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+WEBVTT Kind: captions; Language: en-US
+
+NOTE
+Created on 2024-02-07T20:54:31.1029159Z by ClassTranscribe
+
+00:01:27.710 --> 00:01:28.060
+All right.
+
+00:01:28.060 --> 00:01:28.990
+Good morning, everybody.
+
+00:01:30.560 --> 00:01:32.070
+Hope you had a good weekend.
+
+00:01:33.880 --> 00:01:35.350
+Form relatively.
+
+00:01:37.950 --> 00:01:40.110
+Alright, so I'm going to get started.
+
+00:01:40.110 --> 00:01:42.920
+So in the previous lectures we've
+
+00:01:42.920 --> 00:01:44.820
+mainly learned about how to build and
+
+00:01:44.820 --> 00:01:46.220
+apply single models.
+
+00:01:46.220 --> 00:01:48.550
+So we talked about nearest neighbor,
+
+00:01:48.550 --> 00:01:50.915
+logistic regression, linear regression,
+
+00:01:50.915 --> 00:01:51.960
+and trees.
+
+00:01:51.960 --> 00:01:54.609
+And so now we're going to.
+
+00:01:55.570 --> 00:01:57.676
+Talk about how to build collection of
+
+00:01:57.676 --> 00:01:59.850
+models and use them for prediction.
+
+00:01:59.850 --> 00:02:02.045
+So that technique is called ensembles
+
+00:02:02.045 --> 00:02:05.280
+and ensemble is when you build a bunch
+
+00:02:05.280 --> 00:02:07.420
+of models and then you average their
+
+00:02:07.420 --> 00:02:09.430
+predictions or you train them in a way
+
+00:02:09.430 --> 00:02:11.040
+that they build on top of each other.
+
+00:02:12.270 --> 00:02:14.020
+So some of you might remember this show
+
+00:02:14.020 --> 00:02:15.160
+who wants to be a millionaire?
+
+00:02:16.100 --> 00:02:18.520
+The idea of this show is that there's a
+
+00:02:18.520 --> 00:02:20.490
+contestant and they get asked a series
+
+00:02:20.490 --> 00:02:22.280
+of questions and they have multiple
+
+00:02:22.280 --> 00:02:25.030
+choice answers and if they get it right
+
+00:02:25.030 --> 00:02:27.020
+then like the dollar value that they
+
+00:02:27.020 --> 00:02:29.429
+would bring home increases, but if they
+
+00:02:29.430 --> 00:02:31.280
+ever get it wrong, then they go home
+
+00:02:31.280 --> 00:02:31.910
+with nothing.
+
+00:02:32.620 --> 00:02:35.150
+And they had three forms of help.
+
+00:02:35.150 --> 00:02:37.070
+One of the forms was that they could
+
+00:02:37.070 --> 00:02:39.380
+eliminate 2 of the incorrect choices.
+
+00:02:40.230 --> 00:02:42.517
+Another form is that they could call a
+
+00:02:42.517 --> 00:02:42.769
+friend.
+
+00:02:42.770 --> 00:02:44.610
+So they would have like people.
+
+00:02:44.610 --> 00:02:46.210
+They would have friends at home that
+
+00:02:46.210 --> 00:02:48.695
+they think have like various expertise.
+
+00:02:48.695 --> 00:02:51.135
+And if they see a question that they
+
+00:02:51.135 --> 00:02:52.450
+think is really hard and they're not
+
+00:02:52.450 --> 00:02:54.220
+sure of the answer, they could choose
+
+00:02:54.220 --> 00:02:55.946
+which friend to call to give them the
+
+00:02:55.946 --> 00:02:56.199
+answer.
+
+00:02:57.660 --> 00:03:00.120
+The third, the third form of help they
+
+00:03:00.120 --> 00:03:02.910
+could get is pull the audience so.
+
+00:03:03.680 --> 00:03:06.475
+They would ask the audience to vote on
+
+00:03:06.475 --> 00:03:07.520
+the correct answer.
+
+00:03:08.120 --> 00:03:11.120
+And the audience would all vote, and
+
+00:03:11.120 --> 00:03:12.530
+then they could make a decision based
+
+00:03:12.530 --> 00:03:13.190
+on that.
+
+00:03:14.020 --> 00:03:15.745
+And they could use each of these forms
+
+00:03:15.745 --> 00:03:17.850
+of help one time.
+
+00:03:18.780 --> 00:03:22.369
+What do you which of these do you think
+
+00:03:22.370 --> 00:03:24.270
+between pull the audience and call a
+
+00:03:24.270 --> 00:03:24.900
+friend?
+
+00:03:24.900 --> 00:03:28.369
+Which of these do you think is a is
+
+00:03:28.370 --> 00:03:30.590
+more likely to give the correct answer?
+
+00:03:33.500 --> 00:03:35.020
+Alright, so how many people think it's
+
+00:03:35.020 --> 00:03:36.250
+pulled the audience?
+
+00:03:36.250 --> 00:03:39.710
+How many people think it's for in a
+
+00:03:39.710 --> 00:03:40.210
+friend?
+
+00:03:42.060 --> 00:03:45.000
+So the audience is correct, it's pulled
+
+00:03:45.000 --> 00:03:45.540
+the audience.
+
+00:03:46.250 --> 00:03:49.975
+But they did statistics.
+
+00:03:49.975 --> 00:03:52.910
+They looked at analysis of the show and
+
+00:03:52.910 --> 00:03:55.110
+on average the audience is correct 92%
+
+00:03:55.110 --> 00:03:56.240
+of the time.
+
+00:03:57.050 --> 00:03:59.750
+And call a friend is correct 66% of the
+
+00:03:59.750 --> 00:04:00.150
+time.
+
+00:04:01.780 --> 00:04:04.500
+So that might be kind of unintuitive,
+
+00:04:04.500 --> 00:04:06.970
+especially the margin, because.
+
+00:04:08.210 --> 00:04:09.574
+When you get to call a friend, you get
+
+00:04:09.574 --> 00:04:11.670
+to call somebody who you think knows
+
+00:04:11.670 --> 00:04:13.620
+about the particular subject matter.
+
+00:04:13.620 --> 00:04:15.300
+So they're an expert.
+
+00:04:15.300 --> 00:04:16.562
+You would expect that out of.
+
+00:04:16.562 --> 00:04:18.200
+You would expect that they would be
+
+00:04:18.200 --> 00:04:20.160
+much, much more informed than an
+
+00:04:20.160 --> 00:04:22.770
+average audience member who is just
+
+00:04:22.770 --> 00:04:24.020
+there to be entertained.
+
+00:04:24.880 --> 00:04:28.190
+But the audience is actually much more
+
+00:04:28.190 --> 00:04:30.160
+accurate and that kind of that
+
+00:04:30.160 --> 00:04:32.330
+demonstrates the power of ensembles
+
+00:04:32.330 --> 00:04:34.370
+that averaging multiple weak
+
+00:04:34.370 --> 00:04:35.140
+predictions.
+
+00:04:35.830 --> 00:04:38.720
+Is often more accurate than any single
+
+00:04:38.720 --> 00:04:40.003
+predictor, even if that single
+
+00:04:40.003 --> 00:04:41.150
+predictor is pretty good.
+
+00:04:43.770 --> 00:04:46.464
+It's possible to construct models to
+
+00:04:46.464 --> 00:04:48.269
+construct ensembles in different ways.
+
+00:04:48.270 --> 00:04:49.930
+One of the ways is that you
+
+00:04:49.930 --> 00:04:51.745
+independently train a bunch of
+
+00:04:51.745 --> 00:04:53.540
+different models by resampling the data
+
+00:04:53.540 --> 00:04:55.830
+or resampling features, and then you
+
+00:04:55.830 --> 00:04:57.846
+average those the predictions of those
+
+00:04:57.846 --> 00:04:58.119
+models.
+
+00:04:58.810 --> 00:05:00.780
+Another is that you incrementally train
+
+00:05:00.780 --> 00:05:02.860
+new models that try to fix the mistakes
+
+00:05:02.860 --> 00:05:04.350
+of the previous models.
+
+00:05:04.350 --> 00:05:05.750
+So we're going to talk about both of
+
+00:05:05.750 --> 00:05:06.170
+those.
+
+00:05:06.790 --> 00:05:08.800
+And they work on different principles.
+
+00:05:08.800 --> 00:05:10.758
+There's different reasons why each one
+
+00:05:10.758 --> 00:05:13.460
+is a is a reasonable choice.
+
+00:05:16.420 --> 00:05:19.740
+So the theory behind ensembles really
+
+00:05:19.740 --> 00:05:22.260
+comes down to this theorem called the
+
+00:05:22.260 --> 00:05:24.480
+balance, the bias variance tradeoff.
+
+00:05:25.110 --> 00:05:27.040
+And this is a really fundamental
+
+00:05:27.040 --> 00:05:28.850
+concept in machine learning.
+
+00:05:29.690 --> 00:05:31.730
+And I'm not going to go through the
+
+00:05:31.730 --> 00:05:33.780
+derivation of it, it's at this link
+
+00:05:33.780 --> 00:05:34.084
+here.
+
+00:05:34.084 --> 00:05:34.692
+It's not.
+
+00:05:34.692 --> 00:05:36.280
+It's not really, it's something that
+
+00:05:36.280 --> 00:05:37.960
+anyone could follow along, but it does
+
+00:05:37.960 --> 00:05:38.980
+take a while to get through it.
+
+00:05:40.280 --> 00:05:41.880
+But it's a really fundamental idea in
+
+00:05:41.880 --> 00:05:42.740
+machine learning.
+
+00:05:42.740 --> 00:05:46.390
+So in terms of one way that you can
+
+00:05:46.390 --> 00:05:48.560
+express it is in terms of the squared
+
+00:05:48.560 --> 00:05:49.610
+error of prediction.
+
+00:05:50.620 --> 00:05:53.220
+So for regression, but there's also
+
+00:05:53.220 --> 00:05:55.949
+equivalent theorems for classification,
+
+00:05:55.949 --> 00:05:59.450
+for 01 classification or for log
+
+00:05:59.450 --> 00:06:00.760
+probability loss.
+
+00:06:01.870 --> 00:06:04.460
+And it all works out to the same thing,
+
+00:06:04.460 --> 00:06:06.080
+which is that you're expected test
+
+00:06:06.080 --> 00:06:06.670
+error.
+
+00:06:06.670 --> 00:06:08.599
+So what this means is that.
+
+00:06:09.350 --> 00:06:11.490
+If you were to randomly choose some
+
+00:06:11.490 --> 00:06:13.410
+number of samples from the general
+
+00:06:13.410 --> 00:06:14.680
+distribution of data.
+
+00:06:15.900 --> 00:06:18.530
+Then the expected error that you would
+
+00:06:18.530 --> 00:06:20.410
+get for the model that you've trained
+
+00:06:20.410 --> 00:06:24.230
+on your sample of data compared to what
+
+00:06:24.230 --> 00:06:25.260
+it should have predicted.
+
+00:06:26.680 --> 00:06:29.560
+Has three different components, so one
+
+00:06:29.560 --> 00:06:30.910
+component is the variance.
+
+00:06:31.590 --> 00:06:34.095
+The variance is that if UV sampled that
+
+00:06:34.095 --> 00:06:36.510
+same amount of data multiple times from
+
+00:06:36.510 --> 00:06:38.590
+the general distribution, you'd get
+
+00:06:38.590 --> 00:06:40.390
+different data samples and that would
+
+00:06:40.390 --> 00:06:41.920
+lead to different models that make
+
+00:06:41.920 --> 00:06:43.660
+different predictions on the same test
+
+00:06:43.660 --> 00:06:44.000
+data.
+
+00:06:44.730 --> 00:06:46.710
+So you have some variance in your
+
+00:06:46.710 --> 00:06:47.180
+prediction.
+
+00:06:47.180 --> 00:06:48.470
+That's due to the randomness of
+
+00:06:48.470 --> 00:06:49.600
+sampling your model.
+
+00:06:49.600 --> 00:06:52.049
+Or it could be due to if you have a
+
+00:06:52.050 --> 00:06:53.023
+randomized optimization.
+
+00:06:53.023 --> 00:06:54.390
+It could also be due to the
+
+00:06:54.390 --> 00:06:56.060
+randomization of the optimization.
+
+00:06:57.910 --> 00:07:00.360
+So this is a variance mainly due to
+
+00:07:00.360 --> 00:07:02.580
+resampling data of your model.
+
+00:07:03.580 --> 00:07:05.760
+Compared to your expected model.
+
+00:07:05.760 --> 00:07:08.919
+So this is how the sum of the average
+
+00:07:08.920 --> 00:07:12.310
+square distance between the predictions
+
+00:07:12.310 --> 00:07:15.240
+of an individual model and the average
+
+00:07:15.240 --> 00:07:17.080
+over all possible models that you would
+
+00:07:17.080 --> 00:07:18.500
+learn from sampling the data many
+
+00:07:18.500 --> 00:07:18.940
+times.
+
+00:07:20.570 --> 00:07:23.270
+Then there's a skip over here for now.
+
+00:07:23.270 --> 00:07:25.347
+Then there's a bias component squared.
+
+00:07:25.347 --> 00:07:28.690
+So the bias is if you were to sample
+
+00:07:28.690 --> 00:07:31.820
+the data infinite times, train your
+
+00:07:31.820 --> 00:07:33.375
+infinite models and average them, then
+
+00:07:33.375 --> 00:07:35.497
+you get this expected prediction.
+
+00:07:35.497 --> 00:07:37.940
+So it's the expected the average
+
+00:07:37.940 --> 00:07:39.850
+prediction of all of those infinite
+
+00:07:39.850 --> 00:07:41.240
+models that you trained with the same
+
+00:07:41.240 --> 00:07:41.949
+amount of data.
+
+00:07:43.010 --> 00:07:44.460
+And if you look at the difference
+
+00:07:44.460 --> 00:07:46.790
+between that and the true prediction,
+
+00:07:46.790 --> 00:07:48.030
+then that's your bias.
+
+00:07:49.220 --> 00:07:53.070
+So if you have no bias, then obviously
+
+00:07:53.070 --> 00:07:55.655
+if you have no bias this would be 0.
+
+00:07:55.655 --> 00:07:57.379
+If on average your models would
+
+00:07:57.380 --> 00:07:59.095
+converge to the true answer, this will
+
+00:07:59.095 --> 00:07:59.700
+be 0.
+
+00:07:59.700 --> 00:08:01.660
+But if your models tend to predict too
+
+00:08:01.660 --> 00:08:04.050
+high or too low on average, then this
+
+00:08:04.050 --> 00:08:05.110
+will be nonzero.
+
+00:08:06.440 --> 00:08:07.970
+And then finally there's the noise.
+
+00:08:07.970 --> 00:08:10.710
+So this is kind of like the irreducible
+
+00:08:10.710 --> 00:08:13.000
+error due to the problem that it might
+
+00:08:13.000 --> 00:08:14.780
+be that for the exact same input
+
+00:08:14.780 --> 00:08:16.060
+there's different outputs that are
+
+00:08:16.060 --> 00:08:17.380
+possible, like if you're trying to
+
+00:08:17.380 --> 00:08:20.205
+predict temperature or read characters
+
+00:08:20.205 --> 00:08:22.390
+or something like that, the features
+
+00:08:22.390 --> 00:08:24.250
+are not sufficient to completely
+
+00:08:24.250 --> 00:08:26.150
+identify the correct answer.
+
+00:08:26.970 --> 00:08:29.390
+So there's these three parts to the
+
+00:08:29.390 --> 00:08:29.690
+error.
+
+00:08:29.690 --> 00:08:31.330
+There's the variance due to limited
+
+00:08:31.330 --> 00:08:34.069
+data in your models due to the
+
+00:08:34.070 --> 00:08:35.800
+randomness in a model.
+
+00:08:35.800 --> 00:08:38.083
+That's either due to randomly sampling
+
+00:08:38.083 --> 00:08:40.040
+the data or due to your optimization.
+
+00:08:40.660 --> 00:08:42.340
+There's the bias, which is due to the
+
+00:08:42.340 --> 00:08:44.770
+inability of your model to fit the true
+
+00:08:44.770 --> 00:08:45.390
+solution.
+
+00:08:46.080 --> 00:08:48.740
+And there's a noise which is due to the
+
+00:08:48.740 --> 00:08:50.160
+problem characteristics or the
+
+00:08:50.160 --> 00:08:51.840
+inability to make a perfect prediction
+
+00:08:51.840 --> 00:08:52.600
+from the features.
+
+00:08:54.920 --> 00:08:55.410
+Yeah.
+
+00:08:57.940 --> 00:09:02.930
+So here, so why is a particular?
+
+00:09:04.210 --> 00:09:08.110
+That particular label assigned to X&Y
+
+00:09:08.110 --> 00:09:12.260
+bar is the average of all the labels
+
+00:09:12.260 --> 00:09:14.390
+that you would that could be assigned
+
+00:09:14.390 --> 00:09:15.260
+to ex.
+
+00:09:15.260 --> 00:09:18.337
+So for example, if you had imagine that
+
+00:09:18.337 --> 00:09:20.700
+you had the exact same, let's say your
+
+00:09:20.700 --> 00:09:22.600
+prediction predicting temperature based
+
+00:09:22.600 --> 00:09:23.640
+on the last five days.
+
+00:09:24.360 --> 00:09:26.480
+And you saw that exact same scenario of
+
+00:09:26.480 --> 00:09:29.675
+the last five days like 15 times, but
+
+00:09:29.675 --> 00:09:31.620
+you had different next day
+
+00:09:31.620 --> 00:09:32.340
+temperatures.
+
+00:09:32.960 --> 00:09:35.683
+So why would be like one of those next
+
+00:09:35.683 --> 00:09:37.190
+day temperatures and why bar is the
+
+00:09:37.190 --> 00:09:38.780
+average of those next day temperatures?
+
+00:09:39.980 --> 00:09:40.460
+Question.
+
+00:09:43.200 --> 00:09:44.820
+How is your model?
+
+00:09:44.820 --> 00:09:48.684
+So HD is a model that's trained on a
+
+00:09:48.684 --> 00:09:51.310
+sample on a DF sample of the
+
+00:09:51.310 --> 00:09:51.950
+distribution.
+
+00:09:53.210 --> 00:09:56.310
+And H bar is the average of all such
+
+00:09:56.310 --> 00:09:56.680
+models.
+
+00:10:03.740 --> 00:10:07.270
+So the bias and variance is illustrated
+
+00:10:07.270 --> 00:10:08.215
+here.
+
+00:10:08.215 --> 00:10:10.500
+So imagine that you're trying to shoot
+
+00:10:10.500 --> 00:10:11.040
+a target.
+
+00:10:11.700 --> 00:10:13.833
+Then if you have low bias and low
+
+00:10:13.833 --> 00:10:15.243
+variance, it means that all your shots
+
+00:10:15.243 --> 00:10:17.470
+are clustered in the center of the
+
+00:10:17.470 --> 00:10:17.774
+target.
+
+00:10:17.774 --> 00:10:20.265
+If you have low bias and high variance
+
+00:10:20.265 --> 00:10:22.910
+means that the average of your shots is
+
+00:10:22.910 --> 00:10:24.640
+in the center of your target, but the
+
+00:10:24.640 --> 00:10:26.260
+shots are more widely distributed.
+
+00:10:27.890 --> 00:10:31.360
+If you have high bias and low variance,
+
+00:10:31.360 --> 00:10:33.210
+it means that your shots are clustered
+
+00:10:33.210 --> 00:10:34.730
+tight together, but they're off the
+
+00:10:34.730 --> 00:10:35.160
+center.
+
+00:10:35.940 --> 00:10:37.580
+And if you have high bias and high
+
+00:10:37.580 --> 00:10:40.298
+variance, then both they're dispersed,
+
+00:10:40.298 --> 00:10:42.560
+dispersed, and they're off the center.
+
+00:10:44.230 --> 00:10:45.920
+So you can see from even from this
+
+00:10:45.920 --> 00:10:48.924
+illustration that obviously low bias
+
+00:10:48.924 --> 00:10:51.840
+and low variance is the best, but both
+
+00:10:51.840 --> 00:10:54.267
+variance and bias caused some error,
+
+00:10:54.267 --> 00:10:56.590
+and high bias and high variance has the
+
+00:10:56.590 --> 00:10:57.950
+greatest average error.
+
+00:11:02.670 --> 00:11:04.988
+You also often see a expressed in a
+
+00:11:04.988 --> 00:11:07.147
+plot like this, where you're looking at
+
+00:11:07.147 --> 00:11:09.654
+your model complexity and this is like.
+
+00:11:09.654 --> 00:11:10.990
+This is kind of like a classic
+
+00:11:10.990 --> 00:11:13.580
+overfitting plot, so this model
+
+00:11:13.580 --> 00:11:15.240
+complexity could for example be the
+
+00:11:15.240 --> 00:11:16.440
+height of your tree.
+
+00:11:17.540 --> 00:11:19.420
+So if you train a tree with two leaf
+
+00:11:19.420 --> 00:11:22.930
+nodes with just a height of 1, then
+
+00:11:22.930 --> 00:11:24.754
+you're going to have a very low
+
+00:11:24.754 --> 00:11:25.016
+variance.
+
+00:11:25.016 --> 00:11:26.900
+If you were to resample the data many
+
+00:11:26.900 --> 00:11:29.259
+times and train that short tree, you
+
+00:11:29.260 --> 00:11:30.790
+would very likely get a very similar
+
+00:11:30.790 --> 00:11:33.304
+tree every single time, so the variance
+
+00:11:33.304 --> 00:11:33.980
+is low.
+
+00:11:33.980 --> 00:11:34.870
+That's the blue curve.
+
+00:11:35.760 --> 00:11:37.100
+But the bias is high.
+
+00:11:37.100 --> 00:11:38.580
+You're unlikely to make very good
+
+00:11:38.580 --> 00:11:40.070
+predictions with that really short
+
+00:11:40.070 --> 00:11:40.880
+tree.
+
+00:11:40.880 --> 00:11:43.275
+Even if you averaged an infinite number
+
+00:11:43.275 --> 00:11:44.189
+of them, you would still.
+
+00:11:44.189 --> 00:11:45.570
+You would still have a lot of error.
+
+00:11:46.960 --> 00:11:49.520
+As you increase the depth of the tree,
+
+00:11:49.520 --> 00:11:51.290
+your bias drops.
+
+00:11:51.290 --> 00:11:53.232
+You're able to make better predictions
+
+00:11:53.232 --> 00:11:56.030
+on your on average.
+
+00:11:57.250 --> 00:11:59.340
+But the variance starts to increase.
+
+00:11:59.340 --> 00:12:01.030
+The trees start to look more different
+
+00:12:01.030 --> 00:12:01.920
+from each other.
+
+00:12:01.920 --> 00:12:04.780
+So if you train a full tree so that
+
+00:12:04.780 --> 00:12:06.990
+there's one data point per leaf node,
+
+00:12:06.990 --> 00:12:08.410
+then the trees are going to look pretty
+
+00:12:08.410 --> 00:12:10.230
+different when you resample the data
+
+00:12:10.230 --> 00:12:11.550
+because you'll have different data
+
+00:12:11.550 --> 00:12:12.080
+samples.
+
+00:12:13.850 --> 00:12:16.460
+So eventually, at some point you reach
+
+00:12:16.460 --> 00:12:19.616
+some ideal situation where the bias
+
+00:12:19.616 --> 00:12:21.677
+plus the bias squared plus the variance
+
+00:12:21.677 --> 00:12:23.940
+is minimized, and that's when you'd
+
+00:12:23.940 --> 00:12:25.510
+want to, like, stop if you're trying to
+
+00:12:25.510 --> 00:12:26.165
+choose hyperparameters.
+
+00:12:26.165 --> 00:12:29.530
+And if you train more complex models,
+
+00:12:29.530 --> 00:12:31.330
+it's going to continue to reduce the
+
+00:12:31.330 --> 00:12:32.925
+bias, but the increase in variance is
+
+00:12:32.925 --> 00:12:35.326
+going to cause your test error to
+
+00:12:35.326 --> 00:12:35.629
+increase.
+
+00:12:39.100 --> 00:12:41.404
+So if you're thinking about it in terms
+
+00:12:41.404 --> 00:12:45.510
+of a single model, really this, then
+
+00:12:45.510 --> 00:12:47.111
+you would be thinking about it in terms
+
+00:12:47.111 --> 00:12:49.190
+of the plot that I just showed where
+
+00:12:49.190 --> 00:12:50.690
+you're trying to figure out like what
+
+00:12:50.690 --> 00:12:52.330
+complexity, if it's a model that can
+
+00:12:52.330 --> 00:12:54.450
+have varying complexity trees or neural
+
+00:12:54.450 --> 00:12:57.327
+networks, like how complex should my
+
+00:12:57.327 --> 00:12:59.550
+model be in order to best.
+
+00:13:00.440 --> 00:13:02.285
+Find the balance between the bias and
+
+00:13:02.285 --> 00:13:02.950
+the variance.
+
+00:13:03.710 --> 00:13:05.910
+But ensembles have a different way to
+
+00:13:05.910 --> 00:13:08.050
+directly combat the bias and the
+
+00:13:08.050 --> 00:13:10.430
+variance, so I'm going to talk about a
+
+00:13:10.430 --> 00:13:12.470
+few ensemble methods and how they
+
+00:13:12.470 --> 00:13:12.920
+relate.
+
+00:13:16.400 --> 00:13:19.130
+The first one is called first, like.
+
+00:13:19.130 --> 00:13:20.580
+This is actually not one of these
+
+00:13:20.580 --> 00:13:22.007
+ensemble method, but it is an ensemble
+
+00:13:22.007 --> 00:13:22.245
+method.
+
+00:13:22.245 --> 00:13:23.690
+It's the simplest of these, and it's
+
+00:13:23.690 --> 00:13:25.219
+kind of the foundation of the ensemble
+
+00:13:25.220 --> 00:13:25.810
+methods.
+
+00:13:25.810 --> 00:13:28.010
+So it's a statistical technique called
+
+00:13:28.010 --> 00:13:28.710
+bootstrapping.
+
+00:13:29.860 --> 00:13:32.740
+Imagine that, for example, I wanted to
+
+00:13:32.740 --> 00:13:35.170
+know what is the average age of
+
+00:13:35.170 --> 00:13:36.380
+somebody in this class.
+
+00:13:37.610 --> 00:13:39.990
+One way that I could do it is I could
+
+00:13:39.990 --> 00:13:42.323
+ask each of you your ages and then I
+
+00:13:42.323 --> 00:13:43.840
+could average it, and then that might
+
+00:13:43.840 --> 00:13:45.605
+give me like an estimate for the
+
+00:13:45.605 --> 00:13:47.110
+average age of all the students in the
+
+00:13:47.110 --> 00:13:47.450
+class.
+
+00:13:48.720 --> 00:13:51.700
+But maybe I not only want to know the
+
+00:13:51.700 --> 00:13:53.850
+average age, but I also want some
+
+00:13:53.850 --> 00:13:56.020
+confidence range on that average age.
+
+00:13:56.020 --> 00:13:58.210
+And if all I do is I average all your
+
+00:13:58.210 --> 00:14:00.960
+ages, that doesn't tell me how likely I
+
+00:14:00.960 --> 00:14:02.930
+am to be within, say, like three years.
+
+00:14:04.000 --> 00:14:07.090
+And so one way, one way that I can
+
+00:14:07.090 --> 00:14:09.950
+solve that problem is with bootstrap
+
+00:14:09.950 --> 00:14:13.590
+estimation where I resample the data
+
+00:14:13.590 --> 00:14:15.530
+multiple times so I could choose.
+
+00:14:15.530 --> 00:14:18.800
+I could take 50 samples and sample with
+
+00:14:18.800 --> 00:14:21.235
+repetition so I could potentially call
+
+00:14:21.235 --> 00:14:22.350
+the same person twice.
+
+00:14:23.160 --> 00:14:24.125
+Ask your ages.
+
+00:14:24.125 --> 00:14:26.750
+Ask the ages of 50 individuals.
+
+00:14:26.750 --> 00:14:28.140
+Again, the same individual may be
+
+00:14:28.140 --> 00:14:28.870
+repeated.
+
+00:14:28.870 --> 00:14:31.530
+I take the average from that and repeat
+
+00:14:31.530 --> 00:14:33.810
+that many times, and then I can look at
+
+00:14:33.810 --> 00:14:35.579
+the variance of those estimates that I
+
+00:14:35.580 --> 00:14:35.800
+get.
+
+00:14:36.470 --> 00:14:38.050
+And then I can use the variance of
+
+00:14:38.050 --> 00:14:40.430
+those estimates to get a confidence
+
+00:14:40.430 --> 00:14:42.570
+range on my estimate of the mean.
+
+00:14:43.810 --> 00:14:47.080
+So bootstrap bootstrapping is a way to.
+
+00:14:47.190 --> 00:14:50.710
+To estimate a particular parameter, in
+
+00:14:50.710 --> 00:14:53.035
+this case the average age, as well as
+
+00:14:53.035 --> 00:14:55.040
+my variance of my estimate of that
+
+00:14:55.040 --> 00:14:55.690
+parameter.
+
+00:14:55.690 --> 00:14:58.550
+So like how far off am I would expect
+
+00:14:58.550 --> 00:14:58.970
+to be?
+
+00:15:02.560 --> 00:15:04.300
+We can apply that idea to
+
+00:15:04.300 --> 00:15:08.918
+classification to try to produce a more
+
+00:15:08.918 --> 00:15:11.266
+stable estimate of the mean or to
+
+00:15:11.266 --> 00:15:13.370
+produce a more stable prediction.
+
+00:15:13.370 --> 00:15:15.270
+In other words, to reduce the variance
+
+00:15:15.270 --> 00:15:17.930
+of my classifiers given a particular
+
+00:15:17.930 --> 00:15:18.620
+data sample.
+
+00:15:20.250 --> 00:15:23.010
+So the method is called bagging, which
+
+00:15:23.010 --> 00:15:24.890
+stands for aggregate bootstrapping.
+
+00:15:25.990 --> 00:15:27.390
+And the idea is pretty simple.
+
+00:15:28.630 --> 00:15:32.340
+For M different times capital M, So I'm
+
+00:15:32.340 --> 00:15:34.730
+going to train train M classifiers.
+
+00:15:35.430 --> 00:15:37.620
+I draw some number of samples which
+
+00:15:37.620 --> 00:15:39.533
+should be less than my total number of
+
+00:15:39.533 --> 00:15:40.800
+samples, but I'm going to draw them
+
+00:15:40.800 --> 00:15:41.828
+with replacement.
+
+00:15:41.828 --> 00:15:43.860
+Draw with replacement means I can
+
+00:15:43.860 --> 00:15:45.310
+choose the same sample twice.
+
+00:15:46.750 --> 00:15:48.410
+Then I train a classifier on those
+
+00:15:48.410 --> 00:15:51.120
+samples, and then at the end my final
+
+00:15:51.120 --> 00:15:54.290
+classifier is an average of all of my
+
+00:15:54.290 --> 00:15:55.620
+predictions from the individual
+
+00:15:55.620 --> 00:15:56.340
+classifiers.
+
+00:15:57.080 --> 00:15:59.040
+So if I'm doing regression, I would
+
+00:15:59.040 --> 00:16:01.940
+just be averaging the continuous values
+
+00:16:01.940 --> 00:16:04.200
+that the classifiers are aggressors
+
+00:16:04.200 --> 00:16:04.890
+predicted.
+
+00:16:04.890 --> 00:16:07.555
+If I'm doing classification, I would
+
+00:16:07.555 --> 00:16:10.116
+average the probabilities or average
+
+00:16:10.116 --> 00:16:13.056
+the most likely label from each of the
+
+00:16:13.056 --> 00:16:13.389
+classifiers.
+
+00:16:14.380 --> 00:16:16.810
+And there's lots of theory that shows
+
+00:16:16.810 --> 00:16:19.100
+that this increases the stability of
+
+00:16:19.100 --> 00:16:21.500
+the classifier and reduces reduces the
+
+00:16:21.500 --> 00:16:24.915
+variance, and so the average of a bunch
+
+00:16:24.915 --> 00:16:26.630
+of classifiers trained this way.
+
+00:16:27.300 --> 00:16:30.110
+Typically outperform any individual
+
+00:16:30.110 --> 00:16:30.840
+classifier.
+
+00:16:32.030 --> 00:16:33.870
+In these classifiers will be different
+
+00:16:33.870 --> 00:16:36.490
+from each other because there's a
+
+00:16:36.490 --> 00:16:37.100
+difference.
+
+00:16:37.100 --> 00:16:39.670
+Because the data is, a different sample
+
+00:16:39.670 --> 00:16:41.030
+of data is drawn to train each
+
+00:16:41.030 --> 00:16:41.590
+classifier.
+
+00:16:45.070 --> 00:16:46.790
+So that's the question.
+
+00:17:00.050 --> 00:17:02.463
+So not yeah, but not features, it's
+
+00:17:02.463 --> 00:17:03.186
+samples.
+
+00:17:03.186 --> 00:17:06.700
+So I have say 1000 data samples.
+
+00:17:07.340 --> 00:17:10.770
+And I draw say 900 data samples, but
+
+00:17:10.770 --> 00:17:13.467
+they're not 900 out of the thousand,
+
+00:17:13.467 --> 00:17:16.190
+it's 900 with repetition.
+
+00:17:16.190 --> 00:17:17.720
+So there might be 1 sample that I
+
+00:17:17.720 --> 00:17:19.596
+choose draw three times, others that I
+
+00:17:19.596 --> 00:17:21.259
+draw no times, others that I draw one
+
+00:17:21.260 --> 00:17:21.850
+time.
+
+00:17:21.850 --> 00:17:23.700
+So you can in terms of like
+
+00:17:23.700 --> 00:17:26.840
+programming, you would just do a random
+
+00:17:26.840 --> 00:17:31.290
+like 0 to 1 * N and then and then turn
+
+00:17:31.290 --> 00:17:33.397
+it into an integer and then you get
+
+00:17:33.397 --> 00:17:35.159
+like you get a random sample with
+
+00:17:35.160 --> 00:17:35.660
+replacement.
+
+00:17:46.940 --> 00:17:47.720
+Typically.
+
+00:17:47.720 --> 00:17:49.626
+So usually each of the classifiers is
+
+00:17:49.626 --> 00:17:50.820
+of the same form.
+
+00:17:50.820 --> 00:17:51.190
+Yep.
+
+00:17:53.550 --> 00:17:55.270
+So this is the idea behind random
+
+00:17:55.270 --> 00:17:57.760
+forests, which is a really powerful
+
+00:17:57.760 --> 00:17:59.940
+classifier, but very easy to explain at
+
+00:17:59.940 --> 00:18:01.500
+least once you once you know about
+
+00:18:01.500 --> 00:18:02.270
+decision trees.
+
+00:18:03.780 --> 00:18:06.040
+So in a random forest, train a
+
+00:18:06.040 --> 00:18:07.150
+collection of trees.
+
+00:18:08.140 --> 00:18:09.970
+For each tree that you're going to
+
+00:18:09.970 --> 00:18:11.786
+train, you sample some fraction in the
+
+00:18:11.786 --> 00:18:13.880
+data, for example 90% of the data.
+
+00:18:13.880 --> 00:18:15.620
+Sometimes people just sample all the
+
+00:18:15.620 --> 00:18:15.990
+data.
+
+00:18:16.430 --> 00:18:19.948
+Then you randomly sample some number of
+
+00:18:19.948 --> 00:18:20.325
+features.
+
+00:18:20.325 --> 00:18:23.042
+So for regression, one suggestion is to
+
+00:18:23.042 --> 00:18:24.648
+use 1/3 of the features.
+
+00:18:24.648 --> 00:18:28.003
+For classification you would use like.
+
+00:18:28.003 --> 00:18:30.000
+Some suggestions are to use like a
+
+00:18:30.000 --> 00:18:31.565
+square root of the number of features.
+
+00:18:31.565 --> 00:18:32.240
+So if there's.
+
+00:18:32.970 --> 00:18:36.260
+If there are 400 features, then you
+
+00:18:36.260 --> 00:18:38.290
+randomly sample 20 of them.
+
+00:18:38.290 --> 00:18:40.240
+Or another suggestion is to use log
+
+00:18:40.240 --> 00:18:40.820
+base 2.
+
+00:18:41.650 --> 00:18:43.389
+It's not really that critical, but you
+
+00:18:43.389 --> 00:18:44.820
+want you want the number of features
+
+00:18:44.820 --> 00:18:46.995
+that you select to be much less than
+
+00:18:46.995 --> 00:18:48.430
+the total number of features.
+
+00:18:49.110 --> 00:18:51.800
+So here previously I was talking about
+
+00:18:51.800 --> 00:18:53.760
+when I say sample the data, what I mean
+
+00:18:53.760 --> 00:18:55.870
+is like is choosing a subset of
+
+00:18:55.870 --> 00:18:56.790
+training samples.
+
+00:18:57.910 --> 00:19:00.290
+But when I say sample the features, I
+
+00:19:00.290 --> 00:19:02.699
+mean choose a subset of the features of
+
+00:19:02.699 --> 00:19:05.365
+the columns of your of your matrix if
+
+00:19:05.365 --> 00:19:06.914
+the rows are samples and the columns
+
+00:19:06.914 --> 00:19:07.350
+are features.
+
+00:19:09.360 --> 00:19:11.710
+So the you need to sample the features
+
+00:19:11.710 --> 00:19:13.210
+because otherwise if you train the tree
+
+00:19:13.210 --> 00:19:14.693
+you're going to get the same result if
+
+00:19:14.693 --> 00:19:17.720
+you're doing like minimizing the
+
+00:19:17.720 --> 00:19:19.440
+maximizing mutual information for
+
+00:19:19.440 --> 00:19:19.890
+example.
+
+00:19:20.700 --> 00:19:22.270
+If you were to sample all your data and
+
+00:19:22.270 --> 00:19:23.600
+all the features, you would just train
+
+00:19:23.600 --> 00:19:24.280
+the same tree.
+
+00:19:25.070 --> 00:19:27.660
+MN times and that would give you no
+
+00:19:27.660 --> 00:19:28.160
+benefit.
+
+00:19:28.900 --> 00:19:30.240
+All right, so you randomly sample some
+
+00:19:30.240 --> 00:19:31.540
+features, train a tree.
+
+00:19:32.240 --> 00:19:34.497
+Optionally, you can estimate your
+
+00:19:34.497 --> 00:19:36.020
+validation error on the data that
+
+00:19:36.020 --> 00:19:38.283
+wasn't used to train that tree, and you
+
+00:19:38.283 --> 00:19:41.140
+can use the average of those validation
+
+00:19:41.140 --> 00:19:44.513
+errors in order to get a estimate of
+
+00:19:44.513 --> 00:19:46.930
+your error for the for your final
+
+00:19:46.930 --> 00:19:47.480
+collection.
+
+00:19:50.000 --> 00:19:51.886
+And after you've trained all the trees,
+
+00:19:51.886 --> 00:19:54.610
+you just do that 100 times or whatever.
+
+00:19:54.610 --> 00:19:55.920
+It's completely independent.
+
+00:19:55.920 --> 00:19:58.330
+So it's just like a very if you've got
+
+00:19:58.330 --> 00:19:59.920
+code to train a tree, it's just a very
+
+00:19:59.920 --> 00:20:01.090
+small loop.
+
+00:20:02.370 --> 00:20:04.990
+And then at the end you average the
+
+00:20:04.990 --> 00:20:06.766
+prediction of all the trees.
+
+00:20:06.766 --> 00:20:08.930
+So usually you would train your trees
+
+00:20:08.930 --> 00:20:09.535
+to completion.
+
+00:20:09.535 --> 00:20:12.160
+So if you're doing like classification
+
+00:20:12.160 --> 00:20:14.850
+or in either case you would end up with
+
+00:20:14.850 --> 00:20:16.480
+a leaf node that contains one data
+
+00:20:16.480 --> 00:20:16.926
+sample.
+
+00:20:16.926 --> 00:20:19.060
+So you're training like very high
+
+00:20:19.060 --> 00:20:21.530
+variance trees, they're deep trees.
+
+00:20:22.650 --> 00:20:24.760
+That have low bias, they can fit the
+
+00:20:24.760 --> 00:20:27.580
+training data perfectly, but.
+
+00:20:29.470 --> 00:20:31.027
+But then you're going to average all of
+
+00:20:31.027 --> 00:20:31.235
+them.
+
+00:20:31.235 --> 00:20:34.534
+So you start out with high bias or high
+
+00:20:34.534 --> 00:20:36.650
+variance, low bias classifiers, and
+
+00:20:36.650 --> 00:20:37.743
+then you average them.
+
+00:20:37.743 --> 00:20:40.044
+So you end up with low bias, low
+
+00:20:40.044 --> 00:20:40.669
+variance classifiers.
+
+00:20:49.930 --> 00:20:51.310
+Yes, for each tree.
+
+00:20:51.310 --> 00:20:52.460
+Yeah, for each tree.
+
+00:20:52.630 --> 00:20:53.160
+Yeah.
+
+00:20:59.180 --> 00:21:02.920
+You increase the number of trees, yeah,
+
+00:21:02.920 --> 00:21:03.410
+so.
+
+00:21:04.110 --> 00:21:07.720
+If you if so, think of it this way.
+
+00:21:07.720 --> 00:21:12.075
+If I were to if I were to try to
+
+00:21:12.075 --> 00:21:14.995
+estimate the sum of your ages, then as
+
+00:21:14.995 --> 00:21:17.900
+I ask you your ages and add them up, my
+
+00:21:17.900 --> 00:21:19.463
+estimate of the variance of the
+
+00:21:19.463 --> 00:21:21.288
+variance on the estimate, the sum is
+
+00:21:21.288 --> 00:21:23.400
+going to increase linearly, right?
+
+00:21:23.400 --> 00:21:26.680
+It's going to keep on increasing until
+
+00:21:26.680 --> 00:21:30.660
+sum is 100,000 ± 10,000 or something.
+
+00:21:31.480 --> 00:21:33.168
+But if I'm trying to estimate the
+
+00:21:33.168 --> 00:21:35.700
+average of your ages and I keep on
+
+00:21:35.700 --> 00:21:38.250
+asking your ages, then my variance is
+
+00:21:38.250 --> 00:21:39.950
+going to go down South.
+
+00:21:39.950 --> 00:21:43.040
+The variance of the sum is North Times
+
+00:21:43.040 --> 00:21:47.030
+Sigma squared, but the variance of the
+
+00:21:47.030 --> 00:21:50.980
+average is N over Sigma I think just no
+
+00:21:50.980 --> 00:21:53.688
+over Sigma or sorry, Sigma over N,
+
+00:21:53.688 --> 00:21:56.100
+Sigma squared over N the variance of
+
+00:21:56.100 --> 00:21:58.513
+the average is Sigma squared over N,
+
+00:21:58.513 --> 00:22:01.269
+but the variance of the sum is N.
+
+00:22:01.330 --> 00:22:02.500
+Times Sigma squared.
+
+00:22:04.490 --> 00:22:06.934
+So the average reduces the variance.
+
+00:22:06.934 --> 00:22:08.135
+Yeah, so if I.
+
+00:22:08.135 --> 00:22:09.960
+So by averaging the trees I reduce the
+
+00:22:09.960 --> 00:22:10.160
+variance.
+
+00:22:14.870 --> 00:22:17.250
+So that's random forests and I will
+
+00:22:17.250 --> 00:22:17.840
+talk more.
+
+00:22:17.840 --> 00:22:20.467
+I'll give an example of use of random
+
+00:22:20.467 --> 00:22:22.280
+forests and I'll talk about like some
+
+00:22:22.280 --> 00:22:24.780
+studies about the performance of
+
+00:22:24.780 --> 00:22:26.750
+various classifiers including random
+
+00:22:26.750 --> 00:22:27.320
+forests.
+
+00:22:27.320 --> 00:22:29.946
+But before I do that, I want to talk
+
+00:22:29.946 --> 00:22:31.330
+about boosting, which is the other
+
+00:22:31.330 --> 00:22:31.890
+strategy.
+
+00:22:33.860 --> 00:22:36.080
+So I have the boosting terms here as
+
+00:22:36.080 --> 00:22:36.490
+well.
+
+00:22:37.730 --> 00:22:38.170
+All right.
+
+00:22:38.170 --> 00:22:41.085
+So the first version of boosting and
+
+00:22:41.085 --> 00:22:42.740
+one other thing I want to say about
+
+00:22:42.740 --> 00:22:45.350
+this is random forest was popularized
+
+00:22:45.350 --> 00:22:47.885
+by this paper by Bremen in 2001.
+
+00:22:47.885 --> 00:22:50.460
+So decision trees go back to the 90s at
+
+00:22:50.460 --> 00:22:53.893
+least, but they were never really, like
+
+00:22:53.893 --> 00:22:56.680
+I said, were they're good for helping
+
+00:22:56.680 --> 00:22:59.750
+for making decisions that people can
+
+00:22:59.750 --> 00:23:01.360
+understand, that you can communicate
+
+00:23:01.360 --> 00:23:02.780
+and explain like why it made this
+
+00:23:02.780 --> 00:23:03.130
+decision.
+
+00:23:03.890 --> 00:23:05.710
+And they're good for analyzing data,
+
+00:23:05.710 --> 00:23:07.040
+but they're not really very good
+
+00:23:07.040 --> 00:23:08.770
+classifiers or aggressors compared to
+
+00:23:08.770 --> 00:23:09.880
+other methods that are out there.
+
+00:23:11.210 --> 00:23:14.390
+But Bremen popularized random forests
+
+00:23:14.390 --> 00:23:16.530
+in 2001 and showed that the
+
+00:23:16.530 --> 00:23:19.050
+combinations of trees is actually super
+
+00:23:19.050 --> 00:23:20.380
+powerful and super useful.
+
+00:23:21.840 --> 00:23:23.770
+And provides like the theory for why it
+
+00:23:23.770 --> 00:23:25.800
+works and why you should be sampling
+
+00:23:25.800 --> 00:23:27.780
+different subsets of features, and the
+
+00:23:27.780 --> 00:23:29.160
+idea that you want the trees to be
+
+00:23:29.160 --> 00:23:30.000
+decorrelated.
+
+00:23:31.000 --> 00:23:34.130
+To make different predictions but also
+
+00:23:34.130 --> 00:23:34.800
+be powerful.
+
+00:23:37.140 --> 00:23:37.710
+Alright.
+
+00:23:37.710 --> 00:23:41.140
+So the other strategy is boosting and
+
+00:23:41.140 --> 00:23:42.910
+the first boosting paper I think was
+
+00:23:42.910 --> 00:23:44.630
+Shapira in 1989.
+
+00:23:45.500 --> 00:23:46.900
+And that's one was pretty simple.
+
+00:23:47.680 --> 00:23:51.090
+So the idea was that you first randomly
+
+00:23:51.090 --> 00:23:52.690
+choose a set of samples.
+
+00:23:53.470 --> 00:23:55.280
+Without replacement at this time.
+
+00:23:55.280 --> 00:23:57.970
+So if you've got 1000, you randomly
+
+00:23:57.970 --> 00:24:00.133
+choose, say, 800 of them without
+
+00:24:00.133 --> 00:24:00.539
+replacement.
+
+00:24:01.440 --> 00:24:04.320
+And you train a classifier on those
+
+00:24:04.320 --> 00:24:07.140
+samples, that's the weak learner, C1.
+
+00:24:07.760 --> 00:24:10.170
+So I've got the notation over here in
+
+00:24:10.170 --> 00:24:12.060
+the literature you'll see things like
+
+00:24:12.060 --> 00:24:15.140
+learner, hypothesis, classifier, they
+
+00:24:15.140 --> 00:24:16.130
+all mean the same thing.
+
+00:24:16.130 --> 00:24:17.560
+There's something that's some model
+
+00:24:17.560 --> 00:24:18.810
+that's doing some prediction.
+
+00:24:19.960 --> 00:24:22.530
+A weak learner is just a classifier
+
+00:24:22.530 --> 00:24:25.260
+that can achieve less than 50% training
+
+00:24:25.260 --> 00:24:27.140
+error over any training distribution.
+
+00:24:27.910 --> 00:24:30.120
+So almost any classifier we would
+
+00:24:30.120 --> 00:24:32.217
+consider is a weak learner.
+
+00:24:32.217 --> 00:24:34.000
+As long as you can guarantee that it
+
+00:24:34.000 --> 00:24:35.970
+will be able to get at least chance
+
+00:24:35.970 --> 00:24:38.030
+performance in a two class problem,
+
+00:24:38.030 --> 00:24:39.309
+then it's a weak learner.
+
+00:24:42.560 --> 00:24:45.286
+A strong learner is a combination of
+
+00:24:45.286 --> 00:24:46.182
+the weak learner.
+
+00:24:46.182 --> 00:24:47.852
+It's a predictor that uses a
+
+00:24:47.852 --> 00:24:49.230
+combination of the weak learners.
+
+00:24:49.230 --> 00:24:52.020
+So first you train 1 classifier in a
+
+00:24:52.020 --> 00:24:52.940
+subset of the data.
+
+00:24:53.620 --> 00:24:55.936
+Then you draw a new sample, and this
+
+00:24:55.936 --> 00:24:58.490
+new sample is drawn so that half the
+
+00:24:58.490 --> 00:24:59.310
+samples.
+
+00:25:00.010 --> 00:25:04.960
+Are misclassified by the 1st classifier
+
+00:25:04.960 --> 00:25:06.640
+and this can be drawn with replacement.
+
+00:25:07.460 --> 00:25:10.172
+So half of your N2 samples were
+
+00:25:10.172 --> 00:25:12.310
+misclassified by C1 and half of them
+
+00:25:12.310 --> 00:25:14.009
+were not misclassified by C1.
+
+00:25:14.900 --> 00:25:17.230
+And so now in this new sample of data.
+
+00:25:18.500 --> 00:25:21.220
+Your classifier C1 had a 5050 chance of
+
+00:25:21.220 --> 00:25:22.910
+getting it right by construction.
+
+00:25:22.980 --> 00:25:23.150
+Right.
+
+00:25:23.880 --> 00:25:25.640
+Then you train C2.
+
+00:25:27.060 --> 00:25:29.590
+To try to like do well on this new
+
+00:25:29.590 --> 00:25:30.560
+distribution.
+
+00:25:30.560 --> 00:25:32.590
+So C2 has like a more difficult job,
+
+00:25:32.590 --> 00:25:33.970
+it's going to focus on the things that
+
+00:25:33.970 --> 00:25:35.240
+C1 found more difficult.
+
+00:25:37.140 --> 00:25:39.250
+Then finally you take all the samples
+
+00:25:39.250 --> 00:25:41.830
+that C1 and C2 disagree on, and you
+
+00:25:41.830 --> 00:25:43.590
+train a third week learner 1/3
+
+00:25:43.590 --> 00:25:45.740
+classifier just on those examples.
+
+00:25:46.420 --> 00:25:49.470
+And then at the end you take an average
+
+00:25:49.470 --> 00:25:50.500
+of those votes.
+
+00:25:50.500 --> 00:25:52.621
+So basically you have like you have
+
+00:25:52.621 --> 00:25:54.050
+like one person who's making a
+
+00:25:54.050 --> 00:25:54.740
+prediction.
+
+00:25:55.810 --> 00:25:57.946
+You take half the predictions that
+
+00:25:57.946 --> 00:26:00.770
+person made incorrect and half that
+
+00:26:00.770 --> 00:26:02.320
+were correct, and then you get a second
+
+00:26:02.320 --> 00:26:04.192
+person to make predictions just looking
+
+00:26:04.192 --> 00:26:05.690
+at that at those samples.
+
+00:26:06.470 --> 00:26:08.130
+Then you get a third person to be the
+
+00:26:08.130 --> 00:26:09.915
+tiebreaker between the first two people
+
+00:26:09.915 --> 00:26:11.440
+if they made if they had different
+
+00:26:11.440 --> 00:26:13.320
+answers, and then you take a vote of
+
+00:26:13.320 --> 00:26:14.790
+those three people as you're finally
+
+00:26:14.790 --> 00:26:15.160
+answer.
+
+00:26:16.780 --> 00:26:18.590
+Where you can substitute classifier for
+
+00:26:18.590 --> 00:26:19.290
+people.
+
+00:26:20.660 --> 00:26:22.100
+So this is the boosting idea.
+
+00:26:23.100 --> 00:26:25.120
+Now this actually became much more
+
+00:26:25.120 --> 00:26:27.000
+popular when it was generalized a
+
+00:26:27.000 --> 00:26:28.480
+little bit into this method called
+
+00:26:28.480 --> 00:26:31.450
+Adaboost, which stands for adaptive
+
+00:26:31.450 --> 00:26:31.970
+boosting.
+
+00:26:33.210 --> 00:26:33.650
+So.
+
+00:26:34.390 --> 00:26:38.710
+The in adaptive boosting, instead of
+
+00:26:38.710 --> 00:26:42.940
+justice directly sampling the data, you
+
+00:26:42.940 --> 00:26:44.730
+assign a weight to the data.
+
+00:26:44.730 --> 00:26:46.640
+And I'll explain in the next slide, I
+
+00:26:46.640 --> 00:26:48.564
+think more of what it means to like
+
+00:26:48.564 --> 00:26:49.860
+weight the data when you're doing
+
+00:26:49.860 --> 00:26:50.850
+parameter estimation.
+
+00:26:52.360 --> 00:26:55.200
+But you assign assign new weights to
+
+00:26:55.200 --> 00:26:57.357
+the data so that under that
+
+00:26:57.357 --> 00:27:00.036
+distribution the previous weak learner,
+
+00:27:00.036 --> 00:27:02.140
+the previous classifier has chance
+
+00:27:02.140 --> 00:27:04.150
+accuracy at that weighted distribution.
+
+00:27:04.920 --> 00:27:07.775
+So this was one way of doing achieving
+
+00:27:07.775 --> 00:27:10.010
+the same thing where you just you draw
+
+00:27:10.010 --> 00:27:12.390
+like whole samples so that the previous
+
+00:27:12.390 --> 00:27:14.150
+week learner had a 5050 chance of
+
+00:27:14.150 --> 00:27:16.000
+getting those samples correct.
+
+00:27:16.830 --> 00:27:18.540
+But you can instead assign a softer
+
+00:27:18.540 --> 00:27:20.510
+weight to just say that some samples
+
+00:27:20.510 --> 00:27:23.160
+matter more than others, so that on the
+
+00:27:23.160 --> 00:27:24.950
+distribution the previous classifier
+
+00:27:24.950 --> 00:27:26.330
+has a 5050 chance.
+
+00:27:27.900 --> 00:27:30.680
+Then you train a new classifier on the
+
+00:27:30.680 --> 00:27:31.820
+reweighted samples.
+
+00:27:32.440 --> 00:27:33.350
+And then you iterate.
+
+00:27:33.350 --> 00:27:34.800
+So then you reweigh them again and
+
+00:27:34.800 --> 00:27:36.340
+train a new classifier and keep doing
+
+00:27:36.340 --> 00:27:36.850
+that.
+
+00:27:36.850 --> 00:27:38.870
+And then at the end you take a weighted
+
+00:27:38.870 --> 00:27:41.560
+vote of all of the weak classifiers as
+
+00:27:41.560 --> 00:27:42.510
+your final predictor.
+
+00:27:43.430 --> 00:27:47.810
+So each each sample is going to each
+
+00:27:47.810 --> 00:27:49.600
+classifier is going to try to correct
+
+00:27:49.600 --> 00:27:50.760
+the mistakes of the previous
+
+00:27:50.760 --> 00:27:53.090
+classifiers, and then all of their
+
+00:27:53.090 --> 00:27:54.650
+predictions are combined.
+
+00:27:55.920 --> 00:27:57.240
+So I'm going to show a specific
+
+00:27:57.240 --> 00:27:59.650
+algorithm in a moment, but first I want
+
+00:27:59.650 --> 00:28:00.520
+to clarify.
+
+00:28:01.450 --> 00:28:03.610
+What it means to take A to do, like a
+
+00:28:03.610 --> 00:28:05.880
+weighted estimation or weighting your
+
+00:28:05.880 --> 00:28:06.720
+training samples.
+
+00:28:07.560 --> 00:28:09.600
+So essentially it just means that some
+
+00:28:09.600 --> 00:28:11.795
+samples count more than others towards
+
+00:28:11.795 --> 00:28:13.780
+your parameter estimation or your
+
+00:28:13.780 --> 00:28:14.660
+learning objective.
+
+00:28:15.410 --> 00:28:17.500
+So let's say that we're trying to build
+
+00:28:17.500 --> 00:28:19.880
+a naive Bayes classifier, and so we
+
+00:28:19.880 --> 00:28:21.870
+need to estimate the probability that
+
+00:28:21.870 --> 00:28:24.745
+some feature is equal to 0 given that
+
+00:28:24.745 --> 00:28:26.130
+the label is equal to 0.
+
+00:28:26.130 --> 00:28:28.200
+That's like one of the parameters of
+
+00:28:28.200 --> 00:28:28.940
+our model.
+
+00:28:29.960 --> 00:28:32.250
+If we have an unweighted distribution,
+
+00:28:32.250 --> 00:28:35.940
+then that would be a count of how many
+
+00:28:35.940 --> 00:28:39.290
+times the feature is equal to 0 and the
+
+00:28:39.290 --> 00:28:40.440
+label is equal to 0.
+
+00:28:41.070 --> 00:28:43.380
+Divided by a count of how many times
+
+00:28:43.380 --> 00:28:45.290
+the label is equal to 0, right?
+
+00:28:45.290 --> 00:28:47.489
+So that's probability of X&Y
+
+00:28:47.490 --> 00:28:49.112
+essentially divided by probability of
+
+00:28:49.112 --> 00:28:49.380
+Y.
+
+00:28:51.950 --> 00:28:53.940
+Times north on the numerator and
+
+00:28:53.940 --> 00:28:54.720
+denominator.
+
+00:28:56.520 --> 00:28:58.780
+Then if I want to take a weighted
+
+00:28:58.780 --> 00:29:01.430
+sample, if I wanted an estimate of a
+
+00:29:01.430 --> 00:29:03.490
+weighted distribution, I have a weight
+
+00:29:03.490 --> 00:29:04.840
+assigned to each of these training
+
+00:29:04.840 --> 00:29:07.570
+samples, and that's often done so that
+
+00:29:07.570 --> 00:29:11.140
+the weights sum up to one, but it
+
+00:29:11.140 --> 00:29:12.619
+doesn't have to be, but they have to be
+
+00:29:12.620 --> 00:29:13.240
+non negative.
+
+00:29:15.290 --> 00:29:16.950
+OK, so I have to wait for each of these
+
+00:29:16.950 --> 00:29:18.973
+samples that says how important it is.
+
+00:29:18.973 --> 00:29:20.940
+So when I count the number of times
+
+00:29:20.940 --> 00:29:25.320
+that X n = 0 and Y n = 0, then I am
+
+00:29:25.320 --> 00:29:27.200
+waiting those counts by won.
+
+00:29:27.200 --> 00:29:29.140
+So it's the sum of the weights where
+
+00:29:29.140 --> 00:29:31.185
+for the samples in which this condition
+
+00:29:31.185 --> 00:29:33.698
+is true divided by the sum of the
+
+00:29:33.698 --> 00:29:35.886
+weights for which YN is equal to 0.
+
+00:29:35.886 --> 00:29:37.649
+So that's my weighted estimate of that
+
+00:29:37.650 --> 00:29:38.260
+statistic.
+
+00:29:40.910 --> 00:29:41.470
+Right.
+
+00:29:41.470 --> 00:29:42.960
+So it's your turn.
+
+00:29:44.180 --> 00:29:46.470
+Let's say that we have this table here.
+
+00:29:46.470 --> 00:29:48.810
+So we've got weights on the left side,
+
+00:29:48.810 --> 00:29:51.850
+X in the middle, Y and the right, and
+
+00:29:51.850 --> 00:29:53.735
+I'm trying to estimate probability of X
+
+00:29:53.735 --> 00:29:55.440
+= 0 given y = 0.
+
+00:29:56.140 --> 00:29:57.950
+So I'll give you a moment to think
+
+00:29:57.950 --> 00:29:58.690
+about it.
+
+00:29:58.690 --> 00:30:00.590
+First, what is the unweighted
+
+00:30:00.590 --> 00:30:03.040
+distribution and then what is the
+
+00:30:03.040 --> 00:30:04.380
+weighted distribution?
+
+00:30:12.540 --> 00:30:13.100
+Right.
+
+00:30:20.290 --> 00:30:21.170
+Me too.
+
+00:30:21.170 --> 00:30:23.410
+My daughter woke me up at 4:00 AM and I
+
+00:30:23.410 --> 00:30:24.700
+couldn't fall back asleep.
+
+00:30:39.450 --> 00:30:41.990
+I'll I will go through these are the
+
+00:30:41.990 --> 00:30:43.920
+examples, so I'll go through it.
+
+00:30:45.400 --> 00:30:45.930
+Alright.
+
+00:30:48.690 --> 00:30:50.650
+Going, I'll step through it in a
+
+00:30:50.650 --> 00:30:50.930
+moment.
+
+00:30:52.270 --> 00:30:53.404
+Alright, so let's do the.
+
+00:30:53.404 --> 00:30:55.090
+Let's do the unweighted first.
+
+00:30:56.800 --> 00:31:00.940
+So how many times does X equal 0 and y
+
+00:31:00.940 --> 00:31:01.480
+= 0?
+
+00:31:03.440 --> 00:31:05.030
+Right, three.
+
+00:31:05.030 --> 00:31:06.350
+OK, so I'm going to have three on the
+
+00:31:06.350 --> 00:31:09.665
+numerator and how many times does y =
+
+00:31:09.665 --> 00:31:10.120
+0?
+
+00:31:12.070 --> 00:31:13.000
+OK, right.
+
+00:31:13.000 --> 00:31:15.710
+So unweighted is going to be 3 out of
+
+00:31:15.710 --> 00:31:16.500
+five, right?
+
+00:31:18.560 --> 00:31:20.470
+Now let's do the weighted.
+
+00:31:20.470 --> 00:31:22.990
+So what's the sum of the weights where
+
+00:31:22.990 --> 00:31:25.309
+X = 0 and y = 0?
+
+00:31:31.640 --> 00:31:35.026
+So there's three rows where X = 0 and y
+
+00:31:35.026 --> 00:31:35.619
+= 0.
+
+00:31:36.360 --> 00:31:36.830
+Right.
+
+00:31:39.410 --> 00:31:40.990
+Right, yeah, three.
+
+00:31:40.990 --> 00:31:42.742
+So there's just these three rows, and
+
+00:31:42.742 --> 00:31:44.230
+there's a .1 for each of them.
+
+00:31:44.940 --> 00:31:46.030
+So that's .3.
+
+00:31:46.800 --> 00:31:49.830
+And what is the total weight for y = 0?
+
+00:31:51.710 --> 00:31:52.960
+Right .7.
+
+00:31:54.060 --> 00:31:55.960
+So the weighted distribution.
+
+00:31:55.960 --> 00:31:57.456
+My estimate on the weighted
+
+00:31:57.456 --> 00:31:58.920
+distribution is 3 out of seven.
+
+00:32:00.000 --> 00:32:01.120
+So that's how it works.
+
+00:32:01.830 --> 00:32:04.770
+And if you had so a lot of times we are
+
+00:32:04.770 --> 00:32:06.260
+just estimating counts like this.
+
+00:32:06.260 --> 00:32:08.500
+If we were training a shorter tree for
+
+00:32:08.500 --> 00:32:11.148
+example, then we would be estimating
+
+00:32:11.148 --> 00:32:13.330
+the probability of each class within
+
+00:32:13.330 --> 00:32:14.920
+the leaf node, which would just be by
+
+00:32:14.920 --> 00:32:15.380
+counting.
+
+00:32:17.040 --> 00:32:18.980
+Other times, if you're doing like
+
+00:32:18.980 --> 00:32:21.515
+logistic regression or had some other
+
+00:32:21.515 --> 00:32:24.000
+kind of training or neural network,
+
+00:32:24.000 --> 00:32:26.660
+then usually these weights would show
+
+00:32:26.660 --> 00:32:28.410
+up as some kind of like weight on the
+
+00:32:28.410 --> 00:32:29.140
+loss.
+
+00:32:29.140 --> 00:32:31.290
+So we're going to talk about a
+
+00:32:31.290 --> 00:32:32.740
+sarcastic gradient descent.
+
+00:32:33.750 --> 00:32:35.110
+Starting in the next class.
+
+00:32:35.720 --> 00:32:37.725
+And a higher weight would just be like
+
+00:32:37.725 --> 00:32:39.440
+a direct multiple on how much you
+
+00:32:39.440 --> 00:32:42.230
+adjust your model parameters.
+
+00:32:45.810 --> 00:32:47.920
+So here's a specific algorithm called
+
+00:32:47.920 --> 00:32:49.040
+Adaboost.
+
+00:32:49.440 --> 00:32:52.289
+A real boost, I mean, there's like a
+
+00:32:52.290 --> 00:32:53.816
+ton of boosting algorithms.
+
+00:32:53.816 --> 00:32:56.037
+There's like discrete ETA boost, real
+
+00:32:56.037 --> 00:32:57.695
+boost, logic boost.
+
+00:32:57.695 --> 00:32:59.186
+I don't know.
+
+00:32:59.186 --> 00:33:01.880
+There's like literally like probably 50
+
+00:33:01.880 --> 00:33:02.260
+of them.
+
+00:33:03.670 --> 00:33:05.660
+But here's one of the mainstays.
+
+00:33:05.660 --> 00:33:08.930
+So you start with the weights being
+
+00:33:08.930 --> 00:33:09.560
+uniform.
+
+00:33:09.560 --> 00:33:11.700
+They're one over north with N samples.
+
+00:33:11.700 --> 00:33:13.240
+Then you're going to train M
+
+00:33:13.240 --> 00:33:14.160
+classifiers.
+
+00:33:14.910 --> 00:33:17.605
+You fit the classifier to obtain a
+
+00:33:17.605 --> 00:33:19.690
+probability estimate, the probability
+
+00:33:19.690 --> 00:33:22.630
+of the label being one based on the
+
+00:33:22.630 --> 00:33:23.620
+weighted distribution.
+
+00:33:24.500 --> 00:33:26.130
+So again, if you're doing trees, this
+
+00:33:26.130 --> 00:33:28.460
+would be the fraction of samples in
+
+00:33:28.460 --> 00:33:30.040
+each leaf node of the trees where the
+
+00:33:30.040 --> 00:33:31.000
+label is equal to 1.
+
+00:33:31.850 --> 00:33:33.530
+And where you'd be using a weighted
+
+00:33:33.530 --> 00:33:35.530
+sample to compute that fraction, just
+
+00:33:35.530 --> 00:33:36.580
+like we did in the last slide.
+
+00:33:37.750 --> 00:33:39.860
+Then the prediction of this the score
+
+00:33:39.860 --> 00:33:43.369
+essentially for the label one is this
+
+00:33:43.370 --> 00:33:44.110
+logic.
+
+00:33:44.110 --> 00:33:47.960
+It's the log probability of the label
+
+00:33:47.960 --> 00:33:50.240
+being one over the probability not
+
+00:33:50.240 --> 00:33:51.943
+being one, which is 1 minus the
+
+00:33:51.943 --> 00:33:52.892
+probability of it being one.
+
+00:33:52.892 --> 00:33:54.470
+This is for binary classifier.
+
+00:33:55.650 --> 00:33:57.570
+That's 1/2 of that logic value.
+
+00:33:58.780 --> 00:34:03.040
+And then I re weight the samples and I
+
+00:34:03.040 --> 00:34:05.330
+take the previous weight of each sample
+
+00:34:05.330 --> 00:34:07.240
+and I multiply it by east to the
+
+00:34:07.240 --> 00:34:09.440
+negative yiff FMX.
+
+00:34:09.440 --> 00:34:11.047
+So this again is a score.
+
+00:34:11.047 --> 00:34:13.370
+So this score defined this way, if it's
+
+00:34:13.370 --> 00:34:15.260
+greater than zero that means that.
+
+00:34:16.090 --> 00:34:21.220
+If Y ifm is greater than zero, here Yi
+
+00:34:21.220 --> 00:34:24.144
+is either -, 1 or one, so -, 1 is the
+
+00:34:24.144 --> 00:34:25.900
+negative label, one is the positive
+
+00:34:25.900 --> 00:34:26.200
+label.
+
+00:34:26.910 --> 00:34:28.484
+If this is greater than zero, that
+
+00:34:28.484 --> 00:34:30.449
+means that I'm correct, and if it's
+
+00:34:30.450 --> 00:34:31.969
+less than zero it means that I'm
+
+00:34:31.970 --> 00:34:32.960
+incorrect.
+
+00:34:32.960 --> 00:34:34.846
+So if I predict a score of 1, it means
+
+00:34:34.846 --> 00:34:36.540
+that I think it's positive.
+
+00:34:36.540 --> 00:34:40.597
+But if the label is -, 1, then Y ifm is
+
+00:34:40.597 --> 00:34:41.850
+-, 1, so.
+
+00:34:44.620 --> 00:34:48.350
+So this negative Y ifm, if I'm correct
+
+00:34:48.350 --> 00:34:49.990
+this is going to be less than one
+
+00:34:49.990 --> 00:34:53.450
+because this is going to be east to the
+
+00:34:53.450 --> 00:34:54.860
+negative sum value.
+
+00:34:55.970 --> 00:34:57.700
+And if I'm incorrect, this is going to
+
+00:34:57.700 --> 00:34:58.600
+be greater than one.
+
+00:34:59.270 --> 00:35:00.993
+So if I'm correct, the weight is going
+
+00:35:00.993 --> 00:35:03.141
+to go down, and if I'm incorrect the
+
+00:35:03.141 --> 00:35:04.070
+weight is going to go up.
+
+00:35:04.830 --> 00:35:06.650
+And if I'm like confidently correct,
+
+00:35:06.650 --> 00:35:07.908
+then the way it's going to go down a
+
+00:35:07.908 --> 00:35:08.156
+lot.
+
+00:35:08.156 --> 00:35:09.835
+And if I'm confidently incorrect then
+
+00:35:09.835 --> 00:35:10.960
+the weight is going to go up a lot.
+
+00:35:12.410 --> 00:35:13.480
+That's kind of intuitive.
+
+00:35:14.120 --> 00:35:15.470
+And then I just reweigh.
+
+00:35:15.470 --> 00:35:17.630
+I just sum my.
+
+00:35:18.910 --> 00:35:19.480
+My weight.
+
+00:35:19.480 --> 00:35:22.050
+I renormalize my weights, so I make it
+
+00:35:22.050 --> 00:35:23.460
+so that the weights sum to one by
+
+00:35:23.460 --> 00:35:24.479
+dividing by the sum.
+
+00:35:25.980 --> 00:35:27.630
+So then I just iterate, then I train
+
+00:35:27.630 --> 00:35:29.235
+new classifier and the way distribution
+
+00:35:29.235 --> 00:35:31.430
+recompute this, recompute the weights,
+
+00:35:31.430 --> 00:35:33.300
+do that say 20 times.
+
+00:35:33.910 --> 00:35:36.642
+And then at the end my classifier is.
+
+00:35:36.642 --> 00:35:38.607
+My total score for the classifier is
+
+00:35:38.607 --> 00:35:40.430
+the sum of the individual classifier
+
+00:35:40.430 --> 00:35:40.840
+scores.
+
+00:35:42.130 --> 00:35:43.300
+So it's not too complicated.
+
+00:35:44.220 --> 00:35:47.163
+That theory is somewhat complicated, so
+
+00:35:47.163 --> 00:35:49.310
+the derivation of why this is the right
+
+00:35:49.310 --> 00:35:51.240
+answer and what it's minimizing, and
+
+00:35:51.240 --> 00:35:52.500
+that it's like doing with just
+
+00:35:52.500 --> 00:35:54.840
+aggression, et cetera, that's all a
+
+00:35:54.840 --> 00:35:56.960
+little bit more complicated, but it's
+
+00:35:56.960 --> 00:35:58.250
+well worth reading if you're
+
+00:35:58.250 --> 00:35:58.660
+interested.
+
+00:35:58.660 --> 00:36:00.046
+So there's a link here.
+
+00:36:00.046 --> 00:36:02.085
+This is my favorite boosting paper,
+
+00:36:02.085 --> 00:36:03.780
+that out of logistic regression paper.
+
+00:36:04.510 --> 00:36:07.660
+But this paper is also probably a good
+
+00:36:07.660 --> 00:36:08.080
+one to read.
+
+00:36:08.080 --> 00:36:11.440
+First, the intro to boosting by friend
+
+00:36:11.440 --> 00:36:12.040
+and Shapiro.
+
+00:36:16.960 --> 00:36:18.910
+So we can use this with trees.
+
+00:36:18.910 --> 00:36:21.420
+We initialize the weights to be
+
+00:36:21.420 --> 00:36:22.190
+uniform.
+
+00:36:22.190 --> 00:36:24.250
+Then for each tree, usually you do like
+
+00:36:24.250 --> 00:36:24.840
+maybe 20.
+
+00:36:25.520 --> 00:36:27.740
+You train a small tree this time.
+
+00:36:28.880 --> 00:36:31.370
+So you want to train a small tree,
+
+00:36:31.370 --> 00:36:33.550
+because the idea of boosting is that
+
+00:36:33.550 --> 00:36:36.020
+you're going to reduce the variance by
+
+00:36:36.020 --> 00:36:38.270
+having each subsequent classifier fix
+
+00:36:38.270 --> 00:36:39.810
+the mistakes of the previous ones.
+
+00:36:40.880 --> 00:36:44.580
+So in random forests you have high
+
+00:36:44.580 --> 00:36:46.730
+variance, low bias classifiers that
+
+00:36:46.730 --> 00:36:49.650
+you've averaged to get low biased low
+
+00:36:49.650 --> 00:36:50.490
+variance classifiers.
+
+00:36:51.170 --> 00:36:53.560
+In boosting you have low variance, high
+
+00:36:53.560 --> 00:36:56.400
+bias classifiers that you incrementally
+
+00:36:56.400 --> 00:36:58.730
+train to end up with a low biased, low
+
+00:36:58.730 --> 00:36:59.580
+variance classifier.
+
+00:37:01.600 --> 00:37:04.470
+So you the tree to a depth, typically
+
+00:37:04.470 --> 00:37:05.620
+two to four.
+
+00:37:05.620 --> 00:37:07.960
+So often it might sound silly, but
+
+00:37:07.960 --> 00:37:09.690
+often you only choose one feature and
+
+00:37:09.690 --> 00:37:11.096
+split based on that, and you just have
+
+00:37:11.096 --> 00:37:13.020
+like the shortest tree possible, a tree
+
+00:37:13.020 --> 00:37:16.050
+with two leaf nodes, and you train 200
+
+00:37:16.050 --> 00:37:16.910
+of these trees.
+
+00:37:17.600 --> 00:37:19.975
+That actually is surprisingly it works.
+
+00:37:19.975 --> 00:37:22.810
+It works quite well, but you might
+
+00:37:22.810 --> 00:37:23.840
+train deeper trees.
+
+00:37:25.890 --> 00:37:28.880
+So I've used this method for predicting
+
+00:37:28.880 --> 00:37:31.400
+like whether pixels belong to the
+
+00:37:31.400 --> 00:37:34.300
+ground or sky or et cetera, and I had
+
+00:37:34.300 --> 00:37:37.945
+like trees that were of death three and
+
+00:37:37.945 --> 00:37:39.180
+I trained 20 trees.
+
+00:37:40.810 --> 00:37:43.480
+You estimate you estimate logic
+
+00:37:43.480 --> 00:37:44.810
+prediction at each leaf node.
+
+00:37:44.810 --> 00:37:46.840
+So just based on the count of how many
+
+00:37:46.840 --> 00:37:48.860
+times each class appears in each leaf
+
+00:37:48.860 --> 00:37:50.780
+node, reweigh the samples and repeat.
+
+00:37:52.060 --> 00:37:53.780
+And then at the end you have the
+
+00:37:53.780 --> 00:37:55.290
+prediction is the sum of the logic
+
+00:37:55.290 --> 00:37:56.610
+predictions from all the trees.
+
+00:37:59.890 --> 00:38:02.470
+So this is a.
+
+00:38:03.810 --> 00:38:07.490
+There's like one study by there's a
+
+00:38:07.490 --> 00:38:09.590
+couple of studies by Caruana of
+
+00:38:09.590 --> 00:38:11.110
+comparing different machine learning
+
+00:38:11.110 --> 00:38:11.600
+methods.
+
+00:38:12.320 --> 00:38:14.720
+On a bunch of different datasets, so
+
+00:38:14.720 --> 00:38:16.660
+this one is from 2006.
+
+00:38:17.480 --> 00:38:20.300
+So these are all different data sets.
+
+00:38:20.300 --> 00:38:21.750
+It's not too important what they are.
+
+00:38:22.950 --> 00:38:24.610
+In this case, they're kind of smaller
+
+00:38:24.610 --> 00:38:26.470
+data sets, not too not too many
+
+00:38:26.470 --> 00:38:27.890
+samples, not too many features.
+
+00:38:28.620 --> 00:38:31.520
+And the scores are normalized so that
+
+00:38:31.520 --> 00:38:34.040
+one is like the best achievable score
+
+00:38:34.040 --> 00:38:37.130
+and I guess zero would be like chance.
+
+00:38:37.130 --> 00:38:39.940
+So that way you can average the
+
+00:38:39.940 --> 00:38:41.890
+performance across different data sets
+
+00:38:41.890 --> 00:38:43.300
+in a more meaningful way than if you
+
+00:38:43.300 --> 00:38:44.660
+were just averaging their errors.
+
+00:38:46.020 --> 00:38:47.760
+So here this is like a normalized
+
+00:38:47.760 --> 00:38:50.200
+accuracy, so higher is better.
+
+00:38:51.260 --> 00:38:54.700
+And then this BTDT is boosted decision
+
+00:38:54.700 --> 00:38:56.760
+tree, our F is random forest and north
+
+00:38:56.760 --> 00:38:59.020
+is neural network, Ann SVM, which we'll
+
+00:38:59.020 --> 00:39:01.420
+talk about Thursday night Bayes,
+
+00:39:01.420 --> 00:39:02.630
+logistic regression.
+
+00:39:02.630 --> 00:39:05.580
+So Naive Bayes is like pulling up the
+
+00:39:05.580 --> 00:39:06.980
+rear, not doing so well.
+
+00:39:06.980 --> 00:39:08.055
+It's at the very bottom.
+
+00:39:08.055 --> 00:39:10.236
+The district regression is just above
+
+00:39:10.236 --> 00:39:10.588
+that.
+
+00:39:10.588 --> 00:39:12.370
+Decision trees are just above that.
+
+00:39:13.160 --> 00:39:14.890
+And then boosted stumps.
+
+00:39:14.890 --> 00:39:17.130
+If you train a very shallow tree that
+
+00:39:17.130 --> 00:39:19.540
+only has one feature in each tree,
+
+00:39:19.540 --> 00:39:20.810
+that's the next best.
+
+00:39:20.810 --> 00:39:22.010
+It's actually pretty similar to
+
+00:39:22.010 --> 00:39:22.930
+logistic regression.
+
+00:39:24.050 --> 00:39:29.110
+K&N near neural networks SVMS.
+
+00:39:29.760 --> 00:39:32.860
+And then the top is boosted decision
+
+00:39:32.860 --> 00:39:33.940
+trees and random forests.
+
+00:39:34.680 --> 00:39:36.440
+And there's different versions of this,
+
+00:39:36.440 --> 00:39:37.903
+which is just like different ways of
+
+00:39:37.903 --> 00:39:39.130
+trying to calibrate your final
+
+00:39:39.130 --> 00:39:40.550
+prediction, which means trying to make
+
+00:39:40.550 --> 00:39:41.890
+it better fit of probability.
+
+00:39:41.890 --> 00:39:44.055
+But that's not our topic for now, so
+
+00:39:44.055 --> 00:39:45.290
+that's kind of ignorable.
+
+00:39:46.110 --> 00:39:48.350
+Main the main conclusion is that in
+
+00:39:48.350 --> 00:39:50.690
+this competition among classifiers.
+
+00:39:51.340 --> 00:39:54.690
+Boosted decision trees is #1 and
+
+00:39:54.690 --> 00:39:56.950
+following very close behind is random
+
+00:39:56.950 --> 00:39:58.810
+forests with almost the same average
+
+00:39:58.810 --> 00:39:59.180
+score.
+
+00:40:00.070 --> 00:40:01.890
+So these two ensemble methods of trees
+
+00:40:01.890 --> 00:40:03.070
+are the two best methods.
+
+00:40:04.040 --> 00:40:05.030
+According to the study.
+
+00:40:06.160 --> 00:40:07.990
+Then in 2008 they did another
+
+00:40:07.990 --> 00:40:11.110
+comparison on high dimensional data.
+
+00:40:12.360 --> 00:40:14.570
+So here they had the features range
+
+00:40:14.570 --> 00:40:17.900
+from around 700 features to 685,000
+
+00:40:17.900 --> 00:40:18.870
+features.
+
+00:40:19.750 --> 00:40:21.540
+This is like IMDb where you're trying
+
+00:40:21.540 --> 00:40:25.490
+to predict the rating of movies.
+
+00:40:25.490 --> 00:40:28.750
+I think spam classification and other
+
+00:40:28.750 --> 00:40:29.210
+problems.
+
+00:40:30.100 --> 00:40:32.340
+And then again, they're comparing the
+
+00:40:32.340 --> 00:40:33.460
+different approaches.
+
+00:40:33.460 --> 00:40:36.675
+So again, boosted decision trees gets
+
+00:40:36.675 --> 00:40:38.400
+the best score on average.
+
+00:40:38.400 --> 00:40:41.030
+I don't know exactly how the weighting
+
+00:40:41.030 --> 00:40:42.480
+is done here, they can be greater than
+
+00:40:42.480 --> 00:40:42.580
+one.
+
+00:40:43.270 --> 00:40:45.410
+But boosted decision trees probably
+
+00:40:45.410 --> 00:40:46.963
+compared to some baseline boosted
+
+00:40:46.963 --> 00:40:48.610
+decision trees gets the best score on
+
+00:40:48.610 --> 00:40:49.340
+average.
+
+00:40:49.340 --> 00:40:51.650
+And random forests is number 2.
+
+00:40:51.650 --> 00:40:53.660
+Again, it's naive Bayes on the bottom.
+
+00:40:53.750 --> 00:40:54.210
+
+
+00:40:55.000 --> 00:40:56.420
+Logistic regression does a bit better
+
+00:40:56.420 --> 00:40:57.780
+and this high dimensional data.
+
+00:40:57.780 --> 00:40:59.420
+Again, linear classifiers are more
+
+00:40:59.420 --> 00:41:00.950
+powerful when you have more features,
+
+00:41:00.950 --> 00:41:03.980
+but still not outperforming their
+
+00:41:03.980 --> 00:41:05.750
+neural networks or SVM or random
+
+00:41:05.750 --> 00:41:06.140
+forests.
+
+00:41:07.950 --> 00:41:10.620
+But also, even though boosted decision
+
+00:41:10.620 --> 00:41:13.070
+trees did the best on average, they're
+
+00:41:13.070 --> 00:41:15.150
+not doing so when you have tons of
+
+00:41:15.150 --> 00:41:15.940
+features.
+
+00:41:15.940 --> 00:41:17.926
+They're random forest is doing the
+
+00:41:17.926 --> 00:41:18.189
+best.
+
+00:41:19.490 --> 00:41:22.200
+And the reason for that is that boosted
+
+00:41:22.200 --> 00:41:27.580
+decision trees have a weakness of that.
+
+00:41:27.810 --> 00:41:29.700
+High.
+
+00:41:29.770 --> 00:41:30.380
+
+
+00:41:31.500 --> 00:41:31.932
+They have.
+
+00:41:31.932 --> 00:41:33.480
+They have a weakness of tending to
+
+00:41:33.480 --> 00:41:35.100
+overfit the data if they've got too
+
+00:41:35.100 --> 00:41:36.210
+much flexibility.
+
+00:41:36.210 --> 00:41:39.049
+So if you have 600,000 features and
+
+00:41:39.050 --> 00:41:40.512
+you're trying to just fix the mistakes
+
+00:41:40.512 --> 00:41:42.930
+of the previous classifier iteratively,
+
+00:41:42.930 --> 00:41:44.400
+then there's a pretty good chance that
+
+00:41:44.400 --> 00:41:45.840
+you could fix those mistakes for the
+
+00:41:45.840 --> 00:41:46.365
+wrong reason.
+
+00:41:46.365 --> 00:41:47.970
+And so they tend to be.
+
+00:41:47.970 --> 00:41:49.847
+When you have a lot of features, you
+
+00:41:49.847 --> 00:41:52.596
+end up with high, high variance, high
+
+00:41:52.596 --> 00:41:55.186
+bias features that you then reduce the
+
+00:41:55.186 --> 00:41:57.588
+variance of, but you still end up with
+
+00:41:57.588 --> 00:41:59.840
+high variance, low bias features
+
+00:41:59.840 --> 00:42:00.710
+classifiers.
+
+00:42:05.030 --> 00:42:07.480
+So just to recap that boosted decision
+
+00:42:07.480 --> 00:42:09.150
+trees and random forests work for
+
+00:42:09.150 --> 00:42:10.063
+different reasons.
+
+00:42:10.063 --> 00:42:12.345
+Boosted trees use a lot of small trees
+
+00:42:12.345 --> 00:42:14.430
+to iteratively refine the prediction,
+
+00:42:14.430 --> 00:42:16.445
+and combining the prediction from many
+
+00:42:16.445 --> 00:42:18.020
+trees reduces the bias.
+
+00:42:18.020 --> 00:42:20.380
+But they have a danger of overfitting
+
+00:42:20.380 --> 00:42:22.717
+if you have too many trees, or the
+
+00:42:22.717 --> 00:42:24.640
+trees are too big or you have too many
+
+00:42:24.640 --> 00:42:25.160
+features.
+
+00:42:25.820 --> 00:42:28.470
+Then they may not generalize that well.
+
+00:42:29.740 --> 00:42:32.170
+Random forests used big trees, which
+
+00:42:32.170 --> 00:42:34.050
+are low bias and high variance.
+
+00:42:34.050 --> 00:42:36.000
+They average a lot of those tree
+
+00:42:36.000 --> 00:42:38.303
+predictions, which reduces the
+
+00:42:38.303 --> 00:42:40.170
+variance, and it's kind of hard to make
+
+00:42:40.170 --> 00:42:41.079
+them not work.
+
+00:42:41.080 --> 00:42:42.900
+They're not always like the very best
+
+00:42:42.900 --> 00:42:46.320
+thing you can do, but they always, as
+
+00:42:46.320 --> 00:42:48.240
+far as I can see and I've ever seen,
+
+00:42:48.240 --> 00:42:49.810
+they always work like at least pretty
+
+00:42:49.810 --> 00:42:50.110
+well.
+
+00:42:51.130 --> 00:42:52.790
+As long as you just train enough trees.
+
+00:42:55.870 --> 00:42:56.906
+Ensemble.
+
+00:42:56.906 --> 00:43:00.090
+There's other kinds of ensembles too,
+
+00:43:00.090 --> 00:43:01.635
+so you can average the predictions of
+
+00:43:01.635 --> 00:43:03.280
+any classifiers as long as they're not
+
+00:43:03.280 --> 00:43:04.210
+duplicates of each other.
+
+00:43:04.210 --> 00:43:05.323
+If they're duplicates of each other,
+
+00:43:05.323 --> 00:43:07.150
+you don't get any benefit, obviously,
+
+00:43:07.150 --> 00:43:08.260
+because they'll just make the same
+
+00:43:08.260 --> 00:43:08.720
+prediction.
+
+00:43:10.000 --> 00:43:12.170
+So you can also apply this to deep
+
+00:43:12.170 --> 00:43:13.510
+neural networks, for example.
+
+00:43:13.510 --> 00:43:15.650
+So here is something showing that
+
+00:43:15.650 --> 00:43:19.120
+cascades and averages on average
+
+00:43:19.120 --> 00:43:21.430
+ensembles of classifiers outperform
+
+00:43:21.430 --> 00:43:23.260
+single classifiers even when you're
+
+00:43:23.260 --> 00:43:25.470
+considering the computation required
+
+00:43:25.470 --> 00:43:26.110
+for them.
+
+00:43:27.550 --> 00:43:29.460
+And a cascade is when you train one
+
+00:43:29.460 --> 00:43:30.340
+classifier.
+
+00:43:31.050 --> 00:43:34.512
+And then you let it make its confident
+
+00:43:34.512 --> 00:43:36.180
+decisions, and then subsequent
+
+00:43:36.180 --> 00:43:38.240
+classifiers only make decisions about
+
+00:43:38.240 --> 00:43:39.280
+the less confident.
+
+00:43:40.500 --> 00:43:41.660
+Examples.
+
+00:43:41.660 --> 00:43:42.870
+And then you keep on doing that.
+
+00:43:46.120 --> 00:43:49.770
+Let me give you a two-minute stretch
+
+00:43:49.770 --> 00:43:51.430
+break before I go into a detailed
+
+00:43:51.430 --> 00:43:53.670
+example of using random forests.
+
+00:43:54.690 --> 00:43:56.620
+And you can think about this question
+
+00:43:56.620 --> 00:43:57.220
+if you want.
+
+00:43:57.920 --> 00:44:00.120
+So suppose you had an infinite size
+
+00:44:00.120 --> 00:44:03.100
+audience and where and they could
+
+00:44:03.100 --> 00:44:04.100
+choose ABCD.
+
+00:44:05.500 --> 00:44:07.120
+What is the situation where you're
+
+00:44:07.120 --> 00:44:08.845
+guaranteed to have a correct answer?
+
+00:44:08.845 --> 00:44:11.410
+What if, let's say, a randomly sampled
+
+00:44:11.410 --> 00:44:12.970
+audience member is going to report an
+
+00:44:12.970 --> 00:44:14.800
+answer with probability PY?
+
+00:44:15.770 --> 00:44:17.650
+What guarantees a correct answer?
+
+00:44:17.650 --> 00:44:19.930
+And let's say instead you choose a
+
+00:44:19.930 --> 00:44:21.850
+friend which is a random member of the
+
+00:44:21.850 --> 00:44:22.830
+audience in this case.
+
+00:44:23.570 --> 00:44:24.900
+What's the probability that your
+
+00:44:24.900 --> 00:44:25.930
+friend's answer is correct?
+
+00:44:26.560 --> 00:44:28.950
+So think about those or don't.
+
+00:44:28.950 --> 00:44:30.280
+It's up to you.
+
+00:44:30.280 --> 00:44:31.790
+I'll give you the answer in 2 minutes.
+
+00:45:07.040 --> 00:45:09.180
+Some people would, they would say like
+
+00:45:09.180 --> 00:45:11.130
+cherry or yeah.
+
+00:45:13.980 --> 00:45:14.270
+Yeah.
+
+00:45:15.730 --> 00:45:17.400
+Or they might be color blind.
+
+00:45:18.390 --> 00:45:18.960
+I see.
+
+00:45:24.750 --> 00:45:25.310
+That's true.
+
+00:45:29.140 --> 00:45:31.120
+It's actually pretty hard not get a
+
+00:45:31.120 --> 00:45:32.550
+correct answer, I would say.
+
+00:45:43.340 --> 00:45:46.300
+Correct decision wide away look goes
+
+00:45:46.300 --> 00:45:49.670
+down because you want the subsequent
+
+00:45:49.670 --> 00:45:51.240
+classifiers to focus more on the
+
+00:45:51.240 --> 00:45:52.050
+mistakes.
+
+00:45:52.050 --> 00:45:56.300
+So if it's incorrect then the weight
+
+00:45:56.300 --> 00:45:57.920
+goes up so then it matters more to the
+
+00:45:57.920 --> 00:45:58.730
+next classifier.
+
+00:46:02.730 --> 00:46:04.160
+Unclassified award goes to.
+
+00:46:06.000 --> 00:46:07.700
+It could go back up, yeah.
+
+00:46:10.830 --> 00:46:12.670
+The weights keeping being multiplied by
+
+00:46:12.670 --> 00:46:14.500
+that factor, so yeah.
+
+00:46:15.520 --> 00:46:15.870
+Yeah.
+
+00:46:17.280 --> 00:46:17.700
+You're welcome.
+
+00:46:25.930 --> 00:46:27.410
+All right, times up.
+
+00:46:28.930 --> 00:46:32.470
+So what is like the weakest condition?
+
+00:46:32.470 --> 00:46:34.270
+I should have made it a little harder.
+
+00:46:34.270 --> 00:46:35.900
+Obviously there's one condition, which
+
+00:46:35.900 --> 00:46:37.450
+is that every audience member knows the
+
+00:46:37.450 --> 00:46:37.820
+answer.
+
+00:46:37.820 --> 00:46:38.380
+That's easy.
+
+00:46:39.350 --> 00:46:41.160
+But what's the weakest condition that
+
+00:46:41.160 --> 00:46:43.090
+guarantees a correct answer?
+
+00:46:43.090 --> 00:46:45.725
+So what has to be true for this answer
+
+00:46:45.725 --> 00:46:47.330
+to be correct with an infinite audience
+
+00:46:47.330 --> 00:46:47.710
+size?
+
+00:46:52.040 --> 00:46:52.530
+Right.
+
+00:46:54.740 --> 00:46:56.290
+Yes, one audience member.
+
+00:46:56.290 --> 00:46:57.810
+No, that won't work.
+
+00:46:57.810 --> 00:46:59.550
+So because then the probability would
+
+00:46:59.550 --> 00:47:03.790
+be 0 right of the correct answer if all
+
+00:47:03.790 --> 00:47:05.470
+the other audience members thought it
+
+00:47:05.470 --> 00:47:06.280
+was a different answer.
+
+00:47:10.760 --> 00:47:12.740
+If this size of the audience is one,
+
+00:47:12.740 --> 00:47:14.936
+yeah, but you have an infinite size
+
+00:47:14.936 --> 00:47:15.940
+audience and the problem.
+
+00:47:18.270 --> 00:47:18.770
+Does anybody?
+
+00:47:18.770 --> 00:47:19.940
+Yeah.
+
+00:47:23.010 --> 00:47:24.938
+Yes, the probability of the correct
+
+00:47:24.938 --> 00:47:26.070
+answer has to be the highest.
+
+00:47:26.070 --> 00:47:27.548
+So if the probability of the correct
+
+00:47:27.548 --> 00:47:30.714
+answer is say 26%, but the probability
+
+00:47:30.714 --> 00:47:33.220
+of all the other answers is like just
+
+00:47:33.220 --> 00:47:35.923
+under 25%, then you'll get the correct
+
+00:47:35.923 --> 00:47:36.226
+answer.
+
+00:47:36.226 --> 00:47:38.578
+So even though almost three out of four
+
+00:47:38.578 --> 00:47:41.013
+of the audience members can be wrong,
+
+00:47:41.013 --> 00:47:41.569
+it's.
+
+00:47:41.570 --> 00:47:43.378
+I mean, it's possible for three out of
+
+00:47:43.378 --> 00:47:45.038
+four of the audience members to be
+
+00:47:45.038 --> 00:47:46.698
+wrong almost, but still get the correct
+
+00:47:46.698 --> 00:47:48.140
+answer, still be guaranteed they're
+
+00:47:48.140 --> 00:47:48.760
+correct answer.
+
+00:47:50.250 --> 00:47:52.385
+If you were to pull the infinite size
+
+00:47:52.385 --> 00:47:53.940
+audience, of course with the limited
+
+00:47:53.940 --> 00:47:55.930
+audience you also have then variance,
+
+00:47:55.930 --> 00:47:57.800
+so you would want a bigger margin to be
+
+00:47:57.800 --> 00:47:58.190
+confident.
+
+00:47:59.100 --> 00:48:01.480
+And if a friend is a random member of
+
+00:48:01.480 --> 00:48:02.660
+the audience, this is an easier
+
+00:48:02.660 --> 00:48:03.270
+question.
+
+00:48:03.270 --> 00:48:05.190
+Then what's the probability that your
+
+00:48:05.190 --> 00:48:06.290
+friend's answer is correct?
+
+00:48:09.150 --> 00:48:09.440
+Right.
+
+00:48:10.320 --> 00:48:11.852
+Yeah, P of A, yeah.
+
+00:48:11.852 --> 00:48:13.830
+So in this setting, so it's possible
+
+00:48:13.830 --> 00:48:15.898
+that your friend could only have a 25%
+
+00:48:15.898 --> 00:48:17.650
+chance of being correct, but the
+
+00:48:17.650 --> 00:48:19.595
+audience has a 100% chance of being
+
+00:48:19.595 --> 00:48:19.859
+correct.
+
+00:48:24.800 --> 00:48:26.830
+Alright, so I'm going to give a
+
+00:48:26.830 --> 00:48:29.010
+detailed example of random forests.
+
+00:48:29.010 --> 00:48:30.950
+If you took computational photography
+
+00:48:30.950 --> 00:48:32.850
+with me, then you saw this example, but
+
+00:48:32.850 --> 00:48:34.100
+now you will see it in a new light.
+
+00:48:34.950 --> 00:48:37.960
+And so this is using this is the Kinect
+
+00:48:37.960 --> 00:48:38.490
+algorithm.
+
+00:48:38.490 --> 00:48:40.220
+So you guys might remember the Kinect
+
+00:48:40.220 --> 00:48:42.740
+came out in around 2011.
+
+00:48:43.720 --> 00:48:46.080
+For gaming and then was like widely
+
+00:48:46.080 --> 00:48:47.590
+adopted by the robotics community
+
+00:48:47.590 --> 00:48:48.270
+question.
+
+00:48:56.480 --> 00:48:59.850
+Alright, the answer is probability of a
+
+00:48:59.850 --> 00:49:04.080
+can be just marginally above 25% and
+
+00:49:04.080 --> 00:49:06.360
+the other probabilities are marginally
+
+00:49:06.360 --> 00:49:07.440
+below 25%.
+
+00:49:09.310 --> 00:49:09.720
+Yeah.
+
+00:49:11.560 --> 00:49:15.050
+All right, so the Kinect came out, you
+
+00:49:15.050 --> 00:49:17.280
+could play lots of games with it and it
+
+00:49:17.280 --> 00:49:18.570
+was also used for robotics.
+
+00:49:18.570 --> 00:49:20.864
+But for the games anyway, one of the
+
+00:49:20.864 --> 00:49:22.950
+one of the key things they had to solve
+
+00:49:22.950 --> 00:49:23.943
+was to.
+
+00:49:23.943 --> 00:49:26.635
+So first the Kinect has it does some
+
+00:49:26.635 --> 00:49:28.120
+like structured light thing in order to
+
+00:49:28.120 --> 00:49:28.990
+get a depth image.
+
+00:49:29.660 --> 00:49:30.550
+And then?
+
+00:49:30.720 --> 00:49:31.330
+And.
+
+00:49:32.070 --> 00:49:34.040
+And then the Kinect needs to estimate
+
+00:49:34.040 --> 00:49:37.000
+body purpose given the depth image, so
+
+00:49:37.000 --> 00:49:38.940
+that it can tell if you're like dancing
+
+00:49:38.940 --> 00:49:40.810
+correctly or doing the sport or
+
+00:49:40.810 --> 00:49:44.000
+whatever corresponds to the game.
+
+00:49:45.020 --> 00:49:47.260
+So given this depth image, you have to
+
+00:49:47.260 --> 00:49:50.580
+try to predict for like what are the
+
+00:49:50.580 --> 00:49:52.300
+key points of the body pose.
+
+00:49:52.300 --> 00:49:53.050
+That's the problem.
+
+00:49:54.850 --> 00:49:56.840
+And they need to do it really fast too,
+
+00:49:56.840 --> 00:49:59.230
+because they're because they only get a
+
+00:49:59.230 --> 00:50:02.064
+small fraction of the GPU of the Xbox
+
+00:50:02.064 --> 00:50:05.222
+to do this, 2% of the GPU of the Xbox
+
+00:50:05.222 --> 00:50:06.740
+to do this in real time.
+
+00:50:09.190 --> 00:50:12.370
+So the basic algorithm is from.
+
+00:50:12.370 --> 00:50:15.450
+This is described in this paper by
+
+00:50:15.450 --> 00:50:16.640
+Microsoft Cambridge.
+
+00:50:17.400 --> 00:50:21.430
+And the overall the processes, you go
+
+00:50:21.430 --> 00:50:23.180
+from a depth image and segment it.
+
+00:50:23.180 --> 00:50:25.950
+Then you predict for each pixel which
+
+00:50:25.950 --> 00:50:28.200
+of the body parts corresponds to that
+
+00:50:28.200 --> 00:50:29.200
+pixel.
+
+00:50:29.200 --> 00:50:30.410
+Is it like the right side of the face
+
+00:50:30.410 --> 00:50:31.380
+or left side of the face?
+
+00:50:32.180 --> 00:50:34.540
+And then you take those predictions and
+
+00:50:34.540 --> 00:50:36.210
+combine them to get a key point
+
+00:50:36.210 --> 00:50:36.730
+estimate.
+
+00:50:38.490 --> 00:50:39.730
+So here's another view of it.
+
+00:50:40.400 --> 00:50:42.905
+Given RGB image, that's Jamie shot in
+
+00:50:42.905 --> 00:50:45.846
+the first author you then and a depth
+
+00:50:45.846 --> 00:50:46.223
+image.
+
+00:50:46.223 --> 00:50:48.120
+You don't use the RGB actually, you
+
+00:50:48.120 --> 00:50:49.983
+just segment out the body from the
+
+00:50:49.983 --> 00:50:50.199
+depth.
+
+00:50:50.200 --> 00:50:51.900
+It's like the near pixels.
+
+00:50:52.670 --> 00:50:55.185
+And then you label them into parts and
+
+00:50:55.185 --> 00:50:57.790
+then you assign the joint positions.
+
+00:51:00.690 --> 00:51:03.489
+So the reason this is kind of this is
+
+00:51:03.490 --> 00:51:05.050
+pretty hard because you're going to
+
+00:51:05.050 --> 00:51:06.470
+have a lot of different bodies and
+
+00:51:06.470 --> 00:51:08.370
+orientations and poses and wearing
+
+00:51:08.370 --> 00:51:10.500
+different kinds of clothes, and you
+
+00:51:10.500 --> 00:51:12.490
+want this to work for everybody because
+
+00:51:12.490 --> 00:51:14.400
+if it fails, then the games not any
+
+00:51:14.400 --> 00:51:14.710
+fun.
+
+00:51:15.740 --> 00:51:19.610
+And So what they did is they collected
+
+00:51:19.610 --> 00:51:22.995
+a lot of examples of motion capture
+
+00:51:22.995 --> 00:51:24.990
+they had like different people do like
+
+00:51:24.990 --> 00:51:26.970
+motion capture and got like real
+
+00:51:26.970 --> 00:51:30.190
+examples and then they took those body
+
+00:51:30.190 --> 00:51:33.270
+frames and rigged a synthetic models.
+
+00:51:33.940 --> 00:51:35.700
+And generated even more synthetic
+
+00:51:35.700 --> 00:51:37.550
+examples of people in the same poses.
+
+00:51:38.150 --> 00:51:40.020
+And on these synthetic examples, it was
+
+00:51:40.020 --> 00:51:41.945
+easy to label the parts because they're
+
+00:51:41.945 --> 00:51:42.450
+synthetic.
+
+00:51:42.450 --> 00:51:44.080
+So they could just like essentially
+
+00:51:44.080 --> 00:51:46.740
+texture the parts and then they would
+
+00:51:46.740 --> 00:51:48.880
+know like which pixel corresponds to
+
+00:51:48.880 --> 00:51:49.410
+each label.
+
+00:51:51.640 --> 00:51:53.930
+So the same this is showing that the
+
+00:51:53.930 --> 00:51:58.010
+same body part this wrist or hand here.
+
+00:51:58.740 --> 00:52:00.300
+Can look quite different.
+
+00:52:00.300 --> 00:52:02.050
+It's the same part in all of these
+
+00:52:02.050 --> 00:52:04.200
+images, but depending on where it is
+
+00:52:04.200 --> 00:52:05.700
+and how the body is posed, then the
+
+00:52:05.700 --> 00:52:06.820
+image looks pretty different.
+
+00:52:06.820 --> 00:52:09.060
+So this is a pretty challenging problem
+
+00:52:09.060 --> 00:52:11.590
+to know that this pixel in the center
+
+00:52:11.590 --> 00:52:14.520
+of the cross is the wrist.
+
+00:52:15.390 --> 00:52:16.090
+Where the hand?
+
+00:52:19.180 --> 00:52:21.070
+All right, so the thresholding of the
+
+00:52:21.070 --> 00:52:24.640
+depth is relatively straightforward.
+
+00:52:24.640 --> 00:52:27.190
+And then they need to learn to predict
+
+00:52:27.190 --> 00:52:30.599
+for each pixel whether which of the
+
+00:52:30.600 --> 00:52:32.700
+possible body parts that pixel
+
+00:52:32.700 --> 00:52:33.510
+corresponds to.
+
+00:52:34.910 --> 00:52:37.015
+And these really simple features, the
+
+00:52:37.015 --> 00:52:41.500
+features are either a an offset feature
+
+00:52:41.500 --> 00:52:43.270
+where if you're trying to predict for
+
+00:52:43.270 --> 00:52:46.610
+this pixel at the center, here you
+
+00:52:46.610 --> 00:52:49.570
+shift some number of pixels that are
+
+00:52:49.570 --> 00:52:51.650
+dependent, so some pixels times depth.
+
+00:52:52.360 --> 00:52:54.100
+In some direction, and you look at the
+
+00:52:54.100 --> 00:52:55.740
+depth of that corresponding pixel,
+
+00:52:55.740 --> 00:52:58.230
+which could be like a particular value
+
+00:52:58.230 --> 00:52:59.660
+to indicate that it's off the body.
+
+00:53:01.290 --> 00:53:03.020
+So if you're at this pixel and you use
+
+00:53:03.020 --> 00:53:05.205
+this feature Theta one, then you end up
+
+00:53:05.205 --> 00:53:05.667
+over here.
+
+00:53:05.667 --> 00:53:07.144
+If you're looking at this pixel then
+
+00:53:07.144 --> 00:53:08.770
+you end up on the head over here in
+
+00:53:08.770 --> 00:53:09.450
+this example.
+
+00:53:10.350 --> 00:53:12.440
+And then you have other features that
+
+00:53:12.440 --> 00:53:14.210
+are based on the difference of depths.
+
+00:53:14.210 --> 00:53:16.870
+So given some position, you look at 2
+
+00:53:16.870 --> 00:53:19.000
+offsets and take the difference of
+
+00:53:19.000 --> 00:53:19.600
+those depths.
+
+00:53:21.300 --> 00:53:23.260
+And then you can generate like
+
+00:53:23.260 --> 00:53:25.020
+basically infinite numbers of those
+
+00:53:25.020 --> 00:53:26.010
+features, right?
+
+00:53:26.010 --> 00:53:27.895
+There's like a lot of combinations of
+
+00:53:27.895 --> 00:53:29.655
+features using different offsets that
+
+00:53:29.655 --> 00:53:30.485
+you could create.
+
+00:53:30.485 --> 00:53:32.510
+And they also have lots of data, which
+
+00:53:32.510 --> 00:53:34.500
+as I mentioned came from mocap and then
+
+00:53:34.500 --> 00:53:35.260
+synthetic data.
+
+00:53:36.390 --> 00:53:39.060
+And so they train, they train random
+
+00:53:39.060 --> 00:53:42.990
+forests based on these features on all
+
+00:53:42.990 --> 00:53:43.640
+this data.
+
+00:53:43.640 --> 00:53:45.030
+So again, they have millions of
+
+00:53:45.030 --> 00:53:45.900
+examples.
+
+00:53:45.900 --> 00:53:47.995
+They can like practically infinite
+
+00:53:47.995 --> 00:53:49.680
+features, but you'd sample some number
+
+00:53:49.680 --> 00:53:50.930
+of features and tree in a tree.
+
+00:53:53.210 --> 00:53:54.500
+I think I just explained that.
+
+00:53:56.320 --> 00:53:58.270
+Sorry, I got a little ahead of myself,
+
+00:53:58.270 --> 00:54:00.264
+but this is just an illustration of
+
+00:54:00.264 --> 00:54:03.808
+their training data, 500,000 frames and
+
+00:54:03.808 --> 00:54:07.414
+then they got 3D models for 15 bodies
+
+00:54:07.414 --> 00:54:09.990
+and then they synthesized all the
+
+00:54:09.990 --> 00:54:11.860
+motion capture data on all of those
+
+00:54:11.860 --> 00:54:14.160
+bodies to get their training and test
+
+00:54:14.160 --> 00:54:15.319
+in synthetic test data.
+
+00:54:16.200 --> 00:54:17.730
+So this is showing similar synthetic
+
+00:54:17.730 --> 00:54:18.110
+data.
+
+00:54:21.210 --> 00:54:24.110
+And then so they so they're classifier
+
+00:54:24.110 --> 00:54:26.500
+is a random forest, so again they just.
+
+00:54:26.570 --> 00:54:27.060
+
+
+00:54:27.830 --> 00:54:31.095
+Randomly sample a set of those possible
+
+00:54:31.095 --> 00:54:33.030
+features, or generate a set of features
+
+00:54:33.030 --> 00:54:35.700
+and randomly subsample their training
+
+00:54:35.700 --> 00:54:36.030
+data.
+
+00:54:36.900 --> 00:54:39.315
+And then train a tree to completion and
+
+00:54:39.315 --> 00:54:41.810
+then each tree or maybe to maximum
+
+00:54:41.810 --> 00:54:42.100
+depth.
+
+00:54:42.100 --> 00:54:43.575
+In this case you might not change the
+
+00:54:43.575 --> 00:54:44.820
+completion since you may have like
+
+00:54:44.820 --> 00:54:45.680
+millions of samples.
+
+00:54:46.770 --> 00:54:48.660
+But you trained to some depth and then
+
+00:54:48.660 --> 00:54:50.570
+each node will have some probability
+
+00:54:50.570 --> 00:54:52.160
+estimate for each of the classes.
+
+00:54:52.970 --> 00:54:54.626
+And then you generate a new tree and
+
+00:54:54.626 --> 00:54:56.400
+you keep on doing that independently.
+
+00:54:57.510 --> 00:54:59.100
+And then you at the end you're
+
+00:54:59.100 --> 00:55:01.282
+predictor is an average of the
+
+00:55:01.282 --> 00:55:03.230
+probabilities, the class probabilities
+
+00:55:03.230 --> 00:55:04.530
+that each of the trees predicts.
+
+00:55:05.970 --> 00:55:09.780
+So it may sound like at first glance
+
+00:55:09.780 --> 00:55:11.030
+when you look at this you might think,
+
+00:55:11.030 --> 00:55:13.530
+well this seems really slow you then in
+
+00:55:13.530 --> 00:55:14.880
+order to.
+
+00:55:15.410 --> 00:55:16.040
+Make a prediction.
+
+00:55:16.040 --> 00:55:17.936
+You have to query all of these trees
+
+00:55:17.936 --> 00:55:19.760
+and then sum up their responses.
+
+00:55:19.760 --> 00:55:21.940
+But when you're implementing an GPU,
+
+00:55:21.940 --> 00:55:23.658
+it's actually really fast because these
+
+00:55:23.658 --> 00:55:24.840
+can all be done in parallel.
+
+00:55:24.840 --> 00:55:26.334
+The trees don't depend on each other,
+
+00:55:26.334 --> 00:55:29.161
+so you can do the inference on all the
+
+00:55:29.161 --> 00:55:31.045
+trees simultaneously, and you can do
+
+00:55:31.045 --> 00:55:32.120
+inference for all the pixels
+
+00:55:32.120 --> 00:55:33.600
+simultaneously if you have enough
+
+00:55:33.600 --> 00:55:33.968
+memory.
+
+00:55:33.968 --> 00:55:36.919
+And so it's actually can be done in
+
+00:55:36.920 --> 00:55:38.225
+remarkably fast.
+
+00:55:38.225 --> 00:55:41.300
+So they can do this in real time using
+
+00:55:41.300 --> 00:55:43.506
+2% of the computational resources of
+
+00:55:43.506 --> 00:55:44.280
+the Xbox.
+
+00:55:48.160 --> 00:55:48.770
+
+
+00:55:49.810 --> 00:55:53.730
+And then finally they would get the, so
+
+00:55:53.730 --> 00:55:54.700
+I'll show it here.
+
+00:55:54.700 --> 00:55:56.249
+So first they are like labeling the
+
+00:55:56.250 --> 00:55:57.465
+pixels like this.
+
+00:55:57.465 --> 00:56:01.607
+So this is the, sorry, over here the
+
+00:56:01.607 --> 00:56:03.690
+Pixel labels can be like a little bit
+
+00:56:03.690 --> 00:56:05.410
+of noise, a little bit noisy, but at
+
+00:56:05.410 --> 00:56:07.170
+the end they don't need a pixel perfect
+
+00:56:07.170 --> 00:56:09.430
+segmentation or pixel perfect labeling.
+
+00:56:10.060 --> 00:56:11.990
+What they really care about is the
+
+00:56:11.990 --> 00:56:13.950
+position of the joints, the 3D position
+
+00:56:13.950 --> 00:56:14.790
+of the joints.
+
+00:56:15.710 --> 00:56:17.899
+And so based on the depth and based on
+
+00:56:17.900 --> 00:56:19.416
+which pixels are labeled with each
+
+00:56:19.416 --> 00:56:22.290
+joint, they can get the average 3D
+
+00:56:22.290 --> 00:56:24.420
+position of these labels.
+
+00:56:24.420 --> 00:56:27.280
+And then they just put it like slightly
+
+00:56:27.280 --> 00:56:29.070
+behind that in a joint dependent way.
+
+00:56:29.070 --> 00:56:31.429
+So like if that the average depth of
+
+00:56:31.429 --> 00:56:33.346
+these pixels on my shoulder, then that
+
+00:56:33.346 --> 00:56:34.860
+the center of my shoulder is going to
+
+00:56:34.860 --> 00:56:36.950
+be an inch and 1/2 behind that or
+
+00:56:36.950 --> 00:56:37.619
+something like that.
+
+00:56:38.450 --> 00:56:40.600
+So then you get the 3D position of my
+
+00:56:40.600 --> 00:56:41.030
+shoulder.
+
+00:56:42.480 --> 00:56:44.303
+And so even though they're pixel
+
+00:56:44.303 --> 00:56:46.280
+predictions might be a little noisy,
+
+00:56:46.280 --> 00:56:48.130
+the joint predictions are more accurate
+
+00:56:48.130 --> 00:56:49.550
+because they're based on a combination
+
+00:56:49.550 --> 00:56:50.499
+of pixel predictions.
+
+00:56:54.090 --> 00:56:55.595
+So here is showing the ground truth.
+
+00:56:55.595 --> 00:56:57.360
+This is the depth image, this is a
+
+00:56:57.360 --> 00:57:00.160
+pixel labels and then this is the joint
+
+00:57:00.160 --> 00:57:00.780
+labels.
+
+00:57:01.450 --> 00:57:03.850
+And then and.
+
+00:57:03.850 --> 00:57:06.005
+This is showing the actual predictions
+
+00:57:06.005 --> 00:57:07.210
+and some examples.
+
+00:57:09.420 --> 00:57:11.020
+And here you can see the same thing.
+
+00:57:11.020 --> 00:57:13.630
+So these are the input depth images.
+
+00:57:14.400 --> 00:57:16.480
+This is the pixel predictions on those
+
+00:57:16.480 --> 00:57:17.210
+depth images.
+
+00:57:17.860 --> 00:57:19.870
+And then this is showing the estimated
+
+00:57:19.870 --> 00:57:22.385
+pose from different perspectives so
+
+00:57:22.385 --> 00:57:24.910
+that you can see it looks kind of
+
+00:57:24.910 --> 00:57:25.100
+right.
+
+00:57:25.100 --> 00:57:26.780
+So like in this case for example, it's
+
+00:57:26.780 --> 00:57:28.570
+estimating that the person is standing
+
+00:57:28.570 --> 00:57:30.840
+with his hands like out and slightly in
+
+00:57:30.840 --> 00:57:31.110
+front.
+
+00:57:36.130 --> 00:57:38.440
+And you can see if you vary the number
+
+00:57:38.440 --> 00:57:41.810
+of training samples, you get like
+
+00:57:41.810 --> 00:57:42.670
+pretty good.
+
+00:57:42.670 --> 00:57:45.860
+I mean essentially what I would say is
+
+00:57:45.860 --> 00:57:47.239
+that you need a lot of training samples
+
+00:57:47.240 --> 00:57:48.980
+to do well in this task.
+
+00:57:49.660 --> 00:57:52.330
+So as you start to get up to 100,000 or
+
+00:57:52.330 --> 00:57:53.640
+a million training samples.
+
+00:57:54.300 --> 00:57:58.360
+Your average accuracy gets up to 60%.
+
+00:57:59.990 --> 00:58:02.350
+And 60% might not sound that good, but
+
+00:58:02.350 --> 00:58:04.339
+it's actually fine because a lot of the
+
+00:58:04.340 --> 00:58:05.930
+errors will just be on the margin where
+
+00:58:05.930 --> 00:58:08.050
+you're like whether this pixel is the
+
+00:58:08.050 --> 00:58:09.500
+upper arm or the shoulder.
+
+00:58:09.500 --> 00:58:13.110
+And so the per pixel accuracy of 60%
+
+00:58:13.110 --> 00:58:14.420
+gives you pretty accurate joint
+
+00:58:14.420 --> 00:58:15.030
+positions.
+
+00:58:16.680 --> 00:58:18.460
+One of the surprising things about the
+
+00:58:18.460 --> 00:58:21.979
+paper was that the synthetic data was
+
+00:58:21.980 --> 00:58:24.000
+so effective because in all past
+
+00:58:24.000 --> 00:58:26.322
+research, pretty much when people use
+
+00:58:26.322 --> 00:58:27.720
+synthetic data it didn't like
+
+00:58:27.720 --> 00:58:29.700
+generalize that did the test data.
+
+00:58:29.700 --> 00:58:30.940
+And I think the reason that it
+
+00:58:30.940 --> 00:58:32.580
+generalizes well in this case is that
+
+00:58:32.580 --> 00:58:34.830
+depth data is a lot easier to simulate
+
+00:58:34.830 --> 00:58:35.290
+than.
+
+00:58:35.930 --> 00:58:37.170
+RGB data.
+
+00:58:37.170 --> 00:58:39.810
+So now people have used RGB data
+
+00:58:39.810 --> 00:58:40.340
+somewhat.
+
+00:58:40.340 --> 00:58:43.440
+It's often used in autonomous vehicle
+
+00:58:43.440 --> 00:58:46.760
+training, but at the time it had not
+
+00:58:46.760 --> 00:58:47.920
+really been used effectively.
+
+00:58:58.700 --> 00:58:58.980
+OK.
+
+00:59:00.020 --> 00:59:01.500
+Is there any questions about that?
+
+00:59:04.850 --> 00:59:06.820
+And then the last big thing I want to
+
+00:59:06.820 --> 00:59:08.140
+do you're probably not.
+
+00:59:08.500 --> 00:59:11.210
+Emotionally ready for homework 2 yet,
+
+00:59:11.210 --> 00:59:12.740
+but I'll give it to you anyway.
+
+00:59:14.930 --> 00:59:16.510
+Is to show you homework too.
+
+00:59:25.020 --> 00:59:27.760
+Alright, so at least in some parts of
+
+00:59:27.760 --> 00:59:30.070
+this are going to be a bit familiar.
+
+00:59:32.020 --> 00:59:32.640
+Yeah.
+
+00:59:32.640 --> 00:59:33.140
+Thank you.
+
+00:59:34.070 --> 00:59:34.750
+I always forget.
+
+00:59:35.730 --> 00:59:37.640
+With that, let me get rid of that.
+
+00:59:38.500 --> 00:59:39.000
+OK.
+
+00:59:42.850 --> 00:59:43.480
+Damn it.
+
+00:59:51.800 --> 00:59:55.390
+Alright, let's see me in a bit.
+
+00:59:56.330 --> 00:59:56.840
+OK.
+
+00:59:57.980 --> 00:59:59.290
+All right, so there's three parts of
+
+00:59:59.290 --> 00:59:59.900
+this.
+
+00:59:59.900 --> 01:00:04.780
+The first part is looking at the
+
+01:00:04.780 --> 01:00:06.920
+effects of model complexity with tree
+
+01:00:06.920 --> 01:00:07.610
+regressors.
+
+01:00:08.870 --> 01:00:12.560
+So you train trees with different
+
+01:00:12.560 --> 01:00:13.190
+depths.
+
+01:00:13.800 --> 01:00:17.380
+And Oregon, random forests with
+
+01:00:17.380 --> 01:00:18.090
+different depths.
+
+01:00:19.120 --> 01:00:22.745
+And then you plot the error versus the
+
+01:00:22.745 --> 01:00:24.150
+versus the size.
+
+01:00:25.280 --> 01:00:26.440
+So it's actually.
+
+01:00:26.440 --> 01:00:27.350
+This is actually.
+
+01:00:29.290 --> 01:00:29.980
+Pretty easy.
+
+01:00:29.980 --> 01:00:31.720
+Code wise, it's, I'll show you.
+
+01:00:31.720 --> 01:00:34.240
+It's just to get to just see for
+
+01:00:34.240 --> 01:00:35.890
+yourself like the effects of depth.
+
+01:00:37.260 --> 01:00:38.830
+So in this case you don't need to
+
+01:00:38.830 --> 01:00:40.590
+implement the trees or the random
+
+01:00:40.590 --> 01:00:41.920
+forests, you can use the library.
+
+01:00:42.740 --> 01:00:43.940
+So, and we're going to use the
+
+01:00:43.940 --> 01:00:44.640
+temperature data.
+
+01:00:46.350 --> 01:00:48.910
+Essentially you would iterate over
+
+01:00:48.910 --> 01:00:51.360
+these Max depths which range from 2 to
+
+01:00:51.360 --> 01:00:52.020
+32.
+
+01:00:52.970 --> 01:00:54.890
+And then for each depth you would call
+
+01:00:54.890 --> 01:00:58.790
+these functions and get the error and
+
+01:00:58.790 --> 01:01:00.300
+then you can.
+
+01:01:01.500 --> 01:01:04.570
+And then you can call this code to plot
+
+01:01:04.570 --> 01:01:05.030
+the error.
+
+01:01:05.670 --> 01:01:07.610
+And then you'll look at that plot, and
+
+01:01:07.610 --> 01:01:08.440
+then you'll.
+
+01:01:09.250 --> 01:01:11.580
+Provide the plot and answer some
+
+01:01:11.580 --> 01:01:12.120
+questions.
+
+01:01:12.720 --> 01:01:16.180
+So in the report there's some questions
+
+01:01:16.180 --> 01:01:18.090
+for you to answer based on your
+
+01:01:18.090 --> 01:01:18.820
+analysis.
+
+01:01:20.350 --> 01:01:21.846
+They're like, given a maximum depth
+
+01:01:21.846 --> 01:01:26.130
+tree, which model has the lowest bias
+
+01:01:26.130 --> 01:01:28.089
+for regression trees, what tree depth
+
+01:01:28.090 --> 01:01:29.900
+achieves the minimum validation error?
+
+01:01:31.080 --> 01:01:33.440
+When is which model is least prone to
+
+01:01:33.440 --> 01:01:34.810
+overfitting, for example?
+
+01:01:37.480 --> 01:01:38.970
+So that's the first problem.
+
+01:01:40.030 --> 01:01:41.530
+The second problem, this is the one
+
+01:01:41.530 --> 01:01:43.485
+that's going to take you the most time,
+
+01:01:43.485 --> 01:01:46.950
+is using MLPS, so multilayer
+
+01:01:46.950 --> 01:01:48.390
+perceptrons with MNIST.
+
+01:01:49.590 --> 01:01:52.770
+It takes about 3 minutes to train it,
+
+01:01:52.770 --> 01:01:54.420
+so it's not too bad compared to your
+
+01:01:54.420 --> 01:01:55.360
+nearest neighbor training.
+
+01:01:56.310 --> 01:01:56.840
+And.
+
+01:01:57.680 --> 01:02:01.610
+And you need you need to basically
+
+01:02:01.610 --> 01:02:02.680
+like.
+
+01:02:02.680 --> 01:02:05.225
+We're going to use Pytorch, which is
+
+01:02:05.225 --> 01:02:06.800
+like a really good package for deep
+
+01:02:06.800 --> 01:02:07.160
+learning.
+
+01:02:08.180 --> 01:02:09.990
+And you need to.
+
+01:02:11.750 --> 01:02:15.500
+Fill out the forward and.
+
+01:02:16.850 --> 01:02:20.370
+And the like model specification.
+
+01:02:20.370 --> 01:02:23.650
+So I provide in the chips a link to a
+
+01:02:23.650 --> 01:02:25.500
+tutorial and you can also look up other
+
+01:02:25.500 --> 01:02:28.320
+tutorials that explain in the tips.
+
+01:02:28.320 --> 01:02:30.510
+Also gives you kind of the basic code
+
+01:02:30.510 --> 01:02:30.930
+structure.
+
+01:02:31.640 --> 01:02:33.850
+But you can see like how these things
+
+01:02:33.850 --> 01:02:36.030
+are coded, essentially that you define
+
+01:02:36.030 --> 01:02:37.280
+the layers of the network here.
+
+01:02:37.870 --> 01:02:40.560
+And then you define like how the data
+
+01:02:40.560 --> 01:02:42.030
+progresses through the network to make
+
+01:02:42.030 --> 01:02:45.429
+a prediction and then you and then you
+
+01:02:45.430 --> 01:02:46.430
+can train your network.
+
+01:02:48.040 --> 01:02:49.410
+Obviously we haven't talked about this
+
+01:02:49.410 --> 01:02:50.900
+yet, so it might not make complete
+
+01:02:50.900 --> 01:02:52.200
+sense yet, but it will.
+
+01:02:53.760 --> 01:02:55.048
+So then you're going to train a
+
+01:02:55.048 --> 01:02:57.019
+network, then you're going to try
+
+01:02:57.020 --> 01:02:58.638
+different learning rates, and then
+
+01:02:58.638 --> 01:03:00.230
+you're going to try to get the best
+
+01:03:00.230 --> 01:03:03.340
+network you can with the target of 25%
+
+01:03:03.340 --> 01:03:04.000
+validation error.
+
+01:03:05.770 --> 01:03:07.150
+And then a third problem.
+
+01:03:07.150 --> 01:03:09.450
+We're looking at this new data set
+
+01:03:09.450 --> 01:03:11.820
+called the Penguin data set, the Palmer
+
+01:03:11.820 --> 01:03:13.500
+Archipelago Penguin data set.
+
+01:03:14.410 --> 01:03:16.800
+And this is a data set of like some
+
+01:03:16.800 --> 01:03:18.500
+various physical measurements of the
+
+01:03:18.500 --> 01:03:19.970
+Penguins, whether they're male or
+
+01:03:19.970 --> 01:03:21.813
+female, what island they came from, and
+
+01:03:21.813 --> 01:03:23.140
+what kind of species it is.
+
+01:03:23.990 --> 01:03:25.800
+So we created a clean version of the
+
+01:03:25.800 --> 01:03:28.510
+data here and.
+
+01:03:29.670 --> 01:03:31.500
+And then we have like some starter code
+
+01:03:31.500 --> 01:03:32.380
+to load that data.
+
+01:03:33.210 --> 01:03:35.370
+And you're going to 1st like visualize
+
+01:03:35.370 --> 01:03:36.470
+some of the features.
+
+01:03:36.470 --> 01:03:40.270
+So we did one example for you if you
+
+01:03:40.270 --> 01:03:41.970
+look at the different species of
+
+01:03:41.970 --> 01:03:42.740
+Penguins.
+
+01:03:44.890 --> 01:03:46.880
+This is like a scatter plot of body
+
+01:03:46.880 --> 01:03:48.900
+mass versus flipper length for some
+
+01:03:48.900 --> 01:03:49.980
+different Penguins.
+
+01:03:49.980 --> 01:03:51.950
+So you can see that this would be like
+
+01:03:51.950 --> 01:03:53.880
+pretty good at distinguishing Gentoo
+
+01:03:53.880 --> 01:03:57.230
+from a deli and chinstrap, but not so
+
+01:03:57.230 --> 01:03:59.030
+good at distinguishing chinstrap in a
+
+01:03:59.030 --> 01:03:59.280
+deli.
+
+01:03:59.280 --> 01:04:00.790
+So you can do this for different
+
+01:04:00.790 --> 01:04:01.792
+combinations of features.
+
+01:04:01.792 --> 01:04:03.120
+There's not a lot of features.
+
+01:04:03.120 --> 01:04:03.989
+I think there's 13.
+
+01:04:06.080 --> 01:04:07.020
+And then?
+
+01:04:07.100 --> 01:04:07.730
+
+
+01:04:08.440 --> 01:04:10.140
+And then in the report it asks like
+
+01:04:10.140 --> 01:04:12.410
+some kinds of like analysis questions
+
+01:04:12.410 --> 01:04:14.060
+based on that feature analysis.
+
+01:04:15.490 --> 01:04:17.410
+Then the second question is to come up
+
+01:04:17.410 --> 01:04:19.889
+with a simple, really simple rule A2
+
+01:04:19.890 --> 01:04:21.330
+part rule that will allow you to
+
+01:04:21.330 --> 01:04:22.980
+perfectly classify Gentius.
+
+01:04:24.330 --> 01:04:27.170
+And then the third part is to design an
+
+01:04:27.170 --> 01:04:29.385
+mill model to maximize your accuracy on
+
+01:04:29.385 --> 01:04:30.160
+this problem.
+
+01:04:30.160 --> 01:04:33.070
+And you can use you can use like the
+
+01:04:33.070 --> 01:04:35.280
+library to do cross validation.
+
+01:04:35.280 --> 01:04:37.610
+So essentially you can use the
+
+01:04:37.610 --> 01:04:39.190
+libraries for your models as well.
+
+01:04:39.190 --> 01:04:40.390
+So you just need to choose the
+
+01:04:40.390 --> 01:04:42.100
+parameters of your models and then try
+
+01:04:42.100 --> 01:04:43.569
+to get the best performance you can.
+
+01:04:47.330 --> 01:04:49.180
+Then the stretch goals are to improve
+
+01:04:49.180 --> 01:04:52.020
+the MNIST using MLPS to find a second
+
+01:04:52.020 --> 01:04:54.330
+rule for classifying Gentius.
+
+01:04:55.050 --> 01:04:57.660
+And then this one is positional
+
+01:04:57.660 --> 01:05:00.765
+encoding, which is a way of like
+
+01:05:00.765 --> 01:05:03.130
+encoding positions that lets networks
+
+01:05:03.130 --> 01:05:05.170
+work better on it, but I won't go into
+
+01:05:05.170 --> 01:05:06.490
+details there since we haven't talked
+
+01:05:06.490 --> 01:05:07.070
+about networks.
+
+01:05:09.040 --> 01:05:11.270
+Any questions about homework 2?
+
+01:05:14.740 --> 01:05:16.100
+There will be, yes.
+
+01:05:17.910 --> 01:05:18.190
+OK.
+
+01:05:29.410 --> 01:05:29.700
+No.
+
+01:05:29.700 --> 01:05:31.484
+It says in that you don't need to
+
+01:05:31.484 --> 01:05:31.893
+answer them.
+
+01:05:31.893 --> 01:05:34.470
+You don't need to report on them.
+
+01:05:34.470 --> 01:05:36.450
+So you should answer them in your head
+
+01:05:36.450 --> 01:05:37.936
+and you'll learn more that way, but you
+
+01:05:37.936 --> 01:05:39.220
+don't need to provide the answer.
+
+01:05:40.190 --> 01:05:40.710
+Yeah.
+
+01:05:43.900 --> 01:05:44.230
+Why?
+
+01:05:47.670 --> 01:05:48.830
+Will not make a cost.
+
+01:05:51.690 --> 01:05:53.280
+No, it won't hurt you either.
+
+01:05:54.650 --> 01:05:54.910
+Yeah.
+
+01:05:55.930 --> 01:05:56.740
+You're not required.
+
+01:05:56.740 --> 01:05:58.397
+You're only required to fill out what's
+
+01:05:58.397 --> 01:05:59.172
+in the template.
+
+01:05:59.172 --> 01:06:01.880
+So sometimes I say to do like slightly
+
+01:06:01.880 --> 01:06:03.406
+more than what's in the template.
+
+01:06:03.406 --> 01:06:05.300
+The template is basically to show that
+
+01:06:05.300 --> 01:06:07.226
+you've done it, so sometimes you can
+
+01:06:07.226 --> 01:06:08.520
+show that you've done it without
+
+01:06:08.520 --> 01:06:09.840
+providing all the details.
+
+01:06:09.840 --> 01:06:10.220
+So.
+
+01:06:16.180 --> 01:06:17.810
+So the question is, can you resubmit
+
+01:06:17.810 --> 01:06:18.570
+the assignment?
+
+01:06:18.570 --> 01:06:20.363
+I wouldn't really recommend it.
+
+01:06:20.363 --> 01:06:21.176
+You would get.
+
+01:06:21.176 --> 01:06:23.570
+So the way that it works is that at the
+
+01:06:23.570 --> 01:06:25.653
+time that the T at the, it's mainly T
+
+01:06:25.653 --> 01:06:27.459
+is greeting, so at the time that the
+
+01:06:27.460 --> 01:06:28.250
+tea is green.
+
+01:06:29.270 --> 01:06:31.060
+Whatever is submitted last will be
+
+01:06:31.060 --> 01:06:31.480
+graded.
+
+01:06:32.390 --> 01:06:34.930
+And whatever, like with whatever late
+
+01:06:34.930 --> 01:06:36.950
+days have accrued for that, for that
+
+01:06:36.950 --> 01:06:37.360
+submission.
+
+01:06:37.360 --> 01:06:40.140
+If it's late so you can resubmit, but
+
+01:06:40.140 --> 01:06:41.590
+then once they've graded, then it's
+
+01:06:41.590 --> 01:06:43.270
+graded and then you can't resubmit
+
+01:06:43.270 --> 01:06:43.640
+anymore.
+
+01:06:46.300 --> 01:06:47.150
+There were.
+
+01:06:47.150 --> 01:06:48.910
+We basically assume that if it's past
+
+01:06:48.910 --> 01:06:50.530
+the deadline and you've submitted, then
+
+01:06:50.530 --> 01:06:54.580
+we can grade it and so it might get and
+
+01:06:54.580 --> 01:06:56.750
+generally if you want to get extra
+
+01:06:56.750 --> 01:06:57.170
+points.
+
+01:06:57.900 --> 01:06:59.330
+I would just recommend a move on to
+
+01:06:59.330 --> 01:07:01.053
+homework two and do extra points for
+
+01:07:01.053 --> 01:07:02.430
+homework two rather than getting stuck
+
+01:07:02.430 --> 01:07:03.925
+on homework one and getting late days
+
+01:07:03.925 --> 01:07:06.040
+and then like having trouble getting up
+
+01:07:06.040 --> 01:07:07.250
+getting homework 2 done.
+
+01:07:13.630 --> 01:07:16.730
+All right, so the things to remember
+
+01:07:16.730 --> 01:07:17.420
+from this class.
+
+01:07:18.180 --> 01:07:20.180
+Ensembles improve accuracy and
+
+01:07:20.180 --> 01:07:22.325
+confidence estimates by reducing the
+
+01:07:22.325 --> 01:07:23.990
+bias and Oregon the variance.
+
+01:07:23.990 --> 01:07:25.730
+And there's like this really important
+
+01:07:25.730 --> 01:07:28.100
+principle that test error can be
+
+01:07:28.100 --> 01:07:30.690
+decomposed into variance, bias and
+
+01:07:30.690 --> 01:07:31.670
+irreducible noise.
+
+01:07:32.680 --> 01:07:33.970
+And because the trees and random
+
+01:07:33.970 --> 01:07:35.870
+forests are really powerful and widely
+
+01:07:35.870 --> 01:07:38.000
+applicable classifiers and regressors.
+
+01:07:39.990 --> 01:07:43.440
+So in the next class I'm going to talk
+
+01:07:43.440 --> 01:07:45.765
+about SVM support vector machines,
+
+01:07:45.765 --> 01:07:48.910
+which were very popular approach, and
+
+01:07:48.910 --> 01:07:50.830
+stochastic gradient descent, which is a
+
+01:07:50.830 --> 01:07:52.310
+method to optimize them that also
+
+01:07:52.310 --> 01:07:54.245
+applies to neural Nets and deep Nets.
+
+01:07:54.245 --> 01:07:56.300
+So thank you, I'll see you on Thursday.
+
+01:19:53.620 --> 01:19:54.020
+Yeah.
+
+01:19:56.250 --> 01:19:56.660
+Testing.
+
+01:19:58.350 --> 01:19:58.590
+Yeah.
+