00:20:58.292 --> 00:21:00.690
+If the island is dream then the second
+
+00:21:00.690 --> 00:21:02.850
+value will be one and otherwise it will
+
+00:21:02.850 --> 00:21:03.390
+be 0.
+
+00:21:03.390 --> 00:21:06.620
+And if the island is Torgerson then the
+
+00:21:06.620 --> 00:21:09.028
+third value will be one and otherwise
+
+00:21:09.028 --> 00:21:10.460
+it will be 0.
+
+00:21:10.460 --> 00:21:12.120
+So exactly one of these should be equal
+
+00:21:12.120 --> 00:21:13.646
+to 1 and the other should be equal to
+
+00:21:13.646 --> 00:21:13.820
+0.
+
+00:21:14.710 --> 00:21:16.154
+Then I fell in the floating point
+
+00:21:16.154 --> 00:21:17.980
+values for these other things and then
+
+00:21:17.980 --> 00:21:19.830
+I do the same for this X.
+
+00:21:19.830 --> 00:21:22.420
+So one of these three values, female,
+
+00:21:22.420 --> 00:21:24.892
+male or unknown will be a one and the
+
+00:21:24.892 --> 00:21:26.160
+other two will be a 0.
+
+00:21:26.950 --> 00:21:28.590
+And so at the end of this I have this
+
+00:21:28.590 --> 00:21:32.650
+like now this data vector where each
+
+00:21:32.650 --> 00:21:33.380
+column.
+
+00:21:34.050 --> 00:21:36.340
+Will be either like a binary number or
+
+00:21:36.340 --> 00:21:39.103
+a floating point number that tells me
+
+00:21:39.103 --> 00:21:42.360
+like what island or what sex and what
+
+00:21:42.360 --> 00:21:46.870
+the Penguin had and then the I'll have
+
+00:21:46.870 --> 00:21:50.620
+a row for each data sample and for Y
+
+00:21:50.620 --> 00:21:52.440
+I'll just have her vote for each data
+
+00:21:52.440 --> 00:21:55.360
+sample that has the name of the thing
+
+00:21:55.360 --> 00:21:56.920
+I'm trying to predict, the species.
+
+00:22:01.580 --> 00:22:04.390
+So if we have some data set like that,
+
+00:22:04.390 --> 00:22:06.040
+then how do we measure it?
+
+00:22:06.040 --> 00:22:09.156
+So there's some simple things we can
+
+00:22:09.156 --> 00:22:09.468
+do.
+
+00:22:09.468 --> 00:22:11.235
+One is we can just measure the shape so
+
+00:22:11.235 --> 00:22:15.520
+we can see this has 341 data samples
+
+00:22:15.520 --> 00:22:17.070
+and I've got 10 features.
+
+00:22:18.070 --> 00:22:20.730
+I can also start to think about it now
+
+00:22:20.730 --> 00:22:21.710
+as the distribution.
+
+00:22:21.710 --> 00:22:23.520
+So it's no longer just like an
+
+00:22:23.520 --> 00:22:25.500
+individual point or an individual set
+
+00:22:25.500 --> 00:22:27.940
+of values, but it's a distribution.
+
+00:22:27.940 --> 00:22:29.377
+There's some probability that I'll
+
+00:22:29.377 --> 00:22:31.674
+observe some sets of values, and some
+
+00:22:31.674 --> 00:22:33.520
+probability that I'll observe other
+
+00:22:33.520 --> 00:22:34.309
+sets of values.
+
+00:22:35.020 --> 00:22:37.100
+And so one really simple way that I can
+
+00:22:37.100 --> 00:22:39.460
+measure the distribution is by looking
+
+00:22:39.460 --> 00:22:41.213
+at the mean and the standard deviation.
+
+00:22:41.213 --> 00:22:43.950
+If it were a Gaussian distribution
+
+00:22:43.950 --> 00:22:46.015
+where the values are independent from
+
+00:22:46.015 --> 00:22:47.665
+each other and different if the
+
+00:22:47.665 --> 00:22:49.071
+different features are independent from
+
+00:22:49.071 --> 00:22:50.860
+each other in a Gaussian, this would
+
+00:22:50.860 --> 00:22:52.300
+tell me everything there is to know
+
+00:22:52.300 --> 00:22:53.780
+about the distribution.
+
+00:22:53.780 --> 00:22:55.996
+But in practice you rarely have a
+
+00:22:55.996 --> 00:22:56.339
+Gaussian.
+
+00:22:56.340 --> 00:22:58.210
+Usually it's a bit more complicated.
+
+00:22:58.210 --> 00:22:59.206
+Still, it's a useful thing.
+
+00:22:59.206 --> 00:23:02.680
+So it tells me that like the body mass
+
+00:23:02.680 --> 00:23:05.630
+average is 4200 grams.
+
+00:23:05.950 --> 00:23:08.185
+And the steering deviation is 800, so
+
+00:23:08.185 --> 00:23:10.890
+there's so the average is like 4.1
+
+00:23:10.890 --> 00:23:12.720
+kilograms, but there's like a
+
+00:23:12.720 --> 00:23:14.110
+significant variance there.
+
+00:23:18.640 --> 00:23:23.121
+One of the key things to know is that
+
+00:23:23.121 --> 00:23:25.580
+the is that I'm just getting an
+
+00:23:25.580 --> 00:23:27.270
+empirical estimate of this
+
+00:23:27.270 --> 00:23:29.855
+distribution, so I don't know what the
+
+00:23:29.855 --> 00:23:30.686
+true mean is.
+
+00:23:30.686 --> 00:23:32.625
+I don't know what the true standard
+
+00:23:32.625 --> 00:23:33.179
+deviation is.
+
+00:23:33.180 --> 00:23:34.970
+All I know is what the mean and the
+
+00:23:34.970 --> 00:23:37.240
+standard deviation is of my sample, and
+
+00:23:37.240 --> 00:23:39.240
+if I were to draw different samples, I
+
+00:23:39.240 --> 00:23:41.530
+would get different estimates of the
+
+00:23:41.530 --> 00:23:42.780
+mean and the standard deviation.
+
+00:23:43.750 --> 00:23:46.770
+So in the top row, I'm resampling this
+
+00:23:46.770 --> 00:23:49.640
+data using this convenient sample
+
+00:23:49.640 --> 00:23:52.720
+function that the PANDA framework has,
+
+00:23:52.720 --> 00:23:54.693
+and then taking the mean each time.
+
+00:23:54.693 --> 00:23:57.310
+So you can see that one time 45% of the
+
+00:23:57.310 --> 00:23:59.480
+Penguins come from Cisco, another time
+
+00:23:59.480 --> 00:24:02.770
+it's 54%, and another time it's 44%.
+
+00:24:02.770 --> 00:24:05.330
+So this is drawing 100 samples with
+
+00:24:05.330 --> 00:24:06.070
+replacement.
+
+00:24:06.990 --> 00:24:10.570
+And by the way, is like is like
+
+00:24:10.570 --> 00:24:11.220
+bootstrapping.
+
+00:24:11.220 --> 00:24:12.795
+If I want to say what's the variance of
+
+00:24:12.795 --> 00:24:13.232
+my estimate?
+
+00:24:13.232 --> 00:24:16.240
+If I had 100 samples of data, I could
+
+00:24:16.240 --> 00:24:18.920
+repeat this random sampling 100 times
+
+00:24:18.920 --> 00:24:20.800
+and then take the variance of my mean
+
+00:24:20.800 --> 00:24:22.528
+and that would give me the variance of
+
+00:24:22.528 --> 00:24:24.718
+my estimate, even though I don't have
+
+00:24:24.718 --> 00:24:27.360
+like even even though I have a rather
+
+00:24:27.360 --> 00:24:29.270
+small sample to draw that estimate
+
+00:24:29.270 --> 00:24:29.820
+from.
+
+00:24:31.210 --> 00:24:33.040
+If I have more data, I'm going to get
+
+00:24:33.040 --> 00:24:34.900
+more accurate estimates.
+
+00:24:34.900 --> 00:24:39.189
+So if I sample 1000 samples, I'm
+
+00:24:39.190 --> 00:24:40.780
+drawing samples with replacement.
+
+00:24:42.390 --> 00:24:44.749
+Then the averages become much more
+
+00:24:44.750 --> 00:24:45.140
+similar.
+
+00:24:45.140 --> 00:24:49.650
+So now Biscoe goes from 475 to 473 to
+
+00:24:49.650 --> 00:24:52.220
+484, so it's a much smaller range than
+
+00:24:52.220 --> 00:24:54.382
+it was when I drew 100 samples.
+
+00:24:54.382 --> 00:24:56.635
+So in general like, the more I'm able
+
+00:24:56.635 --> 00:24:59.970
+to draw, the tighter my estimate of the
+
+00:24:59.970 --> 00:25:01.260
+distribution will be.
+
+00:25:01.870 --> 00:25:03.525
+But it's always an estimate of the
+
+00:25:03.525 --> 00:25:03.757
+distribution.
+
+00:25:03.757 --> 00:25:05.120
+It's not the true distribution.
+
+00:25:08.870 --> 00:25:10.560
+So there's also other ways that we can
+
+00:25:10.560 --> 00:25:12.100
+try to measure this data set.
+
+00:25:12.100 --> 00:25:16.120
+So one idea is to try to measure the
+
+00:25:16.120 --> 00:25:18.110
+entropy of a particular variable.
+
+00:25:19.420 --> 00:25:21.610
+If the variable is discrete, which
+
+00:25:21.610 --> 00:25:24.015
+means that it has like integer values,
+
+00:25:24.015 --> 00:25:26.400
+it has a finite number of values.
+
+00:25:27.450 --> 00:25:29.870
+And then we can measure it by counting.
+
+00:25:29.870 --> 00:25:34.100
+So we can say that the entropy will be
+
+00:25:34.100 --> 00:25:36.040
+the negative sum all the different
+
+00:25:36.040 --> 00:25:37.670
+values of that variable of the
+
+00:25:37.670 --> 00:25:39.360
+probability of that value times the log
+
+00:25:39.360 --> 00:25:40.470
+probability of that value.
+
+00:25:41.340 --> 00:25:42.550
+And I can count it like this.
+
+00:25:42.550 --> 00:25:44.300
+I can just say in this case these are
+
+00:25:44.300 --> 00:25:47.080
+binary, so I just count how many times
+
+00:25:47.080 --> 00:25:49.190
+XI equals zero or the fraction of times
+
+00:25:49.190 --> 00:25:51.030
+that's the probability of X I = 0.
+
+00:25:52.240 --> 00:25:54.494
+The fraction times XI equals one and
+
+00:25:54.494 --> 00:25:57.222
+then my cross and then my not cross
+
+00:25:57.222 --> 00:25:57.675
+entropy.
+
+00:25:57.675 --> 00:25:59.623
+My entropy is the negative probability
+
+00:25:59.623 --> 00:26:02.090
+of XI equals zero times the log base
+
+00:26:02.090 --> 00:26:04.290
+two probability of XI equals 0 minus
+
+00:26:04.290 --> 00:26:07.269
+probability XI equals one times log
+
+00:26:07.269 --> 00:26:09.310
+probability of XI equal 1.
+
+00:26:10.770 --> 00:26:13.460
+The log base two thing is like a
+
+00:26:13.460 --> 00:26:15.360
+convention, and it means that this
+
+00:26:15.360 --> 00:26:17.600
+entropy is measured in bits.
+
+00:26:17.600 --> 00:26:20.550
+So it's essentially how many bits you
+
+00:26:20.550 --> 00:26:23.686
+would need theoretically to be able to
+
+00:26:23.686 --> 00:26:25.570
+like disambiguate this value or specify
+
+00:26:25.570 --> 00:26:26.310
+this value.
+
+00:26:27.030 --> 00:26:29.690
+If you had a, if your data were all
+
+00:26:29.690 --> 00:26:31.540
+ones, then you really don't need any
+
+00:26:31.540 --> 00:26:32.929
+bits to represent it because it's
+
+00:26:32.930 --> 00:26:33.870
+always A1.
+
+00:26:33.870 --> 00:26:35.930
+But if it's like a completely random
+
+00:26:35.930 --> 00:26:38.469
+value, 5050 chance that it's a zero or
+
+00:26:38.469 --> 00:26:40.942
+one, then you need one bit to represent
+
+00:26:40.942 --> 00:26:42.965
+it because you until you observe it,
+
+00:26:42.965 --> 00:26:44.245
+you have no idea what it is, so you
+
+00:26:44.245 --> 00:26:47.030
+need a full bit to represent that bit.
+
+00:26:48.460 --> 00:26:50.470
+So if I look at Island Biscoe, it's
+
+00:26:50.470 --> 00:26:53.010
+almost a 5050 chance, so the entropy is
+
+00:26:53.010 --> 00:26:53.510
+very high.
+
+00:26:53.510 --> 00:26:54.580
+It's .999.
+
+00:26:55.280 --> 00:26:57.050
+If I look at a different feature index,
+
+00:26:57.050 --> 00:26:58.400
+the one for Torgerson.
+
+00:26:59.510 --> 00:27:02.460
+Only like 15% of the Penguins come from
+
+00:27:02.460 --> 00:27:05.100
+tergesen and so the entropy is much
+
+00:27:05.100 --> 00:27:05.690
+lower.
+
+00:27:05.690 --> 00:27:07.020
+It's .69.
+
+00:27:11.760 --> 00:27:14.140
+We can also measure the entropy of
+
+00:27:14.140 --> 00:27:16.130
+continuous variables.
+
+00:27:16.130 --> 00:27:19.030
+So if I have, for example the Cullman
+
+00:27:19.030 --> 00:27:19.700
+length.
+
+00:27:19.700 --> 00:27:21.500
+Now I can't just like count how many
+
+00:27:21.500 --> 00:27:23.450
+times I observe each value of Coleman
+
+00:27:23.450 --> 00:27:25.030
+length, because those values may be
+
+00:27:25.030 --> 00:27:25.420
+unique.
+
+00:27:25.420 --> 00:27:26.880
+I'll probably observe each value
+
+00:27:26.880 --> 00:27:27.620
+exactly once.
+
+00:27:28.730 --> 00:27:31.589
+And so instead we need to we need to
+
+00:27:31.590 --> 00:27:34.130
+have other ways of estimating that
+
+00:27:34.130 --> 00:27:35.560
+continuous distribution.
+
+00:27:36.890 --> 00:27:39.610
+So mathematically, the entropy of the
+
+00:27:39.610 --> 00:27:42.630
+variable X is now the negative integral
+
+00:27:42.630 --> 00:27:44.760
+over all the possible values X of
+
+00:27:44.760 --> 00:27:47.395
+probability of X times log probability
+
+00:27:47.395 --> 00:27:48.550
+of X.
+
+00:27:48.550 --> 00:27:51.300
+But this becomes a kind of complicated
+
+00:27:51.300 --> 00:27:55.110
+in a way because our data, while the
+
+00:27:55.110 --> 00:27:56.780
+values may be continuous, we don't have
+
+00:27:56.780 --> 00:27:58.850
+access to a continuous or infinite
+
+00:27:58.850 --> 00:27:59.510
+amount of data.
+
+00:28:00.160 --> 00:28:02.350
+And so we always need to estimate this
+
+00:28:02.350 --> 00:28:04.520
+continuous distribution based on our
+
+00:28:04.520 --> 00:28:05.400
+discrete sample.
+
+00:28:07.160 --> 00:28:08.500
+There's a lot of different ways of
+
+00:28:08.500 --> 00:28:10.550
+doing this, but one of the most common
+
+00:28:10.550 --> 00:28:14.467
+is to break up our continuous variable
+
+00:28:14.467 --> 00:28:17.882
+into smaller discrete variables into
+
+00:28:17.882 --> 00:28:20.430
+smaller discrete ranges, and then count
+
+00:28:20.430 --> 00:28:22.220
+for each of those discrete ranges.
+
+00:28:22.220 --> 00:28:23.460
+So that's what I did here.
+
+00:28:24.260 --> 00:28:27.320
+So I get the XI for the.
+
+00:28:27.320 --> 00:28:28.690
+This is for the Coleman length.
+
+00:28:30.780 --> 00:28:33.060
+I forgot to include this printed value,
+
+00:28:33.060 --> 00:28:35.790
+but there's if I the printed value here
+
+00:28:35.790 --> 00:28:37.600
+is just like a lot I think like all the
+
+00:28:37.600 --> 00:28:38.420
+values are unique.
+
+00:28:39.230 --> 00:28:42.000
+And I'm creating like empty indices
+
+00:28:42.000 --> 00:28:44.604
+because I'm being lazy here for the X
+
+00:28:44.604 --> 00:28:47.915
+value and for the probability of each X
+
+00:28:47.915 --> 00:28:48.290
+value.
+
+00:28:49.190 --> 00:28:51.000
+And I'm setting a step size of 1.
+
+00:28:52.010 --> 00:28:54.635
+Then I loop from the minimum value plus
+
+00:28:54.635 --> 00:28:57.167
+half a step to the maximum value minus
+
+00:28:57.167 --> 00:28:58.094
+half a step.
+
+00:28:58.094 --> 00:28:59.020
+I take steps.
+
+00:28:59.020 --> 00:29:01.799
+So I take steps of 1 from maybe like
+
+00:29:01.800 --> 00:29:05.348
+whoops, from maybe like 30, stop from
+
+00:29:05.348 --> 00:29:07.340
+maybe 30 to 60.
+
+00:29:07.340 --> 00:29:10.460
+And for each of those steps I count how
+
+00:29:10.460 --> 00:29:14.870
+many times I see a value within a range
+
+00:29:14.870 --> 00:29:16.750
+of like my current value minus half
+
+00:29:16.750 --> 00:29:18.050
+step plus half step.
+
+00:29:18.050 --> 00:29:20.485
+So for example, the first one will be
+
+00:29:20.485 --> 00:29:21.890
+from say like.
+
+00:29:21.950 --> 00:29:24.860
+How many times do I observe the common
+
+00:29:24.860 --> 00:29:27.900
+length between like 31 and 32?
+
+00:29:28.670 --> 00:29:30.676
+And so that will be my mean.
+
+00:29:30.676 --> 00:29:32.370
+So this is I'm estimating the
+
+00:29:32.370 --> 00:29:34.010
+probability that it falls within this
+
+00:29:34.010 --> 00:29:34.440
+range.
+
+00:29:35.380 --> 00:29:37.130
+And then I can turn this into a
+
+00:29:37.130 --> 00:29:39.940
+continuous distribution by dividing by
+
+00:29:39.940 --> 00:29:40.850
+the step size.
+
+00:29:42.310 --> 00:29:43.820
+So that will make it comparable.
+
+00:29:43.820 --> 00:29:44.960
+If I were to choose different step
+
+00:29:44.960 --> 00:29:47.050
+sizes, I should get like fairly similar
+
+00:29:47.050 --> 00:29:47.620
+plots.
+
+00:29:47.620 --> 00:29:50.330
+And the one -, 20 is just to avoid a
+
+00:29:50.330 --> 00:29:52.140
+divide by zero without really changing
+
+00:29:52.140 --> 00:29:52.610
+much else.
+
+00:29:54.690 --> 00:29:58.290
+So then I plot it and the cross entropy
+
+00:29:58.290 --> 00:30:01.727
+is just the negative sum of all of
+
+00:30:01.727 --> 00:30:04.750
+these different probabilities that the
+
+00:30:04.750 --> 00:30:06.875
+discrete probabilities now of these
+
+00:30:06.875 --> 00:30:10.010
+different ranges times the log 2
+
+00:30:10.010 --> 00:30:12.460
+probability of each of those ranges.
+
+00:30:13.090 --> 00:30:17.120
+And then I need to multiply that by the
+
+00:30:17.120 --> 00:30:18.680
+step size as well, which in this case
+
+00:30:18.680 --> 00:30:19.380
+is just one.
+
+00:30:24.540 --> 00:30:27.018
+OK, and then so I get an estimate.
+
+00:30:27.018 --> 00:30:28.540
+So this is the plot.
+
+00:30:28.540 --> 00:30:30.950
+This is the probability.
+
+00:30:30.950 --> 00:30:32.840
+It's my estimate of the continuous
+
+00:30:32.840 --> 00:30:36.345
+probability now of each variable of
+
+00:30:36.345 --> 00:30:37.270
+each value of X.
+
+00:30:37.950 --> 00:30:39.520
+And then this is my estimate of the
+
+00:30:39.520 --> 00:30:40.180
+entropy.
+
+00:30:45.190 --> 00:30:48.320
+So as I mentioned, I would like
+
+00:30:48.320 --> 00:30:50.640
+continuous features are kind of tricky
+
+00:30:50.640 --> 00:30:52.360
+because it depends on.
+
+00:30:52.360 --> 00:30:54.240
+I can estimate their probabilities in
+
+00:30:54.240 --> 00:30:56.310
+different ways and that will give me
+
+00:30:56.310 --> 00:30:58.790
+different distributions and different
+
+00:30:58.790 --> 00:31:00.400
+measurements of things like entropy.
+
+00:31:01.340 --> 00:31:04.420
+So if I chose a different step size, if
+
+00:31:04.420 --> 00:31:06.950
+I step in .1, that means I'm going to
+
+00:31:06.950 --> 00:31:08.719
+count how many times I observe this
+
+00:31:08.720 --> 00:31:11.220
+continuous variable in little tiny
+
+00:31:11.220 --> 00:31:11.660
+ranges.
+
+00:31:11.660 --> 00:31:14.010
+How many times do I observe it between
+
+00:31:14.010 --> 00:31:16.222
+40.0 and 40.1?
+
+00:31:16.222 --> 00:31:18.030
+And sometimes I might have no
+
+00:31:18.030 --> 00:31:19.630
+observations because I only have like
+
+00:31:19.630 --> 00:31:22.216
+300 data points and so that's why when
+
+00:31:22.216 --> 00:31:24.370
+I plot it as a line plot, I get this
+
+00:31:24.370 --> 00:31:25.965
+like super spiky thing because I've got
+
+00:31:25.965 --> 00:31:27.640
+a bunch of zeros, but I didn't observe
+
+00:31:27.640 --> 00:31:29.390
+anything in those tiny step sizes.
+
+00:31:29.390 --> 00:31:30.950
+And then there's other times when I
+
+00:31:30.950 --> 00:31:31.200
+observe.
+
+00:31:31.250 --> 00:31:32.260
+Several points.
+
+00:31:32.930 --> 00:31:34.630
+Inside of a tiny step size.
+
+00:31:36.100 --> 00:31:37.710
+So these are different representations
+
+00:31:37.710 --> 00:31:40.780
+of the same data and it's kind of like
+
+00:31:40.780 --> 00:31:43.312
+up to us to decide to think about like
+
+00:31:43.312 --> 00:31:45.690
+which of these is a better
+
+00:31:45.690 --> 00:31:47.360
+representation, which one do we think
+
+00:31:47.360 --> 00:31:49.290
+more closely reflects the true
+
+00:31:49.290 --> 00:31:50.100
+distribution?
+
+00:31:51.310 --> 00:31:53.600
+And I guess I'll ask you, so do you
+
+00:31:53.600 --> 00:31:55.750
+think if I had to rely on one of these
+
+00:31:55.750 --> 00:31:58.632
+as a probability density estimate of
+
+00:31:58.632 --> 00:32:01.360
+this, of this variable, would you
+
+00:32:01.360 --> 00:32:03.790
+prefer the left side or the right side?
+
+00:32:06.800 --> 00:32:07.090
+Right.
+
+00:32:08.680 --> 00:32:09.930
+All right, I'll take a vote.
+
+00:32:09.930 --> 00:32:11.590
+So how many prefer the left side?
+
+00:32:13.000 --> 00:32:14.850
+How many prefer the right side?
+
+00:32:14.850 --> 00:32:16.750
+That's interesting.
+
+00:32:17.770 --> 00:32:20.455
+OK, so it's mixed and there's not
+
+00:32:20.455 --> 00:32:22.650
+really a right answer, but I personally
+
+00:32:22.650 --> 00:32:23.853
+would prefer the left side.
+
+00:32:23.853 --> 00:32:25.960
+And the reason is just because I don't
+
+00:32:25.960 --> 00:32:26.433
+really think.
+
+00:32:26.433 --> 00:32:28.580
+It's true that there's like a whole lot
+
+00:32:28.580 --> 00:32:31.898
+of Penguins that would have a length of
+
+00:32:31.898 --> 00:32:32.750
+like 40.5.
+
+00:32:32.750 --> 00:32:35.190
+But then it's almost impossible for a
+
+00:32:35.190 --> 00:32:37.059
+Penguin to have a length of 40.6.
+
+00:32:37.059 --> 00:32:38.900
+But then 40.7 is like pretty likely.
+
+00:32:38.900 --> 00:32:41.185
+Again, that's not, that's not my model
+
+00:32:41.185 --> 00:32:42.440
+of how the world works.
+
+00:32:42.440 --> 00:32:44.370
+I tend to think that this distribution
+
+00:32:44.370 --> 00:32:45.870
+should be pretty smooth, right?
+
+00:32:45.870 --> 00:32:47.020
+It might be a multimodal.
+
+00:32:47.080 --> 00:32:50.486
+Distribution you might have like the
+
+00:32:50.486 --> 00:32:53.250
+adult males, the adult females, and the
+
+00:32:53.250 --> 00:32:54.850
+kid Penguins.
+
+00:32:54.850 --> 00:32:56.260
+Maybe that's what it is.
+
+00:32:57.300 --> 00:32:58.140
+I don't really know.
+
+00:32:58.140 --> 00:32:58.466
+I'm not.
+
+00:32:58.466 --> 00:32:59.700
+I don't study Penguins.
+
+00:32:59.700 --> 00:33:00.770
+But it's possible.
+
+00:33:03.440 --> 00:33:04.040
+That's right.
+
+00:33:07.480 --> 00:33:11.030
+So the as I mentioned, the entropy
+
+00:33:11.030 --> 00:33:12.350
+measures how many bits?
+
+00:33:12.350 --> 00:33:13.130
+Question.
+
+00:33:14.390 --> 00:33:14.960
+Yeah.
+
+00:33:30.580 --> 00:33:34.050
+So that's a good question, comment so.
+
+00:33:35.640 --> 00:33:37.275
+The so you might choose.
+
+00:33:37.275 --> 00:33:38.960
+So you're saying that you chose this
+
+00:33:38.960 --> 00:33:40.870
+because the entropy is lower.
+
+00:33:41.620 --> 00:33:45.100
+The.
+
+00:33:46.510 --> 00:33:48.210
+So that kind of like makes sense
+
+00:33:48.210 --> 00:33:51.420
+intuitively, but I would say the reason
+
+00:33:51.420 --> 00:33:54.369
+that I wouldn't choose the entropy
+
+00:33:54.370 --> 00:33:55.832
+value as a way of choosing the
+
+00:33:55.832 --> 00:33:58.095
+distribution is that these entropy
+
+00:33:58.095 --> 00:33:59.740
+values are actually not like the true
+
+00:33:59.740 --> 00:34:00.590
+entropy values.
+
+00:34:00.590 --> 00:34:02.920
+They're just the estimate of the
+
+00:34:02.920 --> 00:34:04.470
+entropy based on the distribution that
+
+00:34:04.470 --> 00:34:06.050
+we estimated.
+
+00:34:06.050 --> 00:34:08.160
+And for example, if I really want to
+
+00:34:08.160 --> 00:34:10.941
+minimize this distribution or the
+
+00:34:10.941 --> 00:34:12.800
+entropy, I would say that my
+
+00:34:12.800 --> 00:34:14.510
+distribution is just like a bunch of
+
+00:34:14.510 --> 00:34:16.050
+delta functions, which means that.
+
+00:34:16.100 --> 00:34:17.600
+They say that each data point that I
+
+00:34:17.600 --> 00:34:20.235
+observed is equally likely.
+
+00:34:20.235 --> 00:34:22.887
+So if I have 300 data points and each
+
+00:34:22.887 --> 00:34:24.518
+one has a probability of one out of
+
+00:34:24.518 --> 00:34:27.360
+300, and that will minimize my entropy.
+
+00:34:27.360 --> 00:34:29.660
+But it will also mean that basically
+
+00:34:29.660 --> 00:34:31.070
+all I can do is represent those
+
+00:34:31.070 --> 00:34:32.700
+particular data points and I won't have
+
+00:34:32.700 --> 00:34:34.540
+any generalization to new data.
+
+00:34:34.540 --> 00:34:37.386
+So I think that's a really good point
+
+00:34:37.386 --> 00:34:38.200
+to bring up.
+
+00:34:39.540 --> 00:34:42.970
+That the we have to like, always
+
+00:34:42.970 --> 00:34:45.430
+remember that the measurements that we
+
+00:34:45.430 --> 00:34:47.290
+make on data are not like true
+
+00:34:47.290 --> 00:34:47.560
+measurements.
+
+00:34:47.560 --> 00:34:48.012
+They're not.
+
+00:34:48.012 --> 00:34:49.585
+They don't tell us anything, or they
+
+00:34:49.585 --> 00:34:51.354
+tell us something, but they don't
+
+00:34:51.354 --> 00:34:52.746
+reveal the true distribution.
+
+00:34:52.746 --> 00:34:54.690
+They only reveal what we've estimated
+
+00:34:54.690 --> 00:34:55.939
+about the distribution.
+
+00:34:55.940 --> 00:34:57.907
+And those estimates depend not only on
+
+00:34:57.907 --> 00:34:59.519
+the data that we're measuring, but the
+
+00:34:59.520 --> 00:35:00.570
+way that we measure it.
+
+00:35:01.820 --> 00:35:04.593
+So that's like a really tricky, that's
+
+00:35:04.593 --> 00:35:07.590
+like a really tricky concept that is
+
+00:35:07.590 --> 00:35:09.329
+kind of like the main concept that.
+
+00:35:10.330 --> 00:35:12.280
+That I'm trying to illustrate.
+
+00:35:15.110 --> 00:35:17.257
+All right, so the entropy measures like
+
+00:35:17.257 --> 00:35:20.270
+how many bits are required to store an
+
+00:35:20.270 --> 00:35:22.872
+element of data, the true entropy.
+
+00:35:22.872 --> 00:35:25.320
+So the true entropy again, if they
+
+00:35:25.320 --> 00:35:27.250
+were, if we were able to know the
+
+00:35:27.250 --> 00:35:28.965
+distribution, which we almost never
+
+00:35:28.965 --> 00:35:29.350
+know.
+
+00:35:29.350 --> 00:35:31.960
+But if we knew it, and we had an ideal
+
+00:35:31.960 --> 00:35:34.230
+way to store the data, then the entropy
+
+00:35:34.230 --> 00:35:35.900
+tells us how many bits we would need in
+
+00:35:35.900 --> 00:35:37.390
+order to store that data in the most
+
+00:35:37.390 --> 00:35:38.750
+compressed format possible.
+
+00:35:43.500 --> 00:35:46.600
+So does this mean that the entropy is a
+
+00:35:46.600 --> 00:35:48.780
+measure of information?
+
+00:35:50.290 --> 00:35:50.970
+So.
+
+00:35:52.540 --> 00:35:54.419
+How many people would say that the
+
+00:35:54.420 --> 00:35:56.113
+entropy is a measure?
+
+00:35:56.113 --> 00:35:58.130
+Is the information that the data
+
+00:35:58.130 --> 00:35:59.140
+contains?
+
+00:36:00.740 --> 00:36:02.000
+If yes, raise your hand.
+
+00:36:04.860 --> 00:36:07.890
+If no raise, raise your hand.
+
+00:36:07.890 --> 00:36:10.260
+OK, so most people more people say not,
+
+00:36:10.260 --> 00:36:11.400
+so why not?
+
+00:36:13.870 --> 00:36:14.580
+Just measures.
+
+00:36:15.690 --> 00:36:16.130
+Cortana.
+
+00:36:19.330 --> 00:36:21.230
+The information environment more like.
+
+00:36:22.430 --> 00:36:25.340
+The incoming data has like that
+
+00:36:25.340 --> 00:36:25.710
+element.
+
+00:36:27.760 --> 00:36:29.580
+The company information communication,
+
+00:36:29.580 --> 00:36:32.200
+but not correct, right?
+
+00:36:32.200 --> 00:36:33.640
+Yeah, so I think that I think what
+
+00:36:33.640 --> 00:36:36.700
+you're saying is that the entropy
+
+00:36:36.700 --> 00:36:38.920
+measures essentially like how hard it
+
+00:36:38.920 --> 00:36:40.170
+is to predict some variable.
+
+00:36:40.820 --> 00:36:43.680
+But it doesn't mean that variable like
+
+00:36:43.680 --> 00:36:45.320
+tells us anything about anything else,
+
+00:36:45.320 --> 00:36:46.080
+right?
+
+00:36:46.080 --> 00:36:47.870
+It's just how hard this variable is
+
+00:36:47.870 --> 00:36:49.040
+fixed, right?
+
+00:36:49.040 --> 00:36:53.230
+And so you could say so again that both
+
+00:36:53.230 --> 00:36:54.680
+of those answers can be correct.
+
+00:36:55.530 --> 00:36:58.860
+For example, if I have a random array,
+
+00:36:58.860 --> 00:37:00.820
+you would probably say like.
+
+00:37:00.820 --> 00:37:02.210
+Intuitively this doesn't contain
+
+00:37:02.210 --> 00:37:02.863
+information, right?
+
+00:37:02.863 --> 00:37:05.370
+If I just say I generated this random
+
+00:37:05.370 --> 00:37:06.910
+variable, it's a bunch of zeros and
+
+00:37:06.910 --> 00:37:07.300
+ones.
+
+00:37:07.300 --> 00:37:09.260
+I 5050 chance it's each one.
+
+00:37:09.960 --> 00:37:13.120
+Here's a whole TB of this like random
+
+00:37:13.120 --> 00:37:15.325
+variable that I generated for you now.
+
+00:37:15.325 --> 00:37:16.810
+Like how much is this worth?
+
+00:37:17.430 --> 00:37:18.690
+You would probably be like, it's not
+
+00:37:18.690 --> 00:37:20.080
+really worth anything because it
+
+00:37:20.080 --> 00:37:21.926
+doesn't like tell me anything about
+
+00:37:21.926 --> 00:37:23.290
+anything else, right?
+
+00:37:23.290 --> 00:37:26.700
+And so the IT contains in this case,
+
+00:37:26.700 --> 00:37:29.060
+like knowing the value of this random
+
+00:37:29.060 --> 00:37:30.907
+variable only gives me information
+
+00:37:30.907 --> 00:37:32.250
+about itself, it doesn't give me
+
+00:37:32.250 --> 00:37:33.410
+information about anything else.
+
+00:37:34.210 --> 00:37:36.390
+And so information is always a relative
+
+00:37:36.390 --> 00:37:37.040
+term, right?
+
+00:37:37.840 --> 00:37:41.335
+Information is the amount of
+
+00:37:41.335 --> 00:37:43.630
+uncertainty about something that's
+
+00:37:43.630 --> 00:37:45.760
+reduced by knowing something else.
+
+00:37:45.760 --> 00:37:48.190
+So if I know the temperature of today,
+
+00:37:48.190 --> 00:37:50.090
+then that might reduce my uncertainty
+
+00:37:50.090 --> 00:37:52.810
+about the temperature of tomorrow or
+
+00:37:52.810 --> 00:37:54.010
+whether it's a good idea to wear a
+
+00:37:54.010 --> 00:37:55.740
+jacket when I go out, right?
+
+00:37:55.740 --> 00:37:57.330
+So the temperature of today gives me
+
+00:37:57.330 --> 00:37:58.383
+information about that.
+
+00:37:58.383 --> 00:38:00.839
+But the but knowing the temperature of
+
+00:38:00.839 --> 00:38:02.495
+today does not give me any information
+
+00:38:02.495 --> 00:38:04.260
+about who's the President of the United
+
+00:38:04.260 --> 00:38:04.895
+States.
+
+00:38:04.895 --> 00:38:07.040
+So it has information about certain
+
+00:38:07.040 --> 00:38:07.930
+things and doesn't have.
+
+00:38:07.980 --> 00:38:09.300
+Information about other things.
+
+00:38:12.900 --> 00:38:14.570
+So we have this measure called
+
+00:38:14.570 --> 00:38:19.410
+information gain, which is a measure of
+
+00:38:19.410 --> 00:38:23.221
+how much information does one variable
+
+00:38:23.221 --> 00:38:25.711
+give me about another variable, or one
+
+00:38:25.711 --> 00:38:28.201
+set of variables give me about another
+
+00:38:28.201 --> 00:38:29.979
+variable or set of variables.
+
+00:38:31.690 --> 00:38:35.820
+So the information gain of Y given X is
+
+00:38:35.820 --> 00:38:36.480
+the.
+
+00:38:37.590 --> 00:38:39.790
+Is the entropy of Y my initial
+
+00:38:39.790 --> 00:38:41.515
+uncertainty and being able to predict
+
+00:38:41.515 --> 00:38:41.850
+Y?
+
+00:38:42.860 --> 00:38:44.980
+Minus the entropy of Y given X.
+
+00:38:45.570 --> 00:38:47.230
+In other words, like how uncertain am I
+
+00:38:47.230 --> 00:38:50.320
+still about why after I know X and this
+
+00:38:50.320 --> 00:38:51.970
+difference is the information gain.
+
+00:38:51.970 --> 00:38:54.940
+So if I want to know what is the
+
+00:38:54.940 --> 00:38:57.280
+temperature going to be in 5 minutes.
+
+00:38:57.280 --> 00:38:59.389
+So knowing the temperature right now
+
+00:38:59.390 --> 00:39:01.450
+has super high information gain, it
+
+00:39:01.450 --> 00:39:04.350
+reduces my entropy almost completely.
+
+00:39:04.350 --> 00:39:05.530
+Where knowing the temperature right
+
+00:39:05.530 --> 00:39:07.418
+now, if I want to know the temperature
+
+00:39:07.418 --> 00:39:09.900
+in 10 days, my information gain would
+
+00:39:09.900 --> 00:39:10.380
+be low.
+
+00:39:10.380 --> 00:39:12.233
+It might tell me like some guess about
+
+00:39:12.233 --> 00:39:13.890
+what season it is that can help a
+
+00:39:13.890 --> 00:39:15.809
+little bit, but it's not going to be
+
+00:39:15.810 --> 00:39:16.400
+very.
+
+00:39:16.790 --> 00:39:18.450
+Highly predictive of the temperature in
+
+00:39:18.450 --> 00:39:18.910
+10 days.
+
+00:39:22.270 --> 00:39:25.140
+So we can so we can also, of course
+
+00:39:25.140 --> 00:39:25.980
+compute this.
+
+00:39:27.800 --> 00:39:28.590
+With code.
+
+00:39:28.590 --> 00:39:30.430
+So here I'm computing the information
+
+00:39:30.430 --> 00:39:32.560
+gain over binary variables.
+
+00:39:34.990 --> 00:39:39.020
+Of some feature I = 0 in this case.
+
+00:39:40.280 --> 00:39:41.800
+With respect to male, female.
+
+00:39:41.800 --> 00:39:44.120
+So how much does a particular variable
+
+00:39:44.120 --> 00:39:46.390
+tell me about whether whether a Penguin
+
+00:39:46.390 --> 00:39:47.840
+is male or female?
+
+00:39:49.010 --> 00:39:51.430
+And so here this was a little bit
+
+00:39:51.430 --> 00:39:53.600
+tricky code wise because there was also
+
+00:39:53.600 --> 00:39:56.760
+unknown so I have to like ignore the
+
+00:39:56.760 --> 00:39:57.680
+unknown case.
+
+00:39:57.680 --> 00:40:00.947
+So I take I create a variable Y that is
+
+00:40:00.947 --> 00:40:03.430
+one if the Penguin is male and -, 1 if
+
+00:40:03.430 --> 00:40:04.090
+it's female.
+
+00:40:05.160 --> 00:40:09.567
+And then I extracted out the values of
+
+00:40:09.567 --> 00:40:09.905
+XI.
+
+00:40:09.905 --> 00:40:13.150
+So I got XI where I = 0 in this case.
+
+00:40:13.150 --> 00:40:16.822
+And then I took all the Xis where Y was
+
+00:40:16.822 --> 00:40:19.321
+male, where it was male and where it
+
+00:40:19.321 --> 00:40:19.945
+was female.
+
+00:40:19.945 --> 00:40:21.507
+So this is the male.
+
+00:40:21.507 --> 00:40:23.159
+I happens to correspond to island of
+
+00:40:23.160 --> 00:40:23.690
+Bisco.
+
+00:40:23.690 --> 00:40:26.260
+So this is like the bit string of the
+
+00:40:26.260 --> 00:40:26.550
+weather.
+
+00:40:26.550 --> 00:40:28.650
+Penguins came from the island of Biscoe
+
+00:40:28.650 --> 00:40:30.490
+and were male, and this is whether they
+
+00:40:30.490 --> 00:40:32.190
+came from Cisco and they were female.
+
+00:40:34.110 --> 00:40:34.740
+And.
+
+00:40:35.810 --> 00:40:37.870
+Then I'm counting how many times I see
+
+00:40:37.870 --> 00:40:40.232
+either male or female Penguins, and so
+
+00:40:40.232 --> 00:40:42.127
+I can use that to get the probability
+
+00:40:42.127 --> 00:40:43.236
+that a Penguin is male.
+
+00:40:43.236 --> 00:40:44.700
+And of course the probability that's
+
+00:40:44.700 --> 00:40:46.092
+female is 1 minus that.
+
+00:40:46.092 --> 00:40:48.850
+So I compute my entropy of Penguins
+
+00:40:48.850 --> 00:40:50.400
+being male or female.
+
+00:40:50.400 --> 00:40:53.220
+So probability y = 1 times log
+
+00:40:53.220 --> 00:40:54.289
+probability that minus.
+
+00:40:55.070 --> 00:40:58.123
+1 minus probability of y = 1 times log
+
+00:40:58.123 --> 00:40:58.760
+probability of that.
+
+00:41:00.390 --> 00:41:03.180
+And then I can get the probability that
+
+00:41:03.180 --> 00:41:07.340
+a male Penguin.
+
+00:41:07.500 --> 00:41:08.260
+
+
+00:41:09.460 --> 00:41:13.190
+So this is the this is just the
+
+00:41:13.190 --> 00:41:15.562
+probability that a Penguin comes from
+
+00:41:15.562 --> 00:41:15.875
+Biscoe.
+
+00:41:15.875 --> 00:41:17.940
+So the probability that the sum of all
+
+00:41:17.940 --> 00:41:20.015
+the male and female Penguins that do
+
+00:41:20.015 --> 00:41:21.603
+not, sorry that do not come from Biscoe
+
+00:41:21.603 --> 00:41:22.230
+that are 0.
+
+00:41:22.940 --> 00:41:24.070
+Divide by the number.
+
+00:41:25.070 --> 00:41:27.720
+And then I can get the probability that
+
+00:41:27.720 --> 00:41:28.820
+a Penguin is.
+
+00:41:29.950 --> 00:41:33.006
+Is male given that it doesn't come from
+
+00:41:33.006 --> 00:41:34.450
+Biscoe, and the probability that
+
+00:41:34.450 --> 00:41:36.410
+Penguin is male given that it comes
+
+00:41:36.410 --> 00:41:37.150
+from Biscoe.
+
+00:41:38.010 --> 00:41:40.550
+And then finally I can compute my
+
+00:41:40.550 --> 00:41:44.630
+entropy of Y given X, which I can say
+
+00:41:44.630 --> 00:41:46.240
+there's different ways to express that.
+
+00:41:46.240 --> 00:41:49.465
+But here I express as the sum over the
+
+00:41:49.465 --> 00:41:52.490
+probability of whether the Penguin
+
+00:41:52.490 --> 00:41:54.845
+comes from VISCO or not, times the
+
+00:41:54.845 --> 00:41:57.730
+probability that the Penguin is male or
+
+00:41:57.730 --> 00:42:00.290
+female given that it came from Biscoe
+
+00:42:00.290 --> 00:42:03.016
+or not, times the log of that
+
+00:42:03.016 --> 00:42:03.274
+probability.
+
+00:42:03.274 --> 00:42:05.975
+And so I end up with this big term
+
+00:42:05.975 --> 00:42:08.300
+here, and so that's the entropy.
+
+00:42:08.350 --> 00:42:12.720
+The island given or the entropy of the
+
+00:42:12.720 --> 00:42:15.510
+sex of the Penguin given, whether it
+
+00:42:15.510 --> 00:42:16.640
+came from Biscoe or not.
+
+00:42:17.240 --> 00:42:20.080
+And if I compare those, I see that I
+
+00:42:20.080 --> 00:42:21.297
+gained very little information.
+
+00:42:21.297 --> 00:42:23.560
+So the so knowing what island of
+
+00:42:23.560 --> 00:42:25.080
+Penguin came from doesn't tell me much
+
+00:42:25.080 --> 00:42:26.440
+about whether it's male or female.
+
+00:42:26.440 --> 00:42:28.420
+That's not like a huge surprise,
+
+00:42:28.420 --> 00:42:30.710
+although it's not always exactly true.
+
+00:42:30.710 --> 00:42:36.508
+For example, something 49% of people in
+
+00:42:36.508 --> 00:42:40.450
+the United States are male and I think
+
+00:42:40.450 --> 00:42:42.880
+51% of people in China are male.
+
+00:42:42.880 --> 00:42:44.570
+So sometimes there is a slight
+
+00:42:44.570 --> 00:42:45.980
+distribution difference depending on
+
+00:42:45.980 --> 00:42:47.150
+where you come from and maybe that.
+
+00:42:47.230 --> 00:42:49.220
+The figure for some kinds of animals.
+
+00:42:50.000 --> 00:42:51.740
+But in any case, like quantitatively we
+
+00:42:51.740 --> 00:42:54.010
+can see knowing this island.
+
+00:42:54.010 --> 00:42:55.690
+Knowing that island tells me almost
+
+00:42:55.690 --> 00:42:57.230
+nothing about whether Penguins likely
+
+00:42:57.230 --> 00:42:58.850
+to be male or female, so the
+
+00:42:58.850 --> 00:43:00.530
+information gain is very small.
+
+00:43:01.730 --> 00:43:03.230
+Because it doesn't reduce the number of
+
+00:43:03.230 --> 00:43:05.160
+bits I need to represent whether each
+
+00:43:05.160 --> 00:43:06.360
+Penguin is male or female.
+
+00:43:08.780 --> 00:43:10.590
+We can also compute the information
+
+00:43:10.590 --> 00:43:13.510
+gain in a continuous case, so.
+
+00:43:15.230 --> 00:43:18.550
+So here I have again the same initial
+
+00:43:18.550 --> 00:43:21.500
+processing to get the male, female, Y
+
+00:43:21.500 --> 00:43:22.020
+value.
+
+00:43:22.640 --> 00:43:24.980
+And now I do a step through the
+
+00:43:24.980 --> 00:43:28.110
+different discrete ranges of the
+
+00:43:28.110 --> 00:43:29.600
+variable Kalman length.
+
+00:43:30.710 --> 00:43:32.590
+And I compute the probability that a
+
+00:43:32.590 --> 00:43:34.300
+variable falls within this range.
+
+00:43:36.100 --> 00:43:38.855
+And I also compute the probability that
+
+00:43:38.855 --> 00:43:41.300
+a Penguin is male given that it falls
+
+00:43:41.300 --> 00:43:42.060
+within a range.
+
+00:43:42.670 --> 00:43:46.480
+So that is, out of how many times does
+
+00:43:46.480 --> 00:43:49.240
+the value fall within this range and
+
+00:43:49.240 --> 00:43:52.330
+the Penguin is male divide by the
+
+00:43:52.330 --> 00:43:53.855
+number of times that it falls within
+
+00:43:53.855 --> 00:43:55.665
+this range, which was the last element
+
+00:43:55.665 --> 00:43:56.440
+of PX.
+
+00:43:57.160 --> 00:43:59.320
+And then I add this like very tiny
+
+00:43:59.320 --> 00:44:01.110
+value to avoid divide by zero.
+
+00:44:02.830 --> 00:44:05.300
+And then so now I have the probability
+
+00:44:05.300 --> 00:44:07.340
+that's male given each possible like
+
+00:44:07.340 --> 00:44:08.350
+little range of X.
+
+00:44:09.100 --> 00:44:12.590
+And I can then compute the entropy as a
+
+00:44:12.590 --> 00:44:15.606
+over probability of X times
+
+00:44:15.606 --> 00:44:16.209
+probability.
+
+00:44:16.210 --> 00:44:19.240
+Or the entropy of Y is computed as
+
+00:44:19.240 --> 00:44:22.243
+before and then the entropy of Y given
+
+00:44:22.243 --> 00:44:24.681
+X is the sum over probability of X
+
+00:44:24.681 --> 00:44:26.815
+times probability of Y given X times
+
+00:44:26.815 --> 00:44:29.330
+the log probability of Y given X.
+
+00:44:31.430 --> 00:44:32.880
+And then I can look at the information
+
+00:44:32.880 --> 00:44:33.770
+gain.
+
+00:44:33.770 --> 00:44:38.660
+So here here's the probability of X.
+
+00:44:39.040 --> 00:44:39.780
+
+
+00:44:40.400 --> 00:44:43.160
+And here's the probability of y = 1
+
+00:44:43.160 --> 00:44:43.680
+given X.
+
+00:44:44.570 --> 00:44:46.380
+And the reason that these are different
+
+00:44:46.380 --> 00:44:49.608
+ranges is that is that probability of X
+
+00:44:49.608 --> 00:44:52.260
+is a continuous variable, so it should
+
+00:44:52.260 --> 00:44:55.371
+integrate to one, and probability of y
+
+00:44:55.371 --> 00:44:58.600
+= 1 given X will be somewhere between
+
+00:44:58.600 --> 00:44:59.830
+zero and one.
+
+00:44:59.830 --> 00:45:01.442
+But it's only modeling this discrete
+
+00:45:01.442 --> 00:45:04.390
+variable, so given a particular XY is
+
+00:45:04.390 --> 00:45:06.429
+equal to either zero or one, and so
+
+00:45:06.430 --> 00:45:07.880
+sometimes the probability could be as
+
+00:45:07.880 --> 00:45:10.073
+high as one and other times it could be
+
+00:45:10.073 --> 00:45:10.381
+0.
+
+00:45:10.381 --> 00:45:12.660
+It's just a discrete value condition on
+
+00:45:12.660 --> 00:45:14.690
+X where X is a continuous.
+
+00:45:14.750 --> 00:45:17.280
+Variable, but it's sometimes useful to
+
+00:45:17.280 --> 00:45:20.150
+plot these together, so lots and lots
+
+00:45:20.150 --> 00:45:21.890
+of times when I'm trying to solve some
+
+00:45:21.890 --> 00:45:24.180
+new problem, one of the first things
+
+00:45:24.180 --> 00:45:26.510
+I'll do is create plots like this for
+
+00:45:26.510 --> 00:45:28.020
+the different features to give me an
+
+00:45:28.020 --> 00:45:30.650
+understanding of like how linearly.
+
+00:45:30.880 --> 00:45:32.725
+How linear is the relationship between
+
+00:45:32.725 --> 00:45:37.280
+the features and the and the thing that
+
+00:45:37.280 --> 00:45:38.160
+I'm trying to predict?
+
+00:45:39.070 --> 00:45:40.780
+In this case, for example, there's a
+
+00:45:40.780 --> 00:45:44.220
+strong relationship, so if the common
+
+00:45:44.220 --> 00:45:47.920
+length is very high, then this Penguin
+
+00:45:47.920 --> 00:45:49.310
+is almost certainly male.
+
+00:45:51.280 --> 00:45:52.330
+If the.
+
+00:45:53.150 --> 00:45:55.980
+If the common length is moderately
+
+00:45:55.980 --> 00:45:59.090
+high, then it's pretty likely to be
+
+00:45:59.090 --> 00:45:59.840
+female.
+
+00:46:00.900 --> 00:46:05.219
+And if it's even lower, if it's even
+
+00:46:05.220 --> 00:46:09.610
+smaller, then it's kind of like roughly
+
+00:46:09.610 --> 00:46:12.522
+more evenly likely to be male and
+
+00:46:12.522 --> 00:46:13.040
+female.
+
+00:46:13.040 --> 00:46:16.360
+So again, this may not be too, this
+
+00:46:16.360 --> 00:46:17.990
+might not be super intuitive, like, why
+
+00:46:17.990 --> 00:46:19.320
+do we have this step here?
+
+00:46:19.320 --> 00:46:22.454
+But if you take my hypothesis that the
+
+00:46:22.454 --> 00:46:25.580
+adult male Penguins have large common
+
+00:46:25.580 --> 00:46:27.481
+links, and then adult female Penguins
+
+00:46:27.481 --> 00:46:29.010
+have the next largest.
+
+00:46:30.070 --> 00:46:31.670
+And then so there's like these
+
+00:46:31.670 --> 00:46:32.980
+different modes of the distribution,
+
+00:46:32.980 --> 00:46:35.260
+see these three humps, so this could be
+
+00:46:35.260 --> 00:46:37.630
+the adult male, adult female and the
+
+00:46:37.630 --> 00:46:39.380
+kids, which have a big range because
+
+00:46:39.380 --> 00:46:41.290
+they're different, different ages.
+
+00:46:41.960 --> 00:46:44.300
+And if you know it's a kid, then it
+
+00:46:44.300 --> 00:46:44.640
+doesn't.
+
+00:46:44.640 --> 00:46:45.820
+You don't really know if it's male or
+
+00:46:45.820 --> 00:46:46.150
+female.
+
+00:46:46.150 --> 00:46:48.080
+It could be a different, you know,
+
+00:46:48.080 --> 00:46:51.980
+bigger child or smaller child will kind
+
+00:46:51.980 --> 00:46:54.290
+of conflate with the gender.
+
+00:46:56.150 --> 00:46:57.932
+So if I looked at this then I might say
+
+00:46:57.932 --> 00:46:58.861
+I don't want to.
+
+00:46:58.861 --> 00:47:00.610
+I don't want to use this as part of a
+
+00:47:00.610 --> 00:47:01.197
+logistic regressor.
+
+00:47:01.197 --> 00:47:03.650
+I need a tree or I need to like cluster
+
+00:47:03.650 --> 00:47:05.455
+it or process this feature in some way
+
+00:47:05.455 --> 00:47:06.990
+to make this information more
+
+00:47:06.990 --> 00:47:08.600
+informative for my machine learning
+
+00:47:08.600 --> 00:47:08.900
+model.
+
+00:47:10.510 --> 00:47:12.515
+I'll take a break in just a minute, but
+
+00:47:12.515 --> 00:47:13.930
+I want to show him one more thing
+
+00:47:13.930 --> 00:47:14.560
+first.
+
+00:47:14.560 --> 00:47:20.330
+So again, like this is very subject to
+
+00:47:20.330 --> 00:47:22.310
+how I estimate these distributions.
+
+00:47:22.310 --> 00:47:26.225
+So if I choose a different step size,
+
+00:47:26.225 --> 00:47:28.737
+so here I choose a broader one, then I
+
+00:47:28.737 --> 00:47:29.940
+get a different probability
+
+00:47:29.940 --> 00:47:32.060
+distribution, I get a different P of X
+
+00:47:32.060 --> 00:47:33.480
+and I get a different conditional
+
+00:47:33.480 --> 00:47:34.230
+distribution.
+
+00:47:34.910 --> 00:47:38.135
+This P of X it's probably a bit too
+
+00:47:38.135 --> 00:47:40.150
+this step size is probably too big
+
+00:47:40.150 --> 00:47:41.760
+because it seemed like there were three
+
+00:47:41.760 --> 00:47:44.530
+modes which I can sort of interpret in
+
+00:47:44.530 --> 00:47:45.050
+some way.
+
+00:47:45.050 --> 00:47:47.500
+Making some guess where here I just had
+
+00:47:47.500 --> 00:47:49.690
+one mode I like basically smoothed out
+
+00:47:49.690 --> 00:47:52.270
+the whole distribution and I get a very
+
+00:47:52.270 --> 00:47:56.240
+different kind of like very much
+
+00:47:56.240 --> 00:47:59.385
+smoother probability of y = 1 given X
+
+00:47:59.385 --> 00:48:00.010
+estimate.
+
+00:48:00.010 --> 00:48:02.082
+So just using my intuition I think this
+
+00:48:02.082 --> 00:48:03.580
+is probably a better estimate than
+
+00:48:03.580 --> 00:48:05.500
+this, but it's something that you could
+
+00:48:05.500 --> 00:48:06.050
+validate.
+
+00:48:06.110 --> 00:48:07.440
+With their validation set, for example,
+
+00:48:07.440 --> 00:48:09.430
+to see given these two estimates of the
+
+00:48:09.430 --> 00:48:11.520
+distribution, which one better reflects
+
+00:48:11.520 --> 00:48:12.850
+some held out set of data.
+
+00:48:12.850 --> 00:48:14.850
+That's one way that you can that you
+
+00:48:14.850 --> 00:48:16.850
+can try to get a more concrete answer
+
+00:48:16.850 --> 00:48:18.210
+to what's the better way.
+
+00:48:19.350 --> 00:48:21.437
+And then these different ways of
+
+00:48:21.437 --> 00:48:22.910
+estimating this distribution lead to
+
+00:48:22.910 --> 00:48:24.190
+very different estimates of the
+
+00:48:24.190 --> 00:48:25.150
+information gain.
+
+00:48:25.150 --> 00:48:28.142
+So estimating it with a smoother with
+
+00:48:28.142 --> 00:48:30.543
+this bigger step size gives me a
+
+00:48:30.543 --> 00:48:32.920
+smoother distribution that reduces my
+
+00:48:32.920 --> 00:48:35.200
+information gain quite significantly.
+
+00:48:39.480 --> 00:48:42.110
+So let's take let's take a 2 minute
+
+00:48:42.110 --> 00:48:42.680
+break.
+
+00:48:42.680 --> 00:48:46.200
+I've been talking a lot and you can
+
+00:48:46.200 --> 00:48:47.910
+think about this like how can the
+
+00:48:47.910 --> 00:48:49.430
+information gain be different?
+
+00:48:50.300 --> 00:48:52.100
+Depending on our step size and what
+
+00:48:52.100 --> 00:48:55.240
+does this kind of like imply about our
+
+00:48:55.240 --> 00:48:56.420
+machine learning algorithms.
+
+00:48:57.900 --> 00:48:59.390
+Right, so I'll set it.
+
+00:48:59.390 --> 00:49:01.480
+I'll set a timer.
+
+00:49:01.480 --> 00:49:03.240
+Feel free to get up and stretch and
+
+00:49:03.240 --> 00:49:05.170
+talk or clear your brain or whatever.
+
+00:49:59.230 --> 00:50:01.920
+So why is the information, our
+
+00:50:01.920 --> 00:50:04.655
+information gain get improved from this
+
+00:50:04.655 --> 00:50:06.060
+slide to this slide?
+
+00:50:06.060 --> 00:50:08.430
+I'm kind of confused like these are
+
+00:50:08.430 --> 00:50:09.275
+different things.
+
+00:50:09.275 --> 00:50:11.630
+So here it's here, it's based on the
+
+00:50:11.630 --> 00:50:12.246
+common length.
+
+00:50:12.246 --> 00:50:13.970
+So I'm measuring the information gain
+
+00:50:13.970 --> 00:50:15.645
+of the Cullman length.
+
+00:50:15.645 --> 00:50:17.850
+So how much does Coleman length tell me
+
+00:50:17.850 --> 00:50:19.900
+about the male, female and then in the
+
+00:50:19.900 --> 00:50:20.870
+previous slide?
+
+00:50:21.280 --> 00:50:22.515
+Based on the island.
+
+00:50:22.515 --> 00:50:25.723
+So if I know in one case it's like if I
+
+00:50:25.723 --> 00:50:27.300
+know what island that came from, how
+
+00:50:27.300 --> 00:50:29.505
+much does that tell me about its
+
+00:50:29.505 --> 00:50:31.080
+whether it's male or female.
+
+00:50:31.080 --> 00:50:32.850
+And in this case, if I know the Cullman
+
+00:50:32.850 --> 00:50:34.456
+length, how much does that tell me
+
+00:50:34.456 --> 00:50:35.832
+about whether it's male or female?
+
+00:50:35.832 --> 00:50:36.750
+I see I see.
+
+00:50:36.750 --> 00:50:39.093
+So we changed to another feature.
+
+00:50:39.093 --> 00:50:39.794
+Yeah.
+
+00:50:39.794 --> 00:50:42.770
+So that I should have said that more
+
+00:50:42.770 --> 00:50:43.090
+clearly.
+
+00:50:43.090 --> 00:50:45.690
+But the I here is the feature index.
+
+00:50:45.940 --> 00:50:46.353
+I see.
+
+00:50:46.353 --> 00:50:47.179
+I see, I see.
+
+00:50:47.180 --> 00:50:48.360
+That makes sense, yeah.
+
+00:50:50.170 --> 00:50:53.689
+OK, it says we need like a check,
+
+00:50:53.690 --> 00:50:53.980
+right?
+
+00:50:53.980 --> 00:50:54.805
+Yeah.
+
+00:50:54.805 --> 00:50:57.483
+So I'm able to make the decision tree
+
+00:50:57.483 --> 00:51:00.390
+and I get, I get this like I get the
+
+00:51:00.390 --> 00:51:02.226
+first check is just less or equal to
+
+00:51:02.226 --> 00:51:05.560
+26, but the second check it differs
+
+00:51:05.560 --> 00:51:07.897
+from one side, it'll be like less than
+
+00:51:07.897 --> 00:51:10.530
+equal to 14.95 of depth and then one
+
+00:51:10.530 --> 00:51:11.476
+side it will be.
+
+00:51:11.476 --> 00:51:13.603
+So you want to look down on the tree
+
+00:51:13.603 --> 00:51:14.793
+here like here.
+
+00:51:14.793 --> 00:51:17.050
+You have basically a perfect
+
+00:51:17.050 --> 00:51:18.760
+classification here.
+
+00:51:18.820 --> 00:51:21.050
+Right here you have perfect
+
+00:51:21.050 --> 00:51:22.860
+classifications into Gen.
+
+00:51:22.860 --> 00:51:23.260
+2.
+
+00:51:24.000 --> 00:51:28.360
+And so these are two decisions that you
+
+00:51:28.360 --> 00:51:28.970
+could use.
+
+00:51:28.970 --> 00:51:30.460
+For example, right?
+
+00:51:30.460 --> 00:51:32.710
+Each of these paths give you a decision
+
+00:51:32.710 --> 00:51:33.590
+about whether it's a Gen.
+
+00:51:33.590 --> 00:51:34.330
+2 or not.
+
+00:51:36.470 --> 00:51:39.660
+So a decision is 1 path through the OR
+
+00:51:39.660 --> 00:51:41.650
+rule is like one path through the tree.
+
+00:51:42.660 --> 00:51:46.200
+So in so in the case of the work would
+
+00:51:46.200 --> 00:51:48.026
+you just because we need like a two
+
+00:51:48.026 --> 00:51:48.870
+check thing right?
+
+00:51:48.870 --> 00:51:50.793
+So are two check thing would be this
+
+00:51:50.793 --> 00:51:53.770
+and this for example if this is greater
+
+00:51:53.770 --> 00:51:57.010
+than that and if this is less than that
+
+00:51:57.010 --> 00:51:58.420
+then it's that.
+
+00:52:03.860 --> 00:52:06.510
+Yeah, I need to start, OK.
+
+00:52:08.320 --> 00:52:10.760
+Alright, so actually so one thing I
+
+00:52:10.760 --> 00:52:12.585
+want to clarify based is a question is
+
+00:52:12.585 --> 00:52:14.460
+that the things that I'm showing here
+
+00:52:14.460 --> 00:52:15.631
+are for different features.
+
+00:52:15.631 --> 00:52:17.595
+So I is the feature index.
+
+00:52:17.595 --> 00:52:19.390
+So the reason that these have different
+
+00:52:19.390 --> 00:52:21.303
+entropies, this was for island, we're
+
+00:52:21.303 --> 00:52:22.897
+here, I'm talking about Coleman length.
+
+00:52:22.897 --> 00:52:24.970
+So different features will give us
+
+00:52:24.970 --> 00:52:26.655
+different, different information gains
+
+00:52:26.655 --> 00:52:28.300
+about whether the Penguin is male or
+
+00:52:28.300 --> 00:52:30.753
+female and the particular feature index
+
+00:52:30.753 --> 00:52:32.270
+is just like here.
+
+00:52:34.260 --> 00:52:35.550
+All right, so.
+
+00:52:36.750 --> 00:52:39.380
+So why does someone have an answer?
+
+00:52:39.380 --> 00:52:41.655
+So why is it that the information gain
+
+00:52:41.655 --> 00:52:43.040
+is different depending on the step
+
+00:52:43.040 --> 00:52:43.285
+size?
+
+00:52:43.285 --> 00:52:45.050
+That seems a little bit unintuitive,
+
+00:52:45.050 --> 00:52:45.350
+right?
+
+00:52:45.350 --> 00:52:45.870
+Because.
+
+00:52:46.520 --> 00:52:47.560
+The same data.
+
+00:52:47.560 --> 00:52:48.730
+Why does it?
+
+00:52:48.730 --> 00:52:50.830
+Why does information gain depend on
+
+00:52:50.830 --> 00:52:51.290
+this?
+
+00:52:51.290 --> 00:52:52.110
+Yeah?
+
+00:52:52.600 --> 00:52:56.200
+If we have for a bigger step that we
+
+00:52:56.200 --> 00:52:58.130
+might overshoot and like, we might not
+
+00:52:58.130 --> 00:52:59.330
+capture those like.
+
+00:53:01.000 --> 00:53:03.400
+Local like optimized or like local?
+
+00:53:09.790 --> 00:53:10.203
+Right.
+
+00:53:10.203 --> 00:53:13.070
+So the answer was like, if we have a
+
+00:53:13.070 --> 00:53:15.930
+bigger step size, then we might like be
+
+00:53:15.930 --> 00:53:17.525
+grouping too many things together so
+
+00:53:17.525 --> 00:53:19.905
+that it no longer like contains the
+
+00:53:19.905 --> 00:53:21.610
+information that is needed to
+
+00:53:21.610 --> 00:53:24.580
+distinguish whether a Penguin is male
+
+00:53:24.580 --> 00:53:25.417
+or female, right?
+
+00:53:25.417 --> 00:53:27.515
+Or it contains less of that
+
+00:53:27.515 --> 00:53:28.590
+information, right.
+
+00:53:28.590 --> 00:53:30.560
+And so, like, the key concept that's
+
+00:53:30.560 --> 00:53:33.020
+really important to know is that.
+
+00:53:33.590 --> 00:53:34.240
+
+
+00:53:35.310 --> 00:53:37.820
+Is that the information gain?
+
+00:53:37.820 --> 00:53:41.008
+It depends on how we use the data.
+
+00:53:41.008 --> 00:53:43.130
+It depends on how we model the data.
+
+00:53:43.130 --> 00:53:45.110
+So that the information gain is not
+
+00:53:45.110 --> 00:53:47.400
+really inherent in the data itself or
+
+00:53:47.400 --> 00:53:48.400
+even in.
+
+00:53:48.400 --> 00:53:50.580
+It doesn't even depend on the.
+
+00:53:51.600 --> 00:53:54.290
+The true distribution between the data
+
+00:53:54.290 --> 00:53:56.600
+and the thing that we're trying to
+
+00:53:56.600 --> 00:53:57.190
+predict.
+
+00:53:57.190 --> 00:53:58.880
+So there may be a theoretical
+
+00:53:58.880 --> 00:54:00.730
+information gain, which is if you knew
+
+00:54:00.730 --> 00:54:03.360
+the true distribution of and Y then
+
+00:54:03.360 --> 00:54:04.570
+what would be the probability of Y
+
+00:54:04.570 --> 00:54:05.640
+given X?
+
+00:54:05.640 --> 00:54:08.370
+But in practice, we never know the true
+
+00:54:08.370 --> 00:54:08.750
+distribution.
+
+00:54:09.630 --> 00:54:12.540
+It's only the actual information gain
+
+00:54:12.540 --> 00:54:14.695
+depends on how we model the data, how
+
+00:54:14.695 --> 00:54:16.430
+we're able to squeeze the information
+
+00:54:16.430 --> 00:54:17.770
+out and make a prediction.
+
+00:54:17.770 --> 00:54:22.450
+For example, if I were like in China or
+
+00:54:22.450 --> 00:54:24.069
+something and I stopped somebody and I
+
+00:54:24.070 --> 00:54:27.270
+say, how do I get like over how do I
+
+00:54:27.270 --> 00:54:29.110
+get to this place and they start
+
+00:54:29.110 --> 00:54:31.490
+talking to me in Chinese and I have no
+
+00:54:31.490 --> 00:54:32.430
+idea what they're saying.
+
+00:54:33.080 --> 00:54:35.190
+They have like all the information is
+
+00:54:35.190 --> 00:54:36.390
+in that data.
+
+00:54:36.390 --> 00:54:38.390
+Somebody else could use that
+
+00:54:38.390 --> 00:54:40.070
+information to get where they want to
+
+00:54:40.070 --> 00:54:42.050
+go, but I can't use it because I don't
+
+00:54:42.050 --> 00:54:43.560
+have the right model for that data.
+
+00:54:43.560 --> 00:54:45.858
+So the information gained to me is 0,
+
+00:54:45.858 --> 00:54:47.502
+but the information gain is somebody
+
+00:54:47.502 --> 00:54:49.260
+else could be very high because of
+
+00:54:49.260 --> 00:54:49.926
+their model.
+
+00:54:49.926 --> 00:54:52.257
+And in the same way like we can take
+
+00:54:52.257 --> 00:54:54.870
+the same data and that data may have no
+
+00:54:54.870 --> 00:54:57.369
+information gain if we don't model it
+
+00:54:57.370 --> 00:54:58.970
+correctly, if we're not sure how to
+
+00:54:58.970 --> 00:55:01.520
+model it or use the data to extract our
+
+00:55:01.520 --> 00:55:02.490
+predictions.
+
+00:55:02.490 --> 00:55:03.070
+But.
+
+00:55:03.130 --> 00:55:05.670
+As we get better models, we're able to
+
+00:55:05.670 --> 00:55:07.830
+improve the information gain that we
+
+00:55:07.830 --> 00:55:09.130
+can get from that same data.
+
+00:55:09.130 --> 00:55:10.920
+And so that's basically like the goal
+
+00:55:10.920 --> 00:55:13.480
+of machine learning is to be able to
+
+00:55:13.480 --> 00:55:14.740
+model the data and model the
+
+00:55:14.740 --> 00:55:16.850
+relationships in a way that maximizes
+
+00:55:16.850 --> 00:55:19.350
+your information gain for predicting
+
+00:55:19.350 --> 00:55:20.470
+the thing that you're trying to
+
+00:55:20.470 --> 00:55:20.810
+predict.
+
+00:55:23.300 --> 00:55:26.760
+So again, we only have an empirical
+
+00:55:26.760 --> 00:55:28.630
+estimate based on the observed samples.
+
+00:55:30.680 --> 00:55:31.580
+And so.
+
+00:55:32.510 --> 00:55:34.000
+So we don't know the true information
+
+00:55:34.000 --> 00:55:36.070
+gain, just some estimated information
+
+00:55:36.070 --> 00:55:37.850
+gain based on estimated probability
+
+00:55:37.850 --> 00:55:38.560
+distributions.
+
+00:55:39.330 --> 00:55:40.930
+If we had more data, we could probably
+
+00:55:40.930 --> 00:55:42.200
+get a better estimate.
+
+00:55:43.950 --> 00:55:46.870
+And when we're trying to estimate
+
+00:55:46.870 --> 00:55:49.090
+things based on continuous variables,
+
+00:55:49.090 --> 00:55:50.270
+then we have different choices of
+
+00:55:50.270 --> 00:55:50.850
+models.
+
+00:55:50.850 --> 00:55:53.753
+And so there's a tradeoff between like
+
+00:55:53.753 --> 00:55:55.380
+over smoothing or simplifying the
+
+00:55:55.380 --> 00:55:57.770
+distribution and making overly
+
+00:55:57.770 --> 00:55:59.740
+confident predictions based on small
+
+00:55:59.740 --> 00:56:00.720
+data samples.
+
+00:56:00.720 --> 00:56:03.790
+So over here, I may have like very good
+
+00:56:03.790 --> 00:56:06.060
+estimates for the probability that X
+
+00:56:06.060 --> 00:56:07.840
+falls within this broader range.
+
+00:56:09.610 --> 00:56:11.770
+But maybe I have, like, smoothed out
+
+00:56:11.770 --> 00:56:13.960
+the important information for
+
+00:56:13.960 --> 00:56:15.630
+determining whether the Penguin is male
+
+00:56:15.630 --> 00:56:16.230
+or female.
+
+00:56:16.980 --> 00:56:19.090
+Maybe over here I have much more
+
+00:56:19.090 --> 00:56:20.590
+uncertain estimates of each of these
+
+00:56:20.590 --> 00:56:21.360
+probabilities.
+
+00:56:21.360 --> 00:56:23.090
+Like, is the probability distribution
+
+00:56:23.090 --> 00:56:23.920
+really that spiky?
+
+00:56:23.920 --> 00:56:24.990
+It's probably not.
+
+00:56:24.990 --> 00:56:26.000
+It's probably.
+
+00:56:26.000 --> 00:56:27.710
+This is probably a mixture of a few
+
+00:56:27.710 --> 00:56:28.460
+Gaussians.
+
+00:56:29.590 --> 00:56:31.490
+Which would be a smoother bumpy
+
+00:56:31.490 --> 00:56:34.430
+distribution, but on the other hand
+
+00:56:34.430 --> 00:56:35.770
+I've like preserved more of the
+
+00:56:35.770 --> 00:56:37.650
+information that is needed I would
+
+00:56:37.650 --> 00:56:40.860
+think to classify the Penguin as male
+
+00:56:40.860 --> 00:56:41.390
+or female.
+
+00:56:42.260 --> 00:56:43.420
+So there's this tradeoff.
+
+00:56:44.030 --> 00:56:46.010
+And this is just another simple example
+
+00:56:46.010 --> 00:56:47.540
+of the bias variance tradeoff.
+
+00:56:47.540 --> 00:56:51.740
+So here I have a I have a low variance
+
+00:56:51.740 --> 00:56:53.160
+but high bias estimate.
+
+00:56:53.160 --> 00:56:53.960
+My distribution.
+
+00:56:53.960 --> 00:56:55.100
+It's overly smooth.
+
+00:56:56.000 --> 00:57:00.290
+And over there I have a I have a higher
+
+00:57:00.290 --> 00:57:02.575
+variance, lower bias estimate of the
+
+00:57:02.575 --> 00:57:02.896
+distribution.
+
+00:57:02.896 --> 00:57:04.980
+And if I made the step size really
+
+00:57:04.980 --> 00:57:07.175
+small so I had that super spiky
+
+00:57:07.175 --> 00:57:08.973
+distribution, then that would be a
+
+00:57:08.973 --> 00:57:10.852
+really low bias but very high variance
+
+00:57:10.852 --> 00:57:11.135
+estimate.
+
+00:57:11.135 --> 00:57:13.250
+If I resampled it, I might get spikes
+
+00:57:13.250 --> 00:57:14.987
+in totally different places, so a
+
+00:57:14.987 --> 00:57:16.331
+totally different estimate of the
+
+00:57:16.331 --> 00:57:16.600
+distribution.
+
+00:57:20.910 --> 00:57:22.506
+And it's also important to note that
+
+00:57:22.506 --> 00:57:24.040
+the that when you're dealing with
+
+00:57:24.040 --> 00:57:25.570
+something like the bias variance
+
+00:57:25.570 --> 00:57:28.382
+tradeoff, in this case the complexity
+
+00:57:28.382 --> 00:57:29.985
+parameter is a step size.
+
+00:57:29.985 --> 00:57:32.200
+The optimal parameter depends on how
+
+00:57:32.200 --> 00:57:34.210
+much data we have, because the more
+
+00:57:34.210 --> 00:57:36.180
+data we have, the lower the variance of
+
+00:57:36.180 --> 00:57:39.870
+our estimate and so you the ideal
+
+00:57:39.870 --> 00:57:42.610
+complexity changes.
+
+00:57:42.610 --> 00:57:45.256
+So if I had lots of data, lots and lots
+
+00:57:45.256 --> 00:57:47.090
+and lots of data, then maybe I would
+
+00:57:47.090 --> 00:57:47.360
+choose.
+
+00:57:47.430 --> 00:57:49.745
+Step size even smaller than one because
+
+00:57:49.745 --> 00:57:51.660
+I could estimate those probabilities
+
+00:57:51.660 --> 00:57:53.143
+pretty well given all that data.
+
+00:57:53.143 --> 00:57:54.890
+I could estimate those little tiny
+
+00:57:54.890 --> 00:57:57.346
+ranges where if I'd weigh less data
+
+00:57:57.346 --> 00:57:59.060
+than maybe this would become the better
+
+00:57:59.060 --> 00:58:02.470
+choice because I otherwise my estimate
+
+00:58:02.470 --> 00:58:03.910
+was step size of 1 would just be too
+
+00:58:03.910 --> 00:58:04.580
+noisy.
+
+00:58:08.850 --> 00:58:11.050
+So the true probability distribution,
+
+00:58:11.050 --> 00:58:13.990
+entropy and I mean and information gain
+
+00:58:13.990 --> 00:58:14.880
+cannot be known.
+
+00:58:14.880 --> 00:58:16.820
+We can only try to make our best
+
+00:58:16.820 --> 00:58:17.420
+estimate.
+
+00:58:19.140 --> 00:58:21.550
+Alright, so that was all just focusing
+
+00:58:21.550 --> 00:58:22.620
+on X.
+
+00:58:22.620 --> 00:58:23.320
+Pretty much.
+
+00:58:23.320 --> 00:58:25.716
+A little bit of X&Y, but mostly X.
+
+00:58:25.716 --> 00:58:28.130
+So let's come back to how this fits
+
+00:58:28.130 --> 00:58:29.760
+into the whole machine learning
+
+00:58:29.760 --> 00:58:30.310
+framework.
+
+00:58:31.120 --> 00:58:34.240
+So we can say that one way that we can
+
+00:58:34.240 --> 00:58:35.100
+look at this function.
+
+00:58:35.100 --> 00:58:36.515
+Here we're trying to find parameters
+
+00:58:36.515 --> 00:58:39.720
+that minimize the loss of our models
+
+00:58:39.720 --> 00:58:41.020
+predictions compared to the ground
+
+00:58:41.020 --> 00:58:41.910
+truth prediction.
+
+00:58:42.840 --> 00:58:45.126
+One way that we can view this is that
+
+00:58:45.126 --> 00:58:48.380
+we're we're trying to maximize the
+
+00:58:48.380 --> 00:58:52.550
+information gain of Y given X, maybe
+
+00:58:52.550 --> 00:58:54.000
+with some additional constraints and
+
+00:58:54.000 --> 00:58:55.850
+priors that will improve the robustness
+
+00:58:55.850 --> 00:58:57.940
+to limited data that essentially like
+
+00:58:57.940 --> 00:59:00.290
+find that trade off for us in the bias
+
+00:59:00.290 --> 00:59:00.720
+variance.
+
+00:59:01.920 --> 00:59:02.590
+Trade off?
+
+00:59:03.910 --> 00:59:06.960
+So I could rewrite this if I'm if my
+
+00:59:06.960 --> 00:59:09.430
+loss function is the log probability of
+
+00:59:09.430 --> 00:59:10.090
+Y given X.
+
+00:59:11.840 --> 00:59:13.710
+Or let's just say for now that I
+
+00:59:13.710 --> 00:59:16.807
+rewrite this in terms of the in terms
+
+00:59:16.807 --> 00:59:18.940
+of the conditional entropy, or in terms
+
+00:59:18.940 --> 00:59:20.120
+of the information gain.
+
+00:59:20.920 --> 00:59:22.610
+So let's say I want to find the
+
+00:59:22.610 --> 00:59:23.990
+parameters Theta.
+
+00:59:23.990 --> 00:59:25.830
+That means that.
+
+00:59:26.770 --> 00:59:29.390
+Minimize my negative information gain,
+
+00:59:29.390 --> 00:59:31.730
+otherwise maximize my information gain,
+
+00:59:31.730 --> 00:59:32.010
+right?
+
+00:59:32.750 --> 00:59:36.690
+So that is, I want to maximize the
+
+00:59:36.690 --> 00:59:38.670
+difference between the entropy.
+
+00:59:39.690 --> 00:59:43.149
+And the entropy of Y the entropy of Y
+
+00:59:43.150 --> 00:59:45.240
+given X or equivalently, minimize the
+
+00:59:45.240 --> 00:59:45.920
+negative of that.
+
+00:59:46.760 --> 00:59:49.530
+Plus some kind of regularization or
+
+00:59:49.530 --> 00:59:52.300
+penalty on having unlikely parameters.
+
+00:59:52.300 --> 00:59:54.814
+So this would typically be like our
+
+00:59:54.814 --> 00:59:56.380
+squared penalty regularization.
+
+00:59:56.380 --> 00:59:57.480
+I mean our squared weight
+
+00:59:57.480 --> 00:59:58.290
+regularization.
+
+01:00:00.680 --> 01:00:06.810
+And if I write down what this entropy
+
+01:00:06.810 --> 01:00:08.810
+of Y given X is, then it's just the
+
+01:00:08.810 --> 01:00:12.019
+integral over all my data over all
+
+01:00:12.020 --> 01:00:15.839
+possible values X of probability of X
+
+01:00:15.840 --> 01:00:18.120
+times log probability of Y given X.
+
+01:00:19.490 --> 01:00:22.016
+I don't have a continuous distribution
+
+01:00:22.016 --> 01:00:23.685
+of XI don't have infinite samples.
+
+01:00:23.685 --> 01:00:25.810
+I just have an empirical sample.
+
+01:00:25.810 --> 01:00:27.750
+I have a few observations, some limited
+
+01:00:27.750 --> 01:00:30.220
+number of observations, and so my
+
+01:00:30.220 --> 01:00:33.040
+estimate of this of this integral
+
+01:00:33.040 --> 01:00:35.620
+becomes a sum over all the samples I do
+
+01:00:35.620 --> 01:00:36.050
+have.
+
+01:00:36.770 --> 01:00:38.700
+Assuming that each of these are all
+
+01:00:38.700 --> 01:00:40.850
+equally likely, then they'll just be
+
+01:00:40.850 --> 01:00:43.406
+some constant for the probability of X.
+
+01:00:43.406 --> 01:00:46.020
+So I can kind of like ignore that in
+
+01:00:46.020 --> 01:00:47.470
+relative terms, right?
+
+01:00:47.470 --> 01:00:49.830
+So I have a over the probability of X
+
+01:00:49.830 --> 01:00:51.170
+which would just be like one over
+
+01:00:51.170 --> 01:00:51.420
+north.
+
+01:00:52.260 --> 01:00:55.765
+Times the negative log probability of
+
+01:00:55.765 --> 01:00:58.510
+the label or of the thing that I'm
+
+01:00:58.510 --> 01:01:00.919
+trying to predict for the NTH sample
+
+01:01:00.920 --> 01:01:02.900
+given the features of the NTH sample.
+
+01:01:03.910 --> 01:01:06.814
+And this is exactly the cross entropy.
+
+01:01:06.814 --> 01:01:07.998
+This is.
+
+01:01:07.998 --> 01:01:10.180
+If Y is a discrete variable, for
+
+01:01:10.180 --> 01:01:11.663
+example, this would give us our cross
+
+01:01:11.663 --> 01:01:14.718
+entropy, or even if it's not, this is
+
+01:01:14.718 --> 01:01:15.331
+the.
+
+01:01:15.331 --> 01:01:18.870
+This is the negative log likelihood of
+
+01:01:18.870 --> 01:01:21.430
+my labels given the data, and so this
+
+01:01:21.430 --> 01:01:23.420
+gives us the loss term that we use
+
+01:01:23.420 --> 01:01:24.610
+typically for deep network
+
+01:01:24.610 --> 01:01:26.200
+classification or for logistic
+
+01:01:26.200 --> 01:01:26.850
+regression.
+
+01:01:27.470 --> 01:01:29.230
+And so it's exactly the same as
+
+01:01:29.230 --> 01:01:33.330
+maximizing the information gain of the
+
+01:01:33.330 --> 01:01:34.890
+variables that we're trying to predict
+
+01:01:34.890 --> 01:01:36.070
+given the features that we have
+
+01:01:36.070 --> 01:01:36.560
+available.
+
+01:01:39.760 --> 01:01:44.390
+So I've been like manually computing
+
+01:01:44.390 --> 01:01:46.207
+information gain and probabilities and
+
+01:01:46.207 --> 01:01:48.399
+stuff like that using code, but like
+
+01:01:48.400 --> 01:01:50.920
+kind of like hand coding lots of stuff.
+
+01:01:50.920 --> 01:01:53.370
+But that has its limitations.
+
+01:01:53.370 --> 01:01:56.670
+Like I can analyze 11 continuous
+
+01:01:56.670 --> 01:01:59.310
+variable or maybe 2 features at once
+
+01:01:59.310 --> 01:02:00.970
+and I can come up with some function
+
+01:02:00.970 --> 01:02:03.060
+and look at it and use my intuition and
+
+01:02:03.060 --> 01:02:04.570
+try to like create a good model based
+
+01:02:04.570 --> 01:02:05.176
+on that.
+
+01:02:05.176 --> 01:02:06.910
+But if you have thousands of variables,
+
+01:02:06.910 --> 01:02:08.535
+it's just like completely impractical
+
+01:02:08.535 --> 01:02:09.430
+to do this.
+
+01:02:09.490 --> 01:02:12.246
+Right, it would take forever to try to
+
+01:02:12.246 --> 01:02:14.076
+like plot all the different features
+
+01:02:14.076 --> 01:02:16.530
+and plot combinations and try to like
+
+01:02:16.530 --> 01:02:19.420
+manually explore this a big data set.
+
+01:02:19.790 --> 01:02:21.590
+And so.
+
+01:02:22.780 --> 01:02:24.370
+So we need more like automatic
+
+01:02:24.370 --> 01:02:26.110
+approaches to figure out how we can
+
+01:02:26.110 --> 01:02:29.890
+maximize the information gain of Y
+
+01:02:29.890 --> 01:02:31.140
+given X.
+
+01:02:31.140 --> 01:02:32.810
+And so that's basically why we have
+
+01:02:32.810 --> 01:02:33.843
+machine learning.
+
+01:02:33.843 --> 01:02:36.560
+So in machine learning, we're trying to
+
+01:02:36.560 --> 01:02:39.560
+build encoders sometimes to try to
+
+01:02:39.560 --> 01:02:41.740
+automatically transform X into some
+
+01:02:41.740 --> 01:02:44.160
+representation that makes it easier to
+
+01:02:44.160 --> 01:02:45.850
+extract information about why.
+
+01:02:47.110 --> 01:02:49.220
+Sometimes, sometimes people do this
+
+01:02:49.220 --> 01:02:49.517
+part.
+
+01:02:49.517 --> 01:02:51.326
+Sometimes we like hand code the
+
+01:02:51.326 --> 01:02:51.910
+features right.
+
+01:02:51.910 --> 01:02:54.270
+We create histogram, a gradient
+
+01:02:54.270 --> 01:03:00.120
+features for images, or we like I could
+
+01:03:00.120 --> 01:03:01.780
+take that common length and split it
+
+01:03:01.780 --> 01:03:03.409
+into three different ranges that I
+
+01:03:03.410 --> 01:03:06.185
+think represent like the adult male and
+
+01:03:06.185 --> 01:03:08.520
+adult female and children for example.
+
+01:03:09.480 --> 01:03:11.770
+But sometimes some methods do this
+
+01:03:11.770 --> 01:03:13.925
+automatically, and then second we have
+
+01:03:13.925 --> 01:03:15.940
+some decoder, something that predicts Y
+
+01:03:15.940 --> 01:03:18.050
+from X that automatically extracts the
+
+01:03:18.050 --> 01:03:18.730
+information.
+
+01:03:19.530 --> 01:03:22.260
+About why from X so our logistic
+
+01:03:22.260 --> 01:03:23.560
+regressor for example.
+
+01:03:26.940 --> 01:03:29.460
+The most powerful machine learning
+
+01:03:29.460 --> 01:03:32.870
+algorithms smoothly combine the feature
+
+01:03:32.870 --> 01:03:34.940
+extraction with the decoding, the
+
+01:03:34.940 --> 01:03:37.530
+prediction and offer controls or
+
+01:03:37.530 --> 01:03:39.370
+protections against overfitting.
+
+01:03:40.860 --> 01:03:43.910
+So they both try to make as good
+
+01:03:43.910 --> 01:03:45.190
+predictions as possible and the
+
+01:03:45.190 --> 01:03:47.290
+training data, and they try to do it in
+
+01:03:47.290 --> 01:03:49.920
+a way that is not like overfitting or
+
+01:03:49.920 --> 01:03:51.103
+leading to like high variance
+
+01:03:51.103 --> 01:03:52.300
+predictions that aren't going to
+
+01:03:52.300 --> 01:03:52.970
+generalize well.
+
+01:03:53.800 --> 01:03:55.750
+Random forests, for example.
+
+01:03:55.750 --> 01:03:58.070
+We have these deep trees that partition
+
+01:03:58.070 --> 01:04:00.830
+the feature space, chunk it up, and
+
+01:04:00.830 --> 01:04:03.445
+they optimize by optimizing the
+
+01:04:03.445 --> 01:04:04.180
+information gain.
+
+01:04:04.180 --> 01:04:04.770
+At each step.
+
+01:04:04.770 --> 01:04:06.140
+Those trees are trained to try to
+
+01:04:06.140 --> 01:04:07.830
+maximize the information gain for the
+
+01:04:07.830 --> 01:04:08.970
+variable that you're predicting.
+
+01:04:09.940 --> 01:04:13.300
+And until you get some full tree, and
+
+01:04:13.300 --> 01:04:15.910
+so individually each of these trees has
+
+01:04:15.910 --> 01:04:16.710
+low bias.
+
+01:04:16.710 --> 01:04:18.250
+It makes very accurate predictions on
+
+01:04:18.250 --> 01:04:20.480
+the training data, but high variance.
+
+01:04:20.480 --> 01:04:22.560
+You might get different trees if you
+
+01:04:22.560 --> 01:04:24.479
+were to resample the training data.
+
+01:04:25.350 --> 01:04:28.790
+And then in a random forest you train a
+
+01:04:28.790 --> 01:04:30.120
+whole bunch of these trees with
+
+01:04:30.120 --> 01:04:31.570
+different subsets of features.
+
+01:04:32.640 --> 01:04:34.010
+And then you average over their
+
+01:04:34.010 --> 01:04:36.550
+predictions and that averaging reduces
+
+01:04:36.550 --> 01:04:38.820
+the variance and so at the end of the
+
+01:04:38.820 --> 01:04:40.719
+day you have like a low variance, low
+
+01:04:40.720 --> 01:04:42.510
+bias predictor.
+
+01:04:44.560 --> 01:04:46.350
+The boosted trees similarly.
+
+01:04:47.560 --> 01:04:50.020
+You have shallow trees this time that
+
+01:04:50.020 --> 01:04:51.860
+kind of have low variance individually,
+
+01:04:51.860 --> 01:04:53.170
+at least if you have a relatively
+
+01:04:53.170 --> 01:04:54.640
+uniform data distribution.
+
+01:04:56.760 --> 01:04:59.000
+They again partition the feature space
+
+01:04:59.000 --> 01:05:01.250
+by optimizing the information gain, now
+
+01:05:01.250 --> 01:05:02.805
+using all the features but on a
+
+01:05:02.805 --> 01:05:04.120
+weighted data sample.
+
+01:05:04.120 --> 01:05:05.980
+And then each tree is trained on some
+
+01:05:05.980 --> 01:05:07.933
+weighted sample that focuses more on
+
+01:05:07.933 --> 01:05:09.560
+the examples that previous trees
+
+01:05:09.560 --> 01:05:12.245
+misclassified in order to reduce the
+
+01:05:12.245 --> 01:05:12.490
+bias.
+
+01:05:12.490 --> 01:05:14.240
+So that a sequence of these little
+
+01:05:14.240 --> 01:05:16.640
+trees actually has like much lower bias
+
+01:05:16.640 --> 01:05:18.690
+than the first tree because they're
+
+01:05:18.690 --> 01:05:20.200
+incrementally trying to improve their
+
+01:05:20.200 --> 01:05:21.120
+prediction function.
+
+01:05:22.780 --> 01:05:24.690
+Now, the downside of the boosted
+
+01:05:24.690 --> 01:05:27.950
+decision trees, or the danger of them
+
+01:05:27.950 --> 01:05:30.474
+is that they will tend to focus more
+
+01:05:30.474 --> 01:05:32.510
+and more on smaller and smaller amounts
+
+01:05:32.510 --> 01:05:33.840
+of data that are just really hard to
+
+01:05:33.840 --> 01:05:34.810
+misclassify.
+
+01:05:34.810 --> 01:05:36.410
+Maybe some of that data was mislabeled
+
+01:05:36.410 --> 01:05:38.040
+and so that's why it's so hard to
+
+01:05:38.040 --> 01:05:38.850
+classify.
+
+01:05:38.850 --> 01:05:40.626
+And maybe it's just very unusual.
+
+01:05:40.626 --> 01:05:43.250
+And so as you train lots of these
+
+01:05:43.250 --> 01:05:45.666
+boosted trees, eventually they start to
+
+01:05:45.666 --> 01:05:48.326
+focus on like a tiny subset of data and
+
+01:05:48.326 --> 01:05:50.080
+that can cause high variance
+
+01:05:50.080 --> 01:05:50.640
+overfitting.
+
+01:05:51.900 --> 01:05:54.075
+And so random forests are very robust
+
+01:05:54.075 --> 01:05:55.476
+to overfitting boosted trees.
+
+01:05:55.476 --> 01:05:57.700
+You still have to be careful, careful
+
+01:05:57.700 --> 01:06:00.060
+about how big those trees are and how
+
+01:06:00.060 --> 01:06:00.990
+many of them you train.
+
+01:06:02.650 --> 01:06:03.930
+And then deep networks.
+
+01:06:03.930 --> 01:06:05.709
+So we have deep networks.
+
+01:06:05.710 --> 01:06:08.066
+The mantra of deep networks is end to
+
+01:06:08.066 --> 01:06:11.342
+end learning, which means that you just
+
+01:06:11.342 --> 01:06:13.865
+give it your simplest features.
+
+01:06:13.865 --> 01:06:17.080
+You try not to like, preprocess it too
+
+01:06:17.080 --> 01:06:18.610
+much, because then you're just like
+
+01:06:18.610 --> 01:06:20.230
+removing some information.
+
+01:06:20.230 --> 01:06:21.856
+So you don't compute hog features, you
+
+01:06:21.856 --> 01:06:23.060
+just give it pixels.
+
+01:06:24.320 --> 01:06:29.420
+And then the optimization is jointly
+
+01:06:29.420 --> 01:06:32.100
+trying to process those raw inputs into
+
+01:06:32.100 --> 01:06:35.012
+useful features, and then to use those
+
+01:06:35.012 --> 01:06:37.140
+useful features to make predictions.
+
+01:06:37.790 --> 01:06:41.040
+On your on your for your for your final
+
+01:06:41.040 --> 01:06:41.795
+prediction.
+
+01:06:41.795 --> 01:06:44.290
+And it's a joint optimization.
+
+01:06:44.290 --> 01:06:47.010
+So random forests and boosted trees
+
+01:06:47.010 --> 01:06:50.245
+sort of do this, but they're kind of
+
+01:06:50.245 --> 01:06:50.795
+like greedy.
+
+01:06:50.795 --> 01:06:52.519
+You're trying to you're greedy
+
+01:06:52.520 --> 01:06:54.484
+decisions to try to optimize your to
+
+01:06:54.484 --> 01:06:56.070
+try to like select your features and
+
+01:06:56.070 --> 01:06:57.420
+then use them for predictions.
+
+01:06:58.100 --> 01:07:01.390
+While deep networks are like not
+
+01:07:01.390 --> 01:07:02.460
+greedy, they're trying to do this
+
+01:07:02.460 --> 01:07:05.460
+global optimization to try to maximize
+
+01:07:05.460 --> 01:07:07.750
+the information gain of your prediction
+
+01:07:07.750 --> 01:07:08.910
+given your features.
+
+01:07:09.670 --> 01:07:11.760
+And this end to end learning of
+
+01:07:11.760 --> 01:07:13.220
+learning your features and prediction
+
+01:07:13.220 --> 01:07:15.990
+at the same time is a big reason why
+
+01:07:15.990 --> 01:07:18.576
+people often say that deep learning is
+
+01:07:18.576 --> 01:07:20.869
+like the best or it can be the best
+
+01:07:20.870 --> 01:07:22.180
+algorithm, at least if you have enough
+
+01:07:22.180 --> 01:07:23.840
+data to apply it.
+
+01:07:25.250 --> 01:07:27.210
+The intermediate features represent
+
+01:07:27.210 --> 01:07:29.660
+transformations of the data that are
+
+01:07:29.660 --> 01:07:31.520
+more easily reusable than, like tree
+
+01:07:31.520 --> 01:07:32.609
+partitions, for example.
+
+01:07:32.610 --> 01:07:33.925
+So this is another big advantage that
+
+01:07:33.925 --> 01:07:36.433
+you can take, like the output at some
+
+01:07:36.433 --> 01:07:38.520
+intermediate layer, and you can reuse
+
+01:07:38.520 --> 01:07:40.450
+it for some other problem, because it
+
+01:07:40.450 --> 01:07:42.200
+represents some kind of like
+
+01:07:42.200 --> 01:07:44.446
+transformation of image pixels, for
+
+01:07:44.446 --> 01:07:47.510
+example, in a way that may be
+
+01:07:47.510 --> 01:07:49.090
+semantically meaningful or meaningful
+
+01:07:49.090 --> 01:07:51.250
+for a bunch of different tests.
+
+01:07:51.250 --> 01:07:52.870
+I'll talk about that more later.
+
+01:07:53.810 --> 01:07:54.660
+In another lecture.
+
+01:07:55.470 --> 01:07:57.460
+And then the structure of the network,
+
+01:07:57.460 --> 01:07:59.200
+for example like the number of nodes
+
+01:07:59.200 --> 01:08:01.290
+per layer is something that can be used
+
+01:08:01.290 --> 01:08:02.460
+to control the overfitting.
+
+01:08:02.460 --> 01:08:03.840
+So you can kind of like squeeze the
+
+01:08:03.840 --> 01:08:07.160
+representation into say 512 floating
+
+01:08:07.160 --> 01:08:09.660
+point values and that can prevent.
+
+01:08:10.820 --> 01:08:11.810
+Prevent overfitting.
+
+01:08:12.770 --> 01:08:15.000
+And then often deep learning is used in
+
+01:08:15.000 --> 01:08:17.200
+conjunction with massive data sets
+
+01:08:17.200 --> 01:08:18.730
+which help to further reduce the
+
+01:08:18.730 --> 01:08:20.210
+variance so that you can apply a very
+
+01:08:20.210 --> 01:08:21.250
+powerful models.
+
+01:08:22.140 --> 01:08:25.430
+Which have low bias and then rely on
+
+01:08:25.430 --> 01:08:27.240
+your enormous amount of data to reduce
+
+01:08:27.240 --> 01:08:28.050
+the variance.
+
+01:08:31.530 --> 01:08:33.855
+So in deep networks, the big challenge,
+
+01:08:33.855 --> 01:08:35.820
+the long standing problem with deep
+
+01:08:35.820 --> 01:08:37.400
+networks was the optimization.
+
+01:08:37.400 --> 01:08:40.530
+So how do we like optimize a many layer
+
+01:08:40.530 --> 01:08:41.070
+network?
+
+01:08:41.920 --> 01:08:45.500
+And one of the key ideas there was the
+
+01:08:45.500 --> 01:08:47.170
+stochastic gradient descent and back
+
+01:08:47.170 --> 01:08:47.723
+propagation.
+
+01:08:47.723 --> 01:08:50.720
+So we update the weights by summing the
+
+01:08:50.720 --> 01:08:52.875
+products of the error gradients from
+
+01:08:52.875 --> 01:08:55.150
+the input of the weight to the output
+
+01:08:55.150 --> 01:08:55.730
+of the network.
+
+01:08:55.730 --> 01:08:57.710
+So we basically trace all the paths
+
+01:08:57.710 --> 01:09:00.050
+from some weight into our prediction,
+
+01:09:00.050 --> 01:09:01.810
+and then based on that we see how this
+
+01:09:01.810 --> 01:09:03.416
+weight contributed to the error.
+
+01:09:03.416 --> 01:09:05.620
+And we make a small step to try to
+
+01:09:05.620 --> 01:09:07.850
+reduce that error based on a limited
+
+01:09:07.850 --> 01:09:09.510
+set of observations.
+
+01:09:11.150 --> 01:09:13.840
+And then the back propagation is a kind
+
+01:09:13.840 --> 01:09:16.060
+of dynamic program that efficiently
+
+01:09:16.060 --> 01:09:17.970
+reuses the weight gradient computations
+
+01:09:17.970 --> 01:09:21.020
+that each layer to predict the to do
+
+01:09:21.020 --> 01:09:23.460
+the weight updates for the previous
+
+01:09:23.460 --> 01:09:23.890
+layer.
+
+01:09:24.670 --> 01:09:27.389
+So this step, even though it feels
+
+01:09:27.390 --> 01:09:29.170
+backpropagation, feels kind of
+
+01:09:29.170 --> 01:09:31.750
+complicated computationally, it's very
+
+01:09:31.750 --> 01:09:32.480
+efficient.
+
+01:09:32.480 --> 01:09:33.520
+It takes almost.
+
+01:09:33.520 --> 01:09:35.940
+It takes about the same amount of time
+
+01:09:35.940 --> 01:09:38.090
+to update your weights as to do a
+
+01:09:38.090 --> 01:09:38.700
+prediction.
+
+01:09:41.550 --> 01:09:43.160
+The deep networks are composed of
+
+01:09:43.160 --> 01:09:44.225
+layers and activations.
+
+01:09:44.225 --> 01:09:46.590
+So we have these like we talked about
+
+01:09:46.590 --> 01:09:50.350
+sigmoid activations, where the downside
+
+01:09:50.350 --> 01:09:52.710
+the sigmoids map everything from zero
+
+01:09:52.710 --> 01:09:54.420
+to one, and they're downside is that
+
+01:09:54.420 --> 01:09:56.230
+the gradient is always less than zero.
+
+01:09:56.230 --> 01:09:57.800
+Even at the peak the gradient is only
+
+01:09:57.800 --> 01:10:01.000
+.25, and at the gradient is really
+
+01:10:01.000 --> 01:10:01.455
+small.
+
+01:10:01.455 --> 01:10:03.099
+So if you have a lot of layers.
+
+01:10:03.750 --> 01:10:07.740
+The since the gradient update is based
+
+01:10:07.740 --> 01:10:09.900
+on a product of these gradients along
+
+01:10:09.900 --> 01:10:11.800
+the path, then if you have a whole
+
+01:10:11.800 --> 01:10:13.360
+bunch of sigmoids, the gradient keeps
+
+01:10:13.360 --> 01:10:15.209
+getting smaller and smaller and smaller
+
+01:10:15.210 --> 01:10:17.320
+as you go earlier in the network until
+
+01:10:17.320 --> 01:10:19.226
+it's essentially 0 at the beginning of
+
+01:10:19.226 --> 01:10:20.680
+the network, which means that you can't
+
+01:10:20.680 --> 01:10:23.050
+optimize like the early weights.
+
+01:10:23.050 --> 01:10:25.220
+That's the vanishing gradient problem,
+
+01:10:25.220 --> 01:10:27.220
+and that was one of the things that got
+
+01:10:27.220 --> 01:10:29.160
+like neural networks stuck for many
+
+01:10:29.160 --> 01:10:29.800
+years.
+
+01:10:30.950 --> 01:10:31.440
+Can you?
+
+01:10:31.440 --> 01:10:32.210
+Yeah.
+
+01:10:33.700 --> 01:10:37.490
+OK so the OK so first like if you look
+
+01:10:37.490 --> 01:10:40.115
+at the gradient of a sigmoid it looks
+
+01:10:40.115 --> 01:10:41.030
+like this right?
+
+01:10:41.670 --> 01:10:45.460
+And at the peak it's only 25 and then
+
+01:10:45.460 --> 01:10:47.340
+at the extreme values it's extremely
+
+01:10:47.340 --> 01:10:48.175
+small.
+
+01:10:48.175 --> 01:10:51.290
+And So what that means is if you're
+
+01:10:51.290 --> 01:10:52.765
+gradient, let's say this is the end of
+
+01:10:52.765 --> 01:10:54.000
+the network and this is the beginning.
+
+01:10:54.650 --> 01:10:57.030
+Your gradient update for this weight
+
+01:10:57.030 --> 01:10:58.925
+will be based on a product of gradients
+
+01:10:58.925 --> 01:11:00.975
+for all the weights in between this
+
+01:11:00.975 --> 01:11:02.680
+weight and the output.
+
+01:11:03.360 --> 01:11:05.286
+And if they're all sigmoid activations,
+
+01:11:05.286 --> 01:11:07.190
+all of those gradients are going to be
+
+01:11:07.190 --> 01:11:08.072
+less than one.
+
+01:11:08.072 --> 01:11:09.860
+And so when you take the product of a
+
+01:11:09.860 --> 01:11:11.330
+whole bunch of numbers that are less
+
+01:11:11.330 --> 01:11:12.873
+than one, you end up with a really,
+
+01:11:12.873 --> 01:11:14.410
+really small number, right?
+
+01:11:14.410 --> 01:11:16.080
+And so that's why you can't train a
+
+01:11:16.080 --> 01:11:18.230
+deep network using sigmoids, because
+
+01:11:18.230 --> 01:11:20.975
+the gradients get they like vanish by
+
+01:11:20.975 --> 01:11:22.525
+the time you get to the earlier layers.
+
+01:11:22.525 --> 01:11:24.490
+And so the early layers don't train.
+
+01:11:25.120 --> 01:11:26.130
+And then you end up with these
+
+01:11:26.130 --> 01:11:27.960
+uninformative layers that are sitting
+
+01:11:27.960 --> 01:11:29.170
+between the inputs and the final
+
+01:11:29.170 --> 01:11:30.300
+layers, so you get really bad
+
+01:11:30.300 --> 01:11:30.910
+predictions.
+
+01:11:32.510 --> 01:11:34.390
+So that's a sigmoid problem.
+
+01:11:34.390 --> 01:11:36.980
+Very loose have a gradient of zero or
+
+01:11:36.980 --> 01:11:40.195
+one everywhere, so the relay looks like
+
+01:11:40.195 --> 01:11:40.892
+that.
+
+01:11:40.892 --> 01:11:43.996
+And in this part the gradient is 1, and
+
+01:11:43.996 --> 01:11:45.869
+this part the gradient is zero.
+
+01:11:45.870 --> 01:11:48.470
+They helped get networks deeper because
+
+01:11:48.470 --> 01:11:49.880
+that gradient of one is perfect.
+
+01:11:49.880 --> 01:11:51.150
+It doesn't get bigger, it doesn't get
+
+01:11:51.150 --> 01:11:52.010
+smaller as you like.
+
+01:11:52.010 --> 01:11:53.060
+Go through a bunch of ones.
+
+01:11:53.930 --> 01:11:56.310
+But the problem is that you can have
+
+01:11:56.310 --> 01:11:59.420
+these dead Railers where like a
+
+01:11:59.420 --> 01:12:02.140
+activation for some node is 0 for most
+
+01:12:02.140 --> 01:12:04.780
+of the data and then it has no gradient
+
+01:12:04.780 --> 01:12:07.240
+going into the weight and then it never
+
+01:12:07.240 --> 01:12:07.790
+changes.
+
+01:12:10.460 --> 01:12:13.690
+And so then the final thing that kind
+
+01:12:13.690 --> 01:12:15.179
+of fixed this problem was this skip
+
+01:12:15.180 --> 01:12:15.710
+connection.
+
+01:12:15.710 --> 01:12:18.000
+So the skip connections are a shortcut
+
+01:12:18.000 --> 01:12:19.950
+around different layers of the network
+
+01:12:19.950 --> 01:12:22.065
+so that the gradients can flow along
+
+01:12:22.065 --> 01:12:23.130
+the skip connections.
+
+01:12:23.880 --> 01:12:25.080
+All the way to the beginning of the
+
+01:12:25.080 --> 01:12:28.150
+network and with a gradient of 1.
+
+01:12:29.330 --> 01:12:30.900
+So that was that was coming with the
+
+01:12:30.900 --> 01:12:31.520
+Resnet.
+
+01:12:32.980 --> 01:12:33.750
+And then?
+
+01:12:35.510 --> 01:12:37.880
+And then I also talked about how SGD
+
+01:12:37.880 --> 01:12:39.185
+has like a lot of different variants
+
+01:12:39.185 --> 01:12:41.130
+and tricks to improve the speed of the
+
+01:12:41.130 --> 01:12:42.960
+instability of the optimization.
+
+01:12:42.960 --> 01:12:44.830
+For example, we have momentum so that
+
+01:12:44.830 --> 01:12:46.250
+if you keep getting weight updates in
+
+01:12:46.250 --> 01:12:47.730
+the same direction, those weight
+
+01:12:47.730 --> 01:12:49.394
+updates get faster and faster to
+
+01:12:49.394 --> 01:12:50.229
+improve the speed.
+
+01:12:51.200 --> 01:12:52.970
+You also have these normalizations so
+
+01:12:52.970 --> 01:12:54.690
+that you don't focus too much on
+
+01:12:54.690 --> 01:12:56.890
+updating weights updating particular
+
+01:12:56.890 --> 01:12:58.620
+weights, but you try to minimize the
+
+01:12:58.620 --> 01:13:00.420
+overall path of like how much each
+
+01:13:00.420 --> 01:13:01.120
+weight changes.
+
+01:13:02.610 --> 01:13:04.173
+I didn't talk about it, but another
+
+01:13:04.173 --> 01:13:06.320
+another strategy is gradient clipping,
+
+01:13:06.320 --> 01:13:08.990
+where you say that a gradient can't be
+
+01:13:08.990 --> 01:13:10.740
+too big and that can improve further,
+
+01:13:10.740 --> 01:13:13.515
+improve the strategy, the stability of
+
+01:13:13.515 --> 01:13:14.470
+the optimization.
+
+01:13:15.670 --> 01:13:18.570
+And then most commonly people either
+
+01:13:18.570 --> 01:13:21.410
+use SGD plus momentum or atom which is
+
+01:13:21.410 --> 01:13:23.290
+one of the last things I talked about.
+
+01:13:23.290 --> 01:13:25.740
+But there's more advanced methods range
+
+01:13:25.740 --> 01:13:27.760
+or rectified atom with gradient centric
+
+01:13:27.760 --> 01:13:29.860
+gradient centering and look ahead which
+
+01:13:29.860 --> 01:13:31.570
+have like a whole bunch of complicated
+
+01:13:31.570 --> 01:13:34.160
+strategies for doing the same thing but
+
+01:13:34.160 --> 01:13:35.420
+just a better search.
+
+01:13:39.250 --> 01:13:40.270
+Alright, let me see.
+
+01:13:40.270 --> 01:13:42.280
+All right, so I think you probably
+
+01:13:42.280 --> 01:13:44.459
+don't want me to skip this, so let me
+
+01:13:44.460 --> 01:13:45.330
+talk about.
+
+01:13:46.840 --> 01:13:48.860
+Let me just talk about this in the last
+
+01:13:48.860 --> 01:13:49.390
+minute.
+
+01:13:49.900 --> 01:13:53.860
+And so the so the mid term, so this is
+
+01:13:53.860 --> 01:13:55.703
+so the midterm is only going to be on
+
+01:13:55.703 --> 01:13:57.090
+things that we've already covered up to
+
+01:13:57.090 --> 01:13:57.280
+now.
+
+01:13:57.280 --> 01:13:58.935
+It's not going to be on anything that
+
+01:13:58.935 --> 01:14:00.621
+we cover in the next couple of days.
+
+01:14:00.621 --> 01:14:02.307
+The things that we cover in the next
+
+01:14:02.307 --> 01:14:03.550
+couple of days are important for
+
+01:14:03.550 --> 01:14:04.073
+homework three.
+
+01:14:04.073 --> 01:14:06.526
+So don't skip the lectures or anything,
+
+01:14:06.526 --> 01:14:08.986
+but they're not going to be on the
+
+01:14:08.986 --> 01:14:09.251
+midterm.
+
+01:14:09.251 --> 01:14:11.750
+So the midterms on March 9th and now
+
+01:14:11.750 --> 01:14:12.766
+it'll be on Prairie learn.
+
+01:14:12.766 --> 01:14:14.735
+So the exam will be open for most of
+
+01:14:14.735 --> 01:14:15.470
+the day.
+
+01:14:15.470 --> 01:14:17.600
+You don't come here to take it, you
+
+01:14:17.600 --> 01:14:19.650
+just take it somewhere else.
+
+01:14:20.070 --> 01:14:23.000
+Wherever you are and the exam will be
+
+01:14:23.000 --> 01:14:24.740
+75 minutes long or longer.
+
+01:14:24.740 --> 01:14:27.185
+If you have dress accommodations and
+
+01:14:27.185 --> 01:14:29.380
+you sent them to me, it's mainly going
+
+01:14:29.380 --> 01:14:30.730
+to be multiple choice or multiple
+
+01:14:30.730 --> 01:14:31.560
+select.
+
+01:14:31.560 --> 01:14:34.950
+There's no coding complex calculations
+
+01:14:34.950 --> 01:14:36.920
+in it, mainly is like conceptual.
+
+01:14:38.060 --> 01:14:40.350
+You can, as I said, take it at home.
+
+01:14:40.350 --> 01:14:42.670
+It's open book, so it's not cheating to
+
+01:14:42.670 --> 01:14:43.510
+during the exam.
+
+01:14:43.510 --> 01:14:45.630
+Consult your notes, look at practice
+
+01:14:45.630 --> 01:14:47.630
+questions and answers, look at slides,
+
+01:14:47.630 --> 01:14:48.590
+search on the Internet.
+
+01:14:48.590 --> 01:14:49.320
+That's all fine.
+
+01:14:50.030 --> 01:14:51.930
+It would be cheating if you were to
+
+01:14:51.930 --> 01:14:53.940
+talk to a classmate about the exam
+
+01:14:53.940 --> 01:14:55.550
+after one, but not both of you have
+
+01:14:55.550 --> 01:14:56.290
+taken it.
+
+01:14:56.290 --> 01:14:57.510
+So don't try to find out.
+
+01:14:57.510 --> 01:14:59.210
+Don't have like one person or I don't
+
+01:14:59.210 --> 01:15:00.120
+want to give you ideas.
+
+01:15:02.340 --> 01:15:02.970
+I.
+
+01:15:07.170 --> 01:15:09.080
+It's also cheating of course to get
+
+01:15:09.080 --> 01:15:10.490
+help from another person during the
+
+01:15:10.490 --> 01:15:10.910
+exam.
+
+01:15:10.910 --> 01:15:12.510
+So like if I found out about either of
+
+01:15:12.510 --> 01:15:13.960
+those things, it would be a big deal,
+
+01:15:13.960 --> 01:15:16.150
+but I prefer it.
+
+01:15:16.150 --> 01:15:17.260
+Just don't do it.
+
+01:15:17.370 --> 01:15:17.880
+
+
+01:15:19.180 --> 01:15:21.330
+And then also it's important to note
+
+01:15:21.330 --> 01:15:22.717
+you won't have time to look up all the
+
+01:15:22.717 --> 01:15:22.895
+answers.
+
+01:15:22.895 --> 01:15:24.680
+So it might sound like multiple choice.
+
+01:15:24.680 --> 01:15:25.855
+Open book is like really easy.
+
+01:15:25.855 --> 01:15:27.156
+You don't need to study it, just look
+
+01:15:27.156 --> 01:15:28.015
+it up when you get there.
+
+01:15:28.015 --> 01:15:28.930
+That will not work.
+
+01:15:28.930 --> 01:15:31.879
+I can almost guarantee you need to
+
+01:15:31.880 --> 01:15:34.060
+learn it ahead of time so that most of
+
+01:15:34.060 --> 01:15:36.380
+the answers and you may have time to
+
+01:15:36.380 --> 01:15:37.960
+look up one or two, but not more than
+
+01:15:37.960 --> 01:15:38.100
+that.
+
+01:15:40.030 --> 01:15:42.600
+I've got a list of some of the central
+
+01:15:42.600 --> 01:15:44.210
+topics here, and since we're at time,
+
+01:15:44.210 --> 01:15:45.880
+I'm not going to walk through it right
+
+01:15:45.880 --> 01:15:46.970
+now, but you can review it.
+
+01:15:46.970 --> 01:15:48.040
+The slides are posted.
+
+01:15:48.760 --> 01:15:50.540
+And then there's just some review
+
+01:15:50.540 --> 01:15:51.230
+questions.
+
+01:15:51.230 --> 01:15:53.215
+So you can look at these and I think
+
+01:15:53.215 --> 01:15:55.140
+the best way to study is to look at the
+
+01:15:55.140 --> 01:15:56.720
+practice questions that are posted on
+
+01:15:56.720 --> 01:15:59.744
+the website and use that not only to if
+
+01:15:59.744 --> 01:16:01.322
+those questions, but also how familiar
+
+01:16:01.322 --> 01:16:02.970
+are you with each of those concepts.
+
+01:16:02.970 --> 01:16:04.830
+And then go back and review the slides
+
+01:16:04.830 --> 01:16:07.447
+if you're like if you feel less
+
+01:16:07.447 --> 01:16:08.660
+familiar with the topic.
+
+01:16:09.620 --> 01:16:11.186
+Alright, so thank you.
+
+01:16:11.186 --> 01:16:13.330
+And on Thursday we're going to resume
+
+01:16:13.330 --> 01:16:15.783
+with CNN's and computer vision and
+
+01:16:15.783 --> 01:16:17.320
+we're getting into our section on
+
+01:16:17.320 --> 01:16:19.190
+applications, so like natural language
+
+01:16:19.190 --> 01:16:20.510
+processing and all kinds of other
+
+01:16:20.510 --> 01:16:20.860
+things.
+
+01:16:27.120 --> 01:16:30.250
+So we are.
+
+01:16:32.010 --> 01:16:34.620
+Start a code contains the code from
+
+01:16:34.620 --> 01:16:37.380
+homework wise that you normally load
+
+01:16:37.380 --> 01:16:39.650
+the data and numbers and yeah Aries,
+
+01:16:39.650 --> 01:16:42.220
+but essentially we should transform
+
+01:16:42.220 --> 01:16:44.360
+them into like my torch.
+