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+WEBVTT Kind: captions; Language: en-US
+
+NOTE
+Created on 2024-02-07T20:53:55.0930204Z by ClassTranscribe
+
+00:01:12.090 --> 00:01:13.230
+Alright, good morning everybody.
+
+00:01:15.530 --> 00:01:20.650
+So I saw in response to the feedback, I
+
+00:01:20.650 --> 00:01:22.790
+got some feedback on the course and.
+
+00:01:23.690 --> 00:01:26.200
+Overall, there's of course a mix of
+
+00:01:26.200 --> 00:01:28.650
+responses, but some on average people
+
+00:01:28.650 --> 00:01:30.810
+feel like it's moving a little fast and
+
+00:01:30.810 --> 00:01:33.040
+we're and also it's challenging.
+
+00:01:33.980 --> 00:01:37.350
+So I wanted to take some time to like
+
+00:01:37.350 --> 00:01:39.430
+consolidate and to talk about some of
+
+00:01:39.430 --> 00:01:40.890
+the most important points.
+
+00:01:41.790 --> 00:01:45.160
+That we've covered so far, and then so
+
+00:01:45.160 --> 00:01:46.930
+I'll do that for the first half of the
+
+00:01:46.930 --> 00:01:49.280
+lecture, and then I'm also going to go
+
+00:01:49.280 --> 00:01:53.105
+through a detailed example using code
+
+00:01:53.105 --> 00:01:55.200
+to solve a particular problem.
+
+00:01:59.460 --> 00:02:00.000
+So.
+
+00:02:00.690 --> 00:02:01.340
+Let me see.
+
+00:02:04.270 --> 00:02:04.800
+All right.
+
+00:02:06.140 --> 00:02:09.360
+So this is a mostly the same as a slide
+
+00:02:09.360 --> 00:02:10.750
+that I showed in the intro.
+
+00:02:10.750 --> 00:02:12.750
+This is machine learning in general.
+
+00:02:12.750 --> 00:02:15.800
+You've got some raw features and so far
+
+00:02:15.800 --> 00:02:17.430
+we've COVID cases where we have
+
+00:02:17.430 --> 00:02:20.190
+discrete and continuous values and also
+
+00:02:20.190 --> 00:02:21.780
+some simple images in terms of the
+
+00:02:21.780 --> 00:02:22.670
+amnesty characters.
+
+00:02:23.600 --> 00:02:25.590
+And we have some kind of.
+
+00:02:25.590 --> 00:02:28.000
+Sometimes we process those features in
+
+00:02:28.000 --> 00:02:29.740
+some way we have like what's called an
+
+00:02:29.740 --> 00:02:31.970
+encoder or we have feature transforms.
+
+00:02:32.790 --> 00:02:34.290
+We've only gotten into that a little
+
+00:02:34.290 --> 00:02:34.500
+bit.
+
+00:02:35.210 --> 00:02:38.410
+In terms of the decision trees, which
+
+00:02:38.410 --> 00:02:39.670
+you can view as a kind of feature
+
+00:02:39.670 --> 00:02:40.530
+transformation.
+
+00:02:41.290 --> 00:02:43.440
+And feature selection using one the
+
+00:02:43.440 --> 00:02:44.350
+district regression.
+
+00:02:44.980 --> 00:02:47.030
+So the job of the encoder is to take
+
+00:02:47.030 --> 00:02:48.690
+your raw features and turn them into
+
+00:02:48.690 --> 00:02:50.570
+something that's more easily.
+
+00:02:51.340 --> 00:02:53.270
+That more easily yields a predictor.
+
+00:02:54.580 --> 00:02:56.180
+Then you have decoder, the thing that
+
+00:02:56.180 --> 00:02:58.290
+predicts from your encoded features,
+
+00:02:58.290 --> 00:03:00.510
+and we've covered pretty much all the
+
+00:03:00.510 --> 00:03:02.550
+methods here except for SVM, which
+
+00:03:02.550 --> 00:03:04.910
+we're doing next week.
+
+00:03:05.830 --> 00:03:08.110
+And so we've got a linear aggressor, a
+
+00:03:08.110 --> 00:03:09.952
+logistic regressor, nearest neighbor
+
+00:03:09.952 --> 00:03:11.430
+and probabilistic models.
+
+00:03:11.430 --> 00:03:13.035
+Now there's lots of different kinds of
+
+00:03:13.035 --> 00:03:13.650
+probabilistic models.
+
+00:03:13.650 --> 00:03:15.930
+We only talked about a couple of one of
+
+00:03:15.930 --> 00:03:17.420
+them nibs.
+
+00:03:18.750 --> 00:03:20.350
+But still, we've touched on this.
+
+00:03:21.360 --> 00:03:22.690
+And then you have a prediction and
+
+00:03:22.690 --> 00:03:24.047
+there's lots of different things you
+
+00:03:24.047 --> 00:03:24.585
+can predict.
+
+00:03:24.585 --> 00:03:26.480
+You can predict a category or a
+
+00:03:26.480 --> 00:03:28.050
+continuous value, which is what we've
+
+00:03:28.050 --> 00:03:29.205
+talked about South far.
+
+00:03:29.205 --> 00:03:31.420
+You could also be generating clusters
+
+00:03:31.420 --> 00:03:35.595
+or pixel labels or poses or other kinds
+
+00:03:35.595 --> 00:03:36.460
+of predictions.
+
+00:03:37.600 --> 00:03:40.275
+And in training, you've got some data
+
+00:03:40.275 --> 00:03:42.280
+and target labels, and you're trying to
+
+00:03:42.280 --> 00:03:44.060
+update the models of your parameters to
+
+00:03:44.060 --> 00:03:46.200
+get the best prediction possible, where
+
+00:03:46.200 --> 00:03:48.434
+you want to really not only maximize
+
+00:03:48.434 --> 00:03:50.619
+your prediction on the training data,
+
+00:03:50.620 --> 00:03:52.970
+but also to maximize your expected or
+
+00:03:52.970 --> 00:03:55.520
+minimize your expected error on the
+
+00:03:55.520 --> 00:03:56.170
+test data.
+
+00:03:59.950 --> 00:04:02.520
+So one important part of machine
+
+00:04:02.520 --> 00:04:04.255
+learning is learning a model.
+
+00:04:04.255 --> 00:04:04.650
+So.
+
+00:04:05.430 --> 00:04:08.385
+Here this is like this kind of.
+
+00:04:08.385 --> 00:04:10.610
+This function, in one form or another
+
+00:04:10.610 --> 00:04:12.140
+will be part of every machine learning
+
+00:04:12.140 --> 00:04:14.180
+algorithm where you're trying to.
+
+00:04:14.180 --> 00:04:17.720
+You have some model F of X Theta.
+
+00:04:18.360 --> 00:04:20.500
+Where X is the raw features.
+
+00:04:21.890 --> 00:04:23.600
+Beta are the parameters that you're
+
+00:04:23.600 --> 00:04:25.440
+trying to optimize that you're going to
+
+00:04:25.440 --> 00:04:26.840
+optimize to fit your model.
+
+00:04:27.940 --> 00:04:31.080
+And why is the prediction that you're
+
+00:04:31.080 --> 00:04:31.750
+trying to make?
+
+00:04:31.750 --> 00:04:33.359
+So you're given.
+
+00:04:33.360 --> 00:04:35.260
+In supervised learning you're given
+
+00:04:35.260 --> 00:04:40.100
+pairs XY of some features and labels.
+
+00:04:40.990 --> 00:04:42.430
+And then you're trying to solve for
+
+00:04:42.430 --> 00:04:45.570
+parameters that minimizes your loss,
+
+00:04:45.570 --> 00:04:49.909
+and your loss is a is like A is a
+
+00:04:49.910 --> 00:04:51.628
+objective function that you're trying
+
+00:04:51.628 --> 00:04:54.130
+to reduce, and it usually has two
+
+00:04:54.130 --> 00:04:54.860
+components.
+
+00:04:54.860 --> 00:04:56.550
+1 component is that you want your
+
+00:04:56.550 --> 00:04:59.140
+predictions on the training data to be
+
+00:04:59.140 --> 00:05:00.490
+as good as possible.
+
+00:05:00.490 --> 00:05:03.066
+For example, you might say that you
+
+00:05:03.066 --> 00:05:05.525
+want to maximize the probability of
+
+00:05:05.525 --> 00:05:07.210
+your labels given your features.
+
+00:05:07.840 --> 00:05:10.930
+Or, equivalently, you want to minimize
+
+00:05:10.930 --> 00:05:12.795
+the negative sum of log likelihood of
+
+00:05:12.795 --> 00:05:14.450
+your labels given your features.
+
+00:05:14.450 --> 00:05:16.762
+This is the same as maximizing the
+
+00:05:16.762 --> 00:05:17.650
+likelihood of the labels.
+
+00:05:18.280 --> 00:05:22.360
+But we often want to minimize things,
+
+00:05:22.360 --> 00:05:24.679
+so negative log is.
+
+00:05:24.680 --> 00:05:26.581
+Minimizing the negative log is the same
+
+00:05:26.581 --> 00:05:30.056
+as maximizing the log and taking the
+
+00:05:30.056 --> 00:05:30.369
+log.
+
+00:05:30.369 --> 00:05:33.500
+The Max of the log is the same as the
+
+00:05:33.500 --> 00:05:35.040
+Max of the value.
+
+00:05:35.850 --> 00:05:37.510
+And this form tends to be easier to
+
+00:05:37.510 --> 00:05:38.030
+optimize.
+
+00:05:40.730 --> 00:05:41.730
+The second term.
+
+00:05:41.730 --> 00:05:43.720
+So we want to maximize the likelihood
+
+00:05:43.720 --> 00:05:45.590
+of the labels given the data, but we
+
+00:05:45.590 --> 00:05:49.000
+also want to have some likely.
+
+00:05:49.000 --> 00:05:51.750
+We often want to impose some kinds of
+
+00:05:51.750 --> 00:05:53.450
+constraints or some kinds of
+
+00:05:53.450 --> 00:05:56.020
+preferences for the parameters of our
+
+00:05:56.020 --> 00:05:56.450
+model.
+
+00:05:57.210 --> 00:05:58.240
+So.
+
+00:05:58.430 --> 00:05:59.010
+And.
+
+00:06:00.730 --> 00:06:02.549
+So a common thing is that we want to
+
+00:06:02.550 --> 00:06:04.449
+say that the sum of the parameters we
+
+00:06:04.449 --> 00:06:06.119
+want to minimize the sum of the
+
+00:06:06.120 --> 00:06:07.465
+parameter squared, or we want to
+
+00:06:07.465 --> 00:06:09.148
+minimize the sum of the absolute values
+
+00:06:09.148 --> 00:06:10.282
+of the parameters.
+
+00:06:10.282 --> 00:06:11.815
+So this is called regularization.
+
+00:06:11.815 --> 00:06:13.565
+Or if you have a probabilistic model,
+
+00:06:13.565 --> 00:06:16.490
+that might be in the form of a prior on
+
+00:06:16.490 --> 00:06:19.200
+the statistics that you're estimating.
+
+00:06:20.910 --> 00:06:22.850
+So the regularization and priors
+
+00:06:22.850 --> 00:06:24.720
+indicate some kind of preference for a
+
+00:06:24.720 --> 00:06:26.110
+particular solutions.
+
+00:06:26.940 --> 00:06:28.700
+And they tend to improve
+
+00:06:28.700 --> 00:06:29.330
+generalization.
+
+00:06:29.330 --> 00:06:31.700
+And in some cases they're necessary to
+
+00:06:31.700 --> 00:06:33.520
+obtain a unique solution.
+
+00:06:33.520 --> 00:06:35.430
+Like there might be many linear models
+
+00:06:35.430 --> 00:06:37.510
+that can separate your one class from
+
+00:06:37.510 --> 00:06:40.380
+another, and without regularization you
+
+00:06:40.380 --> 00:06:41.820
+have no way of choosing among those
+
+00:06:41.820 --> 00:06:42.510
+different models.
+
+00:06:42.510 --> 00:06:45.660
+The regularization specifies a
+
+00:06:45.660 --> 00:06:46.720
+particular solution.
+
+00:06:48.250 --> 00:06:50.690
+And this is it's more important the
+
+00:06:50.690 --> 00:06:52.040
+less data you have.
+
+00:06:52.950 --> 00:06:55.450
+Or the more features or larger your
+
+00:06:55.450 --> 00:06:56.060
+problem is.
+
+00:07:00.900 --> 00:07:03.240
+Once we've once we've trained a model,
+
+00:07:03.240 --> 00:07:05.020
+then we want to do prediction using
+
+00:07:05.020 --> 00:07:06.033
+that model.
+
+00:07:06.033 --> 00:07:08.300
+So in prediction we're given some new
+
+00:07:08.300 --> 00:07:09.200
+set of features.
+
+00:07:09.860 --> 00:07:10.980
+It will be the same.
+
+00:07:10.980 --> 00:07:14.216
+So in training we might have seen 500
+
+00:07:14.216 --> 00:07:16.870
+examples, and for each of those
+
+00:07:16.870 --> 00:07:19.191
+examples 10 features and some label
+
+00:07:19.191 --> 00:07:20.716
+you're trying to predict.
+
+00:07:20.716 --> 00:07:23.480
+So in testing you'll have a set of
+
+00:07:23.480 --> 00:07:25.860
+testing examples, and each one will
+
+00:07:25.860 --> 00:07:27.272
+also have the same number of features.
+
+00:07:27.272 --> 00:07:29.028
+So it might have 10 features as well,
+
+00:07:29.028 --> 00:07:30.771
+and you're trying to predict the same
+
+00:07:30.771 --> 00:07:31.019
+label.
+
+00:07:31.020 --> 00:07:32.810
+But in testing you don't give the model
+
+00:07:32.810 --> 00:07:34.265
+your label, you're trying to output the
+
+00:07:34.265 --> 00:07:34.510
+label.
+
+00:07:35.550 --> 00:07:37.990
+So in testing, we're given some test
+
+00:07:37.990 --> 00:07:42.687
+sample with input features XT and if
+
+00:07:42.687 --> 00:07:44.084
+we're doing a regression, then we're
+
+00:07:44.084 --> 00:07:45.474
+trying to output yet directly.
+
+00:07:45.474 --> 00:07:48.050
+So we're trying to say, predict the
+
+00:07:48.050 --> 00:07:49.830
+stock price or temperature or something
+
+00:07:49.830 --> 00:07:50.520
+like that.
+
+00:07:50.520 --> 00:07:52.334
+If we're doing classification, we're
+
+00:07:52.334 --> 00:07:54.210
+trying to output the likelihood of a
+
+00:07:54.210 --> 00:07:56.065
+particular category or the most likely
+
+00:07:56.065 --> 00:07:56.470
+category.
+
+00:08:03.280 --> 00:08:03.780
+And.
+
+00:08:04.810 --> 00:08:08.590
+So then there's a so if we're trying to
+
+00:08:08.590 --> 00:08:10.490
+develop a machine learning algorithm.
+
+00:08:11.240 --> 00:08:13.780
+Then we go through this model
+
+00:08:13.780 --> 00:08:15.213
+evaluation process.
+
+00:08:15.213 --> 00:08:18.660
+So the first step is that we need to
+
+00:08:18.660 --> 00:08:19.930
+collect some data.
+
+00:08:19.930 --> 00:08:21.848
+So if we're creating a new problem,
+
+00:08:21.848 --> 00:08:25.900
+then we might need to capture capture
+
+00:08:25.900 --> 00:08:28.940
+images or record observations or
+
+00:08:28.940 --> 00:08:30.950
+download information from the Internet,
+
+00:08:30.950 --> 00:08:31.930
+or whatever.
+
+00:08:31.930 --> 00:08:33.688
+One way or another, you need to get
+
+00:08:33.688 --> 00:08:34.092
+some data.
+
+00:08:34.092 --> 00:08:36.232
+You need to get labels for that data.
+
+00:08:36.232 --> 00:08:37.550
+So it might include.
+
+00:08:37.550 --> 00:08:38.970
+You might need to do some manual
+
+00:08:38.970 --> 00:08:39.494
+annotation.
+
+00:08:39.494 --> 00:08:41.590
+You might need to.
+
+00:08:41.650 --> 00:08:44.080
+Crowd source or use platforms to get
+
+00:08:44.080 --> 00:08:44.820
+the labels.
+
+00:08:44.820 --> 00:08:46.760
+At the end of this you'll have a whole
+
+00:08:46.760 --> 00:08:49.708
+set of samples X&Y where X are the are
+
+00:08:49.708 --> 00:08:51.355
+the features that you want to use to
+
+00:08:51.355 --> 00:08:53.070
+make a prediction and why are the
+
+00:08:53.070 --> 00:08:54.625
+predictions that you want to make.
+
+00:08:54.625 --> 00:08:57.442
+And then you split that data into a
+
+00:08:57.442 --> 00:09:00.190
+training and validation and a test set
+
+00:09:00.190 --> 00:09:01.630
+where you're going to use the training
+
+00:09:01.630 --> 00:09:03.175
+set to optimize parameters, validation
+
+00:09:03.175 --> 00:09:06.130
+set to choose your best model and
+
+00:09:06.130 --> 00:09:08.070
+testing for your final evaluation and
+
+00:09:08.070 --> 00:09:08.680
+performance.
+
+00:09:10.180 --> 00:09:12.330
+So once you have the data, you might
+
+00:09:12.330 --> 00:09:14.134
+spend some time inspecting the features
+
+00:09:14.134 --> 00:09:16.605
+and trying to understand the problem a
+
+00:09:16.605 --> 00:09:17.203
+little bit better.
+
+00:09:17.203 --> 00:09:19.570
+Trying to look at do some little test
+
+00:09:19.570 --> 00:09:23.960
+to see how like baselines work and how
+
+00:09:23.960 --> 00:09:27.320
+certain features predict the label.
+
+00:09:28.410 --> 00:09:29.600
+And then you'll decide on some
+
+00:09:29.600 --> 00:09:31.190
+candidate models and parameters.
+
+00:09:31.870 --> 00:09:34.610
+Then for each candidate you would train
+
+00:09:34.610 --> 00:09:36.970
+the parameters using the train set.
+
+00:09:37.720 --> 00:09:39.970
+And you'll evaluate your trained model
+
+00:09:39.970 --> 00:09:41.170
+on the validation set.
+
+00:09:41.910 --> 00:09:43.870
+And then you choose the best model
+
+00:09:43.870 --> 00:09:45.630
+based on your validation performance.
+
+00:09:46.470 --> 00:09:48.800
+And then you evaluate it on the test
+
+00:09:48.800 --> 00:09:49.040
+set.
+
+00:09:50.320 --> 00:09:54.160
+And sometimes, very often you have like
+
+00:09:54.160 --> 00:09:55.320
+a tree and vowel test set.
+
+00:09:55.320 --> 00:09:56.920
+But an alternative is that you could do
+
+00:09:56.920 --> 00:09:59.320
+cross validation, which I'll show an
+
+00:09:59.320 --> 00:10:02.000
+example of, where you just split your
+
+00:10:02.000 --> 00:10:05.305
+whole set into 10 parts and each time
+
+00:10:05.305 --> 00:10:07.423
+you train on 9 parts and test on the
+
+00:10:07.423 --> 00:10:08.130
+10th part.
+
+00:10:08.130 --> 00:10:09.430
+That becomes.
+
+00:10:09.430 --> 00:10:11.410
+If you have like a very limited amount
+
+00:10:11.410 --> 00:10:13.070
+of data then that can help you make the
+
+00:10:13.070 --> 00:10:14.360
+best use of your limited data.
+
+00:10:16.340 --> 00:10:18.040
+So typically when you're evaluating the
+
+00:10:18.040 --> 00:10:19.500
+performance, you're going to measure
+
+00:10:19.500 --> 00:10:21.370
+like the error, the accuracy like root
+
+00:10:21.370 --> 00:10:23.250
+mean squared error or accuracy, or the
+
+00:10:23.250 --> 00:10:24.810
+amount of variance you can explain.
+
+00:10:26.070 --> 00:10:27.130
+Or you could be doing.
+
+00:10:27.130 --> 00:10:28.555
+If you're doing like a retrieval task,
+
+00:10:28.555 --> 00:10:30.190
+you might do precision recall.
+
+00:10:30.190 --> 00:10:31.600
+So there's a variety of metrics that
+
+00:10:31.600 --> 00:10:32.510
+depend on the problem.
+
+00:10:36.890 --> 00:10:37.390
+So.
+
+00:10:38.160 --> 00:10:39.730
+When we're trying to think about like
+
+00:10:39.730 --> 00:10:41.530
+these mill algorithms, there's actually
+
+00:10:41.530 --> 00:10:43.400
+a lot of different things that we
+
+00:10:43.400 --> 00:10:44.170
+should consider.
+
+00:10:45.300 --> 00:10:48.187
+One of them is like, what is the model?
+
+00:10:48.187 --> 00:10:50.330
+What kinds of things can it represent?
+
+00:10:50.330 --> 00:10:52.139
+For example, in a linear model and a
+
+00:10:52.140 --> 00:10:55.350
+classifier model, it means that all the
+
+00:10:55.350 --> 00:10:57.382
+data that's on one side of the
+
+00:10:57.382 --> 00:10:58.893
+hyperplane is going to be assigned to
+
+00:10:58.893 --> 00:11:00.619
+one class, and all the data on the
+
+00:11:00.620 --> 00:11:02.066
+other side of the hyperplane will be
+
+00:11:02.066 --> 00:11:04.210
+assigned to another class, where for
+
+00:11:04.210 --> 00:11:06.610
+nearest neighbor you can have much more
+
+00:11:06.610 --> 00:11:08.150
+flexible decision boundaries.
+
+00:11:10.010 --> 00:11:11.270
+You can also think about.
+
+00:11:11.270 --> 00:11:13.440
+Maybe the model implies that some kinds
+
+00:11:13.440 --> 00:11:16.160
+of functions are preferred over others.
+
+00:11:18.810 --> 00:11:20.470
+You think about like what is your
+
+00:11:20.470 --> 00:11:21.187
+objective function?
+
+00:11:21.187 --> 00:11:22.870
+So what is it that you're trying to
+
+00:11:22.870 --> 00:11:25.100
+minimize, and what kinds of like values
+
+00:11:25.100 --> 00:11:26.060
+does that imply?
+
+00:11:26.060 --> 00:11:26.960
+So do you prefer?
+
+00:11:26.960 --> 00:11:27.890
+Does it mean?
+
+00:11:27.890 --> 00:11:29.840
+Does your regularization, for example,
+
+00:11:29.840 --> 00:11:32.620
+mean that you prefer that you're using
+
+00:11:32.620 --> 00:11:34.230
+a few features or that you have low
+
+00:11:34.230 --> 00:11:35.520
+weight on a lot of features?
+
+00:11:36.270 --> 00:11:39.126
+Are you trying to minimize a likelihood
+
+00:11:39.126 --> 00:11:42.190
+or maximize the likelihood, or are you
+
+00:11:42.190 --> 00:11:45.250
+trying to just get high enough
+
+00:11:45.250 --> 00:11:46.899
+confidence on each example to get
+
+00:11:46.900 --> 00:11:47.610
+things correct?
+
+00:11:49.430 --> 00:11:50.850
+And it's important to note that the
+
+00:11:50.850 --> 00:11:53.080
+objective function often does not match
+
+00:11:53.080 --> 00:11:54.290
+your final evaluation.
+
+00:11:54.290 --> 00:11:57.590
+So nobody really trains a model to
+
+00:11:57.590 --> 00:12:00.170
+minimize the classification error, even
+
+00:12:00.170 --> 00:12:01.960
+though they often evaluate based on
+
+00:12:01.960 --> 00:12:03.000
+classification error.
+
+00:12:03.940 --> 00:12:06.576
+And there's two reasons for that.
+
+00:12:06.576 --> 00:12:09.388
+So one reason is that it's really hard
+
+00:12:09.388 --> 00:12:11.550
+to minimize classification error over
+
+00:12:11.550 --> 00:12:13.510
+training set, because a small change in
+
+00:12:13.510 --> 00:12:15.000
+parameters may not change your
+
+00:12:15.000 --> 00:12:15.680
+classification error.
+
+00:12:15.680 --> 00:12:18.200
+So it's hard to for an optimization
+
+00:12:18.200 --> 00:12:19.850
+algorithm to figure out how it should
+
+00:12:19.850 --> 00:12:21.400
+change to minimize that error.
+
+00:12:22.430 --> 00:12:25.823
+The second reason is that there might
+
+00:12:25.823 --> 00:12:27.730
+be many different models that can have
+
+00:12:27.730 --> 00:12:29.620
+similar classification error, the same
+
+00:12:29.620 --> 00:12:31.980
+classification error, and so you need
+
+00:12:31.980 --> 00:12:33.560
+some way of choosing among them.
+
+00:12:33.560 --> 00:12:35.670
+So many algorithms, many times the
+
+00:12:35.670 --> 00:12:37.422
+objective function will also say that
+
+00:12:37.422 --> 00:12:39.160
+you want to be very confident about
+
+00:12:39.160 --> 00:12:41.274
+your examples, not only that, you want
+
+00:12:41.274 --> 00:12:42.010
+to be correct.
+
+00:12:45.380 --> 00:12:47.140
+The third thing is that you would think
+
+00:12:47.140 --> 00:12:50.070
+about how you can optimize the model.
+
+00:12:50.070 --> 00:12:51.610
+So does it.
+
+00:12:51.680 --> 00:12:56.200
+For example for like logistic
+
+00:12:56.200 --> 00:12:56.880
+regression.
+
+00:12:58.760 --> 00:13:01.480
+You're able to reach a global optimum.
+
+00:13:01.480 --> 00:13:04.220
+It's a convex problem so that you're
+
+00:13:04.220 --> 00:13:06.290
+going to find the best solution, where
+
+00:13:06.290 --> 00:13:08.020
+for something a neural network it may
+
+00:13:08.020 --> 00:13:09.742
+not be possible to get the best
+
+00:13:09.742 --> 00:13:11.000
+solution, but you can usually get a
+
+00:13:11.000 --> 00:13:11.860
+pretty good solution.
+
+00:13:12.680 --> 00:13:14.430
+You also will think about like how long
+
+00:13:14.430 --> 00:13:17.260
+does it take to train and how does that
+
+00:13:17.260 --> 00:13:18.709
+depend on the number of examples and
+
+00:13:18.709 --> 00:13:19.950
+the number of features.
+
+00:13:19.950 --> 00:13:22.010
+So if you're later we'll talk about
+
+00:13:22.010 --> 00:13:25.260
+SVMS and Kernelized SVM is one of the
+
+00:13:25.260 --> 00:13:27.560
+problems, is that it's the training is
+
+00:13:27.560 --> 00:13:29.761
+quadratic in the number of examples, so
+
+00:13:29.761 --> 00:13:32.600
+it becomes a pretty expensive, at least
+
+00:13:32.600 --> 00:13:34.976
+according to the earlier optimization
+
+00:13:34.976 --> 00:13:35.582
+algorithms.
+
+00:13:35.582 --> 00:13:38.120
+So some algorithms can be used with a
+
+00:13:38.120 --> 00:13:39.710
+lot of examples, but some are just too
+
+00:13:39.710 --> 00:13:40.370
+expensive.
+
+00:13:40.440 --> 00:13:40.880
+Yeah.
+
+00:13:43.520 --> 00:13:47.060
+So the objective function is your, it's
+
+00:13:47.060 --> 00:13:48.120
+your loss essentially.
+
+00:13:48.120 --> 00:13:50.470
+So it usually has that data term where
+
+00:13:50.470 --> 00:13:51.540
+you're trying to maximize the
+
+00:13:51.540 --> 00:13:52.910
+likelihood of the data or the labels
+
+00:13:52.910 --> 00:13:53.960
+given the data.
+
+00:13:53.960 --> 00:13:56.075
+And it has some regularization term
+
+00:13:56.075 --> 00:13:58.130
+that says that you prefer some models
+
+00:13:58.130 --> 00:13:58.670
+over others.
+
+00:14:05.090 --> 00:14:07.890
+So yeah, feel free to please do ask as
+
+00:14:07.890 --> 00:14:11.140
+many questions as pop into your mind.
+
+00:14:11.140 --> 00:14:13.010
+I'm happy to answer them and I want to
+
+00:14:13.010 --> 00:14:14.992
+make sure, hopefully at the end of this
+
+00:14:14.992 --> 00:14:17.670
+lecture, or if it's or if you like
+
+00:14:17.670 --> 00:14:18.630
+further review the lecture.
+
+00:14:18.630 --> 00:14:20.345
+Again, I hope that all of this stuff is
+
+00:14:20.345 --> 00:14:22.340
+like really clear, and if it's not,
+
+00:14:22.340 --> 00:14:26.847
+just don't feel don't be afraid to ask
+
+00:14:26.847 --> 00:14:28.680
+questions in office hours or after
+
+00:14:28.680 --> 00:14:29.660
+class or whatever.
+
+00:14:31.920 --> 00:14:34.065
+So then finally, how does the
+
+00:14:34.065 --> 00:14:34.670
+prediction work?
+
+00:14:34.670 --> 00:14:36.340
+So then you want to think about like
+
+00:14:36.340 --> 00:14:37.740
+can I make a prediction really quickly?
+
+00:14:37.740 --> 00:14:39.730
+So like for a nearest neighbor it's not
+
+00:14:39.730 --> 00:14:41.579
+necessarily so quick, but for the
+
+00:14:41.580 --> 00:14:43.050
+linear models it's pretty fast.
+
+00:14:44.750 --> 00:14:46.580
+Can I find the most likely prediction
+
+00:14:46.580 --> 00:14:48.260
+according to my model?
+
+00:14:48.260 --> 00:14:50.390
+So sometimes even after you've
+
+00:14:50.390 --> 00:14:53.790
+optimized your model, you don't have a
+
+00:14:53.790 --> 00:14:55.530
+guarantee that you can generate the
+
+00:14:55.530 --> 00:14:57.410
+best solution for a new sample.
+
+00:14:57.410 --> 00:14:59.930
+So for example with these image
+
+00:14:59.930 --> 00:15:02.090
+generation algorithms even though.
+
+00:15:02.890 --> 00:15:05.060
+Even after you optimize your model
+
+00:15:05.060 --> 00:15:08.150
+given some phrase, you're not
+
+00:15:08.150 --> 00:15:09.720
+necessarily going to generate the most
+
+00:15:09.720 --> 00:15:11.630
+likely image given that phrase.
+
+00:15:11.630 --> 00:15:13.710
+You'll just generate like an image that
+
+00:15:13.710 --> 00:15:16.199
+is like consistent with the phrase
+
+00:15:16.200 --> 00:15:18.010
+according to some scoring function.
+
+00:15:18.010 --> 00:15:20.810
+So not all models can even be perfectly
+
+00:15:20.810 --> 00:15:22.040
+optimized for prediction.
+
+00:15:23.100 --> 00:15:25.110
+And then finally, does my algorithm
+
+00:15:25.110 --> 00:15:27.180
+output confidence as well as
+
+00:15:27.180 --> 00:15:27.710
+prediction?
+
+00:15:27.710 --> 00:15:30.770
+Usually it's helpful if your model not
+
+00:15:30.770 --> 00:15:32.193
+only gives you an answer, but also
+
+00:15:32.193 --> 00:15:33.930
+gives you a confidence in how to write
+
+00:15:33.930 --> 00:15:34.790
+that answer is.
+
+00:15:35.420 --> 00:15:37.580
+And it's nice if that confidence is
+
+00:15:37.580 --> 00:15:38.030
+accurate.
+
+00:15:39.240 --> 00:15:41.580
+Meaning that if it says that you've got
+
+00:15:41.580 --> 00:15:44.000
+like a 99% chance of being correct,
+
+00:15:44.000 --> 00:15:46.250
+then hopefully 99 out of 100 times
+
+00:15:46.250 --> 00:15:48.640
+you'll be correct in that situation.
+
+00:15:55.440 --> 00:15:57.234
+So we looked at.
+
+00:15:57.234 --> 00:15:59.300
+We looked at several different
+
+00:15:59.300 --> 00:16:00.870
+classification algorithms.
+
+00:16:01.560 --> 00:16:04.440
+And so here they're all compared
+
+00:16:04.440 --> 00:16:05.890
+side-by-side according to some
+
+00:16:05.890 --> 00:16:06.290
+criteria.
+
+00:16:06.290 --> 00:16:08.130
+So we can think about like what type of
+
+00:16:08.130 --> 00:16:10.290
+algorithm it is it a nearest neighbor
+
+00:16:10.290 --> 00:16:12.480
+is instance based, and that the
+
+00:16:12.480 --> 00:16:14.120
+parameters are the instances
+
+00:16:14.120 --> 00:16:14.740
+themselves.
+
+00:16:14.740 --> 00:16:17.870
+There's additional like linear model or
+
+00:16:17.870 --> 00:16:19.450
+something that's parametric that you're
+
+00:16:19.450 --> 00:16:20.590
+trying to fit to your data.
+
+00:16:22.150 --> 00:16:24.170
+Naive Bayes is probabilistic is
+
+00:16:24.170 --> 00:16:26.060
+logistic regression, but.
+
+00:16:26.910 --> 00:16:29.090
+Naive Bayes, you're maximizing the
+
+00:16:29.090 --> 00:16:31.210
+likelihood of your features given the
+
+00:16:31.210 --> 00:16:33.020
+data or your features, and I mean
+
+00:16:33.020 --> 00:16:34.270
+sorry, you're maximizing likelihood of
+
+00:16:34.270 --> 00:16:35.720
+your features and the label.
+
+00:16:36.600 --> 00:16:37.230
+
+
+00:16:38.790 --> 00:16:40.800
+Under the assumption that your features
+
+00:16:40.800 --> 00:16:42.610
+are independent given the label.
+
+00:16:43.450 --> 00:16:45.450
+Where in logistic regression you're
+
+00:16:45.450 --> 00:16:47.695
+directly maximizing the likelihood of
+
+00:16:47.695 --> 00:16:48.970
+the label given the data.
+
+00:16:51.820 --> 00:16:53.880
+They both often end up being linear
+
+00:16:53.880 --> 00:16:55.750
+models, but you're modeling different
+
+00:16:55.750 --> 00:16:57.659
+things in these two in these two
+
+00:16:57.660 --> 00:16:58.170
+settings.
+
+00:16:58.790 --> 00:17:01.880
+And in logistic regression, the model
+
+00:17:01.880 --> 00:17:04.460
+the linear part, so it's, I just wrote
+
+00:17:04.460 --> 00:17:05.890
+logistic regression, but often we're
+
+00:17:05.890 --> 00:17:07.176
+doing linear logistic regression.
+
+00:17:07.176 --> 00:17:09.490
+The linear part is that we're seeing
+
+00:17:09.490 --> 00:17:11.993
+that this logic function is linear.
+
+00:17:11.993 --> 00:17:15.896
+The log ratio of the probability of the
+
+00:17:15.896 --> 00:17:19.830
+of label equals one given the features
+
+00:17:19.830 --> 00:17:21.460
+over probability of label equals zero
+
+00:17:21.460 --> 00:17:22.319
+given the features.
+
+00:17:22.319 --> 00:17:24.323
+That thing is the linear thing that
+
+00:17:24.323 --> 00:17:24.970
+we're fitting.
+
+00:17:27.290 --> 00:17:28.700
+And then we talked about decision
+
+00:17:28.700 --> 00:17:29.350
+trees.
+
+00:17:29.350 --> 00:17:31.706
+I would also say that's a kind of a
+
+00:17:31.706 --> 00:17:33.040
+probabilistic function in the sense
+
+00:17:33.040 --> 00:17:35.555
+that we're choosing our splits to
+
+00:17:35.555 --> 00:17:38.700
+maximize the mutual information or to,
+
+00:17:38.700 --> 00:17:41.200
+sorry, to maximize the information gain
+
+00:17:41.200 --> 00:17:44.870
+to minimize the conditional entropy.
+
+00:17:44.870 --> 00:17:47.780
+And that's like a probabilistic basis
+
+00:17:47.780 --> 00:17:49.400
+for the optimization.
+
+00:17:50.080 --> 00:17:51.810
+And then at the end of the prediction,
+
+00:17:51.810 --> 00:17:53.560
+you would typically be estimating the
+
+00:17:53.560 --> 00:17:55.330
+probability of each label given the
+
+00:17:55.330 --> 00:17:57.170
+data that has fallen into some leaf
+
+00:17:57.170 --> 00:17:57.430
+node.
+
+00:17:59.490 --> 00:18:01.024
+But that has quite different rules than
+
+00:18:01.024 --> 00:18:01.460
+the other.
+
+00:18:01.460 --> 00:18:03.260
+So nearest neighbor is just going to be
+
+00:18:03.260 --> 00:18:05.189
+like finding the sample that has the
+
+00:18:05.190 --> 00:18:06.750
+closest distance.
+
+00:18:06.750 --> 00:18:08.422
+Naive Bayes and logistic regression
+
+00:18:08.422 --> 00:18:11.363
+will be these probability functions
+
+00:18:11.363 --> 00:18:13.540
+that will tend to give you like linear
+
+00:18:13.540 --> 00:18:14.485
+classifiers.
+
+00:18:14.485 --> 00:18:17.480
+And Decision Tree has these conjunctive
+
+00:18:17.480 --> 00:18:19.840
+rules that you say if this feature is
+
+00:18:19.840 --> 00:18:22.249
+greater than this value then you go
+
+00:18:22.249 --> 00:18:22.615
+this way.
+
+00:18:22.615 --> 00:18:23.955
+And then if this other thing happens
+
+00:18:23.955 --> 00:18:26.090
+then you go another way and then at the
+
+00:18:26.090 --> 00:18:29.350
+end you can express that as a series of
+
+00:18:29.350 --> 00:18:29.700
+rules.
+
+00:18:29.750 --> 00:18:31.425
+Where you have a bunch of and
+
+00:18:31.425 --> 00:18:32.850
+conditions, and if all of those
+
+00:18:32.850 --> 00:18:34.220
+conditions are met, then you make a
+
+00:18:34.220 --> 00:18:35.290
+particular prediction.
+
+00:18:38.370 --> 00:18:40.150
+So these algorithms have different
+
+00:18:40.150 --> 00:18:42.480
+strengths, like nearest neighbor has
+
+00:18:42.480 --> 00:18:45.547
+low bias, so that means that you can
+
+00:18:45.547 --> 00:18:47.340
+almost always get perfect training
+
+00:18:47.340 --> 00:18:47.970
+accuracy.
+
+00:18:47.970 --> 00:18:49.706
+You can fit like almost anything with
+
+00:18:49.706 --> 00:18:50.279
+nearest neighbor.
+
+00:18:52.310 --> 00:18:54.725
+On the other hand, I guess I didn't put
+
+00:18:54.725 --> 00:18:56.640
+it here, but limitation is that it has
+
+00:18:56.640 --> 00:18:57.300
+high variance.
+
+00:18:58.000 --> 00:18:59.650
+You might get very different prediction
+
+00:18:59.650 --> 00:19:01.590
+functions if you resample your data.
+
+00:19:03.390 --> 00:19:05.150
+It has no training time.
+
+00:19:06.230 --> 00:19:08.200
+It's very widely applicable and it's
+
+00:19:08.200 --> 00:19:08.900
+very simple.
+
+00:19:09.690 --> 00:19:12.110
+Another limitation is that it can take
+
+00:19:12.110 --> 00:19:13.780
+a long time to do inference, but if you
+
+00:19:13.780 --> 00:19:15.642
+use approximate nearest neighbor
+
+00:19:15.642 --> 00:19:17.790
+inference, which we'll talk about
+
+00:19:17.790 --> 00:19:21.230
+later, then it can be like relatively
+
+00:19:21.230 --> 00:19:21.608
+fast.
+
+00:19:21.608 --> 00:19:23.881
+You can do approximate nearest neighbor
+
+00:19:23.881 --> 00:19:26.600
+in log N time, where N is the number of
+
+00:19:26.600 --> 00:19:29.310
+training samples, where so far we're
+
+00:19:29.310 --> 00:19:31.470
+just doing brute force, which is linear
+
+00:19:31.470 --> 00:19:32.460
+in the number of samples.
+
+00:19:34.620 --> 00:19:35.770
+Naive bayes.
+
+00:19:35.770 --> 00:19:37.980
+The strengths are that you can estimate
+
+00:19:37.980 --> 00:19:39.950
+these parameters reasonably well from
+
+00:19:39.950 --> 00:19:40.680
+limited data.
+
+00:19:41.690 --> 00:19:43.000
+It's also pretty simple.
+
+00:19:43.000 --> 00:19:45.380
+It's fast to train, and the downside is
+
+00:19:45.380 --> 00:19:48.030
+that as limited modeling power, so even
+
+00:19:48.030 --> 00:19:49.876
+on the training set you often won't get
+
+00:19:49.876 --> 00:19:52.049
+0 error or even close to 0 error.
+
+00:19:53.520 --> 00:19:55.290
+Logistic regression is really powerful
+
+00:19:55.290 --> 00:19:57.250
+in high dimensions, so remember that
+
+00:19:57.250 --> 00:19:59.050
+even though it's a linear classifier,
+
+00:19:59.050 --> 00:20:01.400
+which feels like it can't do much in
+
+00:20:01.400 --> 00:20:04.830
+terms of separation in high dimensions,
+
+00:20:04.830 --> 00:20:05.530
+you can.
+
+00:20:05.530 --> 00:20:07.330
+These classifiers are actually very
+
+00:20:07.330 --> 00:20:07.850
+powerful.
+
+00:20:08.510 --> 00:20:10.710
+If you have 1000 dimensional feature.
+
+00:20:11.330 --> 00:20:13.930
+And you have 1000 data points, then you
+
+00:20:13.930 --> 00:20:16.094
+can assign those data points arbitrary
+
+00:20:16.094 --> 00:20:18.210
+labels, arbitrary binary labels, and
+
+00:20:18.210 --> 00:20:19.590
+still get a perfect classifier.
+
+00:20:19.590 --> 00:20:21.770
+You're guaranteed a perfect classifier
+
+00:20:21.770 --> 00:20:23.050
+in terms of the training data.
+
+00:20:23.860 --> 00:20:26.740
+Now, that power power is always a
+
+00:20:26.740 --> 00:20:27.750
+double edged sword.
+
+00:20:27.750 --> 00:20:29.740
+You, if you have a powerful classifier,
+
+00:20:29.740 --> 00:20:32.040
+means you can fit your training data
+
+00:20:32.040 --> 00:20:34.140
+really well, but it also means that
+
+00:20:34.140 --> 00:20:35.850
+you're more susceptible to overfitting
+
+00:20:35.850 --> 00:20:37.510
+your training data, which means that
+
+00:20:37.510 --> 00:20:38.510
+you perform well.
+
+00:20:39.460 --> 00:20:41.160
+And the training data, but your test
+
+00:20:41.160 --> 00:20:43.170
+performance is not so good, you get
+
+00:20:43.170 --> 00:20:43.940
+higher test error.
+
+00:20:45.780 --> 00:20:47.830
+It's also widely applicable.
+
+00:20:47.830 --> 00:20:50.480
+It produces good confidence estimates,
+
+00:20:50.480 --> 00:20:52.130
+so that can be helpful if you want to
+
+00:20:52.130 --> 00:20:54.170
+know whether the prediction is correct.
+
+00:20:54.780 --> 00:20:56.640
+And it gives you fast prediction
+
+00:20:56.640 --> 00:20:57.840
+because it's the linear model.
+
+00:20:59.470 --> 00:21:01.470
+Similar to nearest neighbor has a
+
+00:21:01.470 --> 00:21:03.380
+limitation that it relies on good input
+
+00:21:03.380 --> 00:21:04.330
+features.
+
+00:21:04.330 --> 00:21:05.730
+So nearest neighbor if you have a
+
+00:21:05.730 --> 00:21:06.160
+simple.
+
+00:21:07.240 --> 00:21:10.040
+If you have a simple distance function
+
+00:21:10.040 --> 00:21:13.660
+like Euclidian distance, that assumes
+
+00:21:13.660 --> 00:21:15.665
+that all your features are scaled so
+
+00:21:15.665 --> 00:21:17.110
+that there are like comparable scales
+
+00:21:17.110 --> 00:21:18.930
+to each other, and that they're all
+
+00:21:18.930 --> 00:21:19.540
+predictive.
+
+00:21:20.400 --> 00:21:22.310
+Nearest logistic regression doesn't
+
+00:21:22.310 --> 00:21:23.970
+make assumptions that strong.
+
+00:21:23.970 --> 00:21:25.799
+It can kind of choose which features to
+
+00:21:25.800 --> 00:21:27.420
+use and it can rescale them
+
+00:21:27.420 --> 00:21:29.790
+essentially, but it does.
+
+00:21:29.790 --> 00:21:33.230
+But it's not able to model like joint
+
+00:21:33.230 --> 00:21:35.425
+combinations of features, so the
+
+00:21:35.425 --> 00:21:37.360
+features should be individually useful.
+
+00:21:39.270 --> 00:21:41.340
+And then finally, decision trees are
+
+00:21:41.340 --> 00:21:42.930
+good because they can provide an
+
+00:21:42.930 --> 00:21:44.600
+explainable decision function.
+
+00:21:44.600 --> 00:21:47.040
+You get these nice rules that are easy
+
+00:21:47.040 --> 00:21:47.750
+to communicate.
+
+00:21:48.360 --> 00:21:49.740
+It's also widely applicable.
+
+00:21:49.740 --> 00:21:51.400
+You can use that on continuous discrete
+
+00:21:51.400 --> 00:21:52.040
+data.
+
+00:21:52.040 --> 00:21:54.162
+You don't need to scale the features.
+
+00:21:54.162 --> 00:21:55.740
+It's like it doesn't really matter if
+
+00:21:55.740 --> 00:21:57.930
+you multiply the features by 10, it
+
+00:21:57.930 --> 00:21:59.230
+just means that you'd be choosing a
+
+00:21:59.230 --> 00:22:00.790
+threshold that's 10 times bigger.
+
+00:22:01.820 --> 00:22:03.510
+And you can deal with a mix of discrete
+
+00:22:03.510 --> 00:22:05.720
+and continuous variables.
+
+00:22:05.720 --> 00:22:07.380
+The downside is that.
+
+00:22:08.330 --> 00:22:11.780
+One tree by itself either tends to
+
+00:22:11.780 --> 00:22:14.170
+generalize poorly, meaning like you
+
+00:22:14.170 --> 00:22:15.870
+train a full tree and you do perfect
+
+00:22:15.870 --> 00:22:18.140
+training, but you get bad test error.
+
+00:22:18.770 --> 00:22:20.240
+Or you tend to underfit the data.
+
+00:22:20.240 --> 00:22:21.910
+If you train a short tree then you
+
+00:22:21.910 --> 00:22:23.510
+don't get very good training or test
+
+00:22:23.510 --> 00:22:23.770
+error.
+
+00:22:24.650 --> 00:22:26.920
+And so a single tree by itself is not
+
+00:22:26.920 --> 00:22:28.160
+usually the best predictor.
+
+00:22:31.530 --> 00:22:34.085
+So there's just like you can also think
+
+00:22:34.085 --> 00:22:35.530
+about these methods, I won't talk
+
+00:22:35.530 --> 00:22:37.366
+through this whole slide, but you can
+
+00:22:37.366 --> 00:22:39.290
+also think about the methods in terms
+
+00:22:39.290 --> 00:22:42.130
+of like the learning objectives, the
+
+00:22:42.130 --> 00:22:44.556
+training, like how you optimize those
+
+00:22:44.556 --> 00:22:46.350
+learning objectives and then the
+
+00:22:46.350 --> 00:22:47.840
+inference, how you make your final
+
+00:22:47.840 --> 00:22:48.430
+prediction.
+
+00:22:49.040 --> 00:22:52.460
+And so here I also included linear
+
+00:22:52.460 --> 00:22:54.870
+SVMS, which we'll talk about next week,
+
+00:22:54.870 --> 00:22:57.590
+but you can see for example that.
+
+00:22:59.260 --> 00:23:01.730
+That these in terms of inference,
+
+00:23:01.730 --> 00:23:04.200
+linear SVM, logistic regression, Naive
+
+00:23:04.200 --> 00:23:06.790
+Bayes are all linear models, at least
+
+00:23:06.790 --> 00:23:08.230
+in the case where you're dealing with
+
+00:23:08.230 --> 00:23:11.190
+discrete variables or Gaussians for 9
+
+00:23:11.190 --> 00:23:11.630
+days.
+
+00:23:11.630 --> 00:23:13.948
+But they have different ways, they have
+
+00:23:13.948 --> 00:23:15.695
+different learning objectives and then
+
+00:23:15.695 --> 00:23:17.000
+different ways of doing the training.
+
+00:23:22.330 --> 00:23:24.790
+And then question go ahead.
+
+00:23:36.030 --> 00:23:37.450
+Yeah.
+
+00:23:37.450 --> 00:23:39.810
+Thank you for the clarification, so.
+
+00:23:40.710 --> 00:23:42.850
+So what I mean by that it doesn't
+
+00:23:42.850 --> 00:23:46.110
+require feature scaling is that if you
+
+00:23:46.110 --> 00:23:47.909
+could have one feature that ranges from
+
+00:23:47.910 --> 00:23:50.495
+like zero to 1000 and another feature
+
+00:23:50.495 --> 00:23:52.160
+that ranges from zero to 1.
+
+00:23:52.960 --> 00:23:56.090
+And decision trees are perfectly fine
+
+00:23:56.090 --> 00:23:57.770
+with that, because it can like freely
+
+00:23:57.770 --> 00:23:59.390
+choose the threshold and stuff.
+
+00:23:59.390 --> 00:24:01.450
+And if you multiply 1 feature value by
+
+00:24:01.450 --> 00:24:03.700
+50, it doesn't really change the
+
+00:24:03.700 --> 00:24:05.643
+function, it can still choose like
+
+00:24:05.643 --> 00:24:07.300
+threshold that's 50 times larger.
+
+00:24:08.050 --> 00:24:10.220
+Where nearest neighbor, for example, if
+
+00:24:10.220 --> 00:24:13.084
+one feature ranges from zero to 1001
+
+00:24:13.084 --> 00:24:15.880
+ranges from zero to 1, then it's not
+
+00:24:15.880 --> 00:24:17.673
+going to care at all about the zero to
+
+00:24:17.673 --> 00:24:19.270
+1 feature because like that difference
+
+00:24:19.270 --> 00:24:21.790
+of like 200 on the scale of zero to
+
+00:24:21.790 --> 00:24:23.738
+1000 is going to overwhelm completely a
+
+00:24:23.738 --> 00:24:26.290
+difference of 1 on the 0 to one
+
+00:24:26.290 --> 00:24:26.609
+feature.
+
+00:24:35.130 --> 00:24:36.275
+Right, it doesn't.
+
+00:24:36.275 --> 00:24:37.910
+It's not influenced.
+
+00:24:37.910 --> 00:24:40.040
+I guess it's not influenced by the
+
+00:24:40.040 --> 00:24:41.370
+variance of the features, yeah.
+
+00:24:46.320 --> 00:24:49.130
+So I don't need to read talk through
+
+00:24:49.130 --> 00:24:51.260
+all of this because even for
+
+00:24:51.260 --> 00:24:53.480
+aggression, most of these algorithms
+
+00:24:53.480 --> 00:24:55.219
+are the same and they have the same
+
+00:24:55.220 --> 00:24:56.710
+strengths and the same weaknesses.
+
+00:24:57.500 --> 00:24:59.630
+The only difference between regression
+
+00:24:59.630 --> 00:25:01.310
+and classification is that you tend to
+
+00:25:01.310 --> 00:25:03.235
+have a different loss function where
+
+00:25:03.235 --> 00:25:04.820
+you because you're trying to predict a
+
+00:25:04.820 --> 00:25:06.790
+continuous value instead of predicting
+
+00:25:06.790 --> 00:25:09.590
+a likelihood of a categorical value, or
+
+00:25:09.590 --> 00:25:11.240
+trying to just output the categorical
+
+00:25:11.240 --> 00:25:12.000
+value directly.
+
+00:25:14.330 --> 00:25:17.450
+Linear regression though is A1 new
+
+00:25:17.450 --> 00:25:18.290
+algorithm here.
+
+00:25:18.980 --> 00:25:21.923
+So in linear regression, you're trying
+
+00:25:21.923 --> 00:25:24.585
+to fit the data, so you're not trying
+
+00:25:24.585 --> 00:25:24.940
+to.
+
+00:25:26.480 --> 00:25:28.396
+Fit like a probability model like
+
+00:25:28.396 --> 00:25:29.590
+linear logistic regression.
+
+00:25:29.590 --> 00:25:31.860
+You're just trying to directly fit the
+
+00:25:31.860 --> 00:25:33.680
+prediction given the data, and so you
+
+00:25:33.680 --> 00:25:35.575
+have like a linear function like W
+
+00:25:35.575 --> 00:25:37.960
+transpose X or West transpose X + B.
+
+00:25:37.960 --> 00:25:41.120
+That should ideally output output Y
+
+00:25:41.120 --> 00:25:41.710
+directly.
+
+00:25:43.830 --> 00:25:45.670
+Similar to linear to logistic
+
+00:25:45.670 --> 00:25:47.030
+regression, though it's powerful and
+
+00:25:47.030 --> 00:25:48.220
+high dimensions, it's widely
+
+00:25:48.220 --> 00:25:48.820
+applicable.
+
+00:25:48.820 --> 00:25:50.650
+You get fast prediction.
+
+00:25:50.650 --> 00:25:52.770
+Also, it can be useful to interpret the
+
+00:25:52.770 --> 00:25:54.300
+coefficients to say like what the
+
+00:25:54.300 --> 00:25:56.040
+correlations are of the features with
+
+00:25:56.040 --> 00:25:58.110
+your prediction, or to see which
+
+00:25:58.110 --> 00:25:59.900
+features are more predictive than
+
+00:25:59.900 --> 00:26:00.300
+others.
+
+00:26:01.410 --> 00:26:03.440
+And similar to logistic regression, it
+
+00:26:03.440 --> 00:26:06.140
+relies to some extent on good features.
+
+00:26:06.140 --> 00:26:07.720
+In fact, I would say even more.
+
+00:26:08.320 --> 00:26:12.220
+Because this is assuming that Y is
+
+00:26:12.220 --> 00:26:15.040
+going to be a linear function of X and
+
+00:26:15.040 --> 00:26:17.130
+West, which is in a way a stronger
+
+00:26:17.130 --> 00:26:18.140
+assumption than that.
+
+00:26:18.140 --> 00:26:20.670
+Like a binary classification will be a
+
+00:26:20.670 --> 00:26:21.870
+linear function of the features.
+
+00:26:23.360 --> 00:26:24.940
+So you often have to do some kind of
+
+00:26:24.940 --> 00:26:26.950
+feature transformations to make it work
+
+00:26:26.950 --> 00:26:27.220
+well.
+
+00:26:28.520 --> 00:26:28.960
+Question.
+
+00:26:40.800 --> 00:26:43.402
+So naive bayes.
+
+00:26:43.402 --> 00:26:46.295
+The example I gave was a semi semi
+
+00:26:46.295 --> 00:26:48.850
+Naive Bayes algorithm for classifying
+
+00:26:48.850 --> 00:26:50.650
+faces and cars.
+
+00:26:50.650 --> 00:26:52.618
+So there they took groups of features
+
+00:26:52.618 --> 00:26:54.190
+and modeled the probabilities of small
+
+00:26:54.190 --> 00:26:55.720
+groups of features and then took the
+
+00:26:55.720 --> 00:26:57.090
+product of those to give you your
+
+00:26:57.090 --> 00:26:58.190
+probabilistic model.
+
+00:26:58.190 --> 00:27:01.770
+I also would use like Naive Bayes if
+
+00:27:01.770 --> 00:27:03.719
+I'm trying to do like color like
+
+00:27:03.720 --> 00:27:05.600
+segmentation based on color and I need
+
+00:27:05.600 --> 00:27:08.000
+to estimate the probability of color
+
+00:27:08.000 --> 00:27:09.490
+given that it's in one region versus
+
+00:27:09.490 --> 00:27:11.470
+another, I might assume that.
+
+00:27:11.530 --> 00:27:15.320
+By that, my color features like the hue
+
+00:27:15.320 --> 00:27:17.920
+versus intensity for example, are
+
+00:27:17.920 --> 00:27:19.380
+independent given the region that it
+
+00:27:19.380 --> 00:27:22.260
+came from and so use that as part of my
+
+00:27:22.260 --> 00:27:23.760
+probabilistic model for doing the
+
+00:27:23.760 --> 00:27:24.670
+segmentation.
+
+00:27:25.880 --> 00:27:30.940
+Logistic regression you would like any
+
+00:27:30.940 --> 00:27:32.610
+neural network is doing logistic
+
+00:27:32.610 --> 00:27:35.807
+regression in the last layer.
+
+00:27:35.807 --> 00:27:38.703
+So most things are using logistic
+
+00:27:38.703 --> 00:27:40.770
+regression now as part of it.
+
+00:27:40.770 --> 00:27:42.775
+So you can view like the early layers
+
+00:27:42.775 --> 00:27:44.674
+as feature learning and the last layer
+
+00:27:44.674 --> 00:27:45.519
+is logistic regression.
+
+00:27:46.490 --> 00:27:49.250
+And then decision trees are.
+
+00:27:50.660 --> 00:27:52.200
+We'll see an example.
+
+00:27:52.200 --> 00:27:53.670
+It's used in the example I'm going to
+
+00:27:53.670 --> 00:27:55.723
+give, but like medical analysis is a is
+
+00:27:55.723 --> 00:27:57.680
+a good one because you often want some
+
+00:27:57.680 --> 00:28:00.631
+interpretable function as well as some
+
+00:28:00.631 --> 00:28:01.620
+good prediction.
+
+00:28:03.820 --> 00:28:04.090
+Yep.
+
+00:28:09.200 --> 00:28:11.450
+All right, so one of the one of the key
+
+00:28:11.450 --> 00:28:15.360
+concepts is like how performance varies
+
+00:28:15.360 --> 00:28:17.230
+with the number of training samples.
+
+00:28:17.230 --> 00:28:20.080
+So as you get more training data, you
+
+00:28:20.080 --> 00:28:21.670
+should be able to fit a more accurate
+
+00:28:21.670 --> 00:28:22.120
+model.
+
+00:28:23.310 --> 00:28:25.600
+And so you would expect that your test
+
+00:28:25.600 --> 00:28:27.746
+error should decrease as you get more
+
+00:28:27.746 --> 00:28:29.760
+training samples, because if you have
+
+00:28:29.760 --> 00:28:33.640
+only like 1 training sample, then you
+
+00:28:33.640 --> 00:28:34.700
+don't know if that's like really
+
+00:28:34.700 --> 00:28:36.420
+representative, if it's covering all
+
+00:28:36.420 --> 00:28:37.195
+the different cases.
+
+00:28:37.195 --> 00:28:39.263
+As you get more and more training
+
+00:28:39.263 --> 00:28:41.020
+samples, you can fit more complex
+
+00:28:41.020 --> 00:28:43.858
+models and you can be more assured that
+
+00:28:43.858 --> 00:28:46.110
+the training samples that you've seen
+
+00:28:46.110 --> 00:28:47.850
+fully represent the distribution that
+
+00:28:47.850 --> 00:28:48.710
+you'll see in testing.
+
+00:28:50.040 --> 00:28:52.040
+But as you get more training, it
+
+00:28:52.040 --> 00:28:53.700
+becomes harder to fit the training
+
+00:28:53.700 --> 00:28:54.060
+data.
+
+00:28:54.920 --> 00:28:57.655
+So maybe a linear model can perfectly
+
+00:28:57.655 --> 00:29:00.340
+classify like 500 examples, but it
+
+00:29:00.340 --> 00:29:02.350
+can't perfectly classify 500 million
+
+00:29:02.350 --> 00:29:04.900
+examples, even if they're even in the
+
+00:29:04.900 --> 00:29:05.430
+training set.
+
+00:29:07.110 --> 00:29:10.420
+As you get more data, these will test
+
+00:29:10.420 --> 00:29:12.630
+and the training error will converge.
+
+00:29:13.380 --> 00:29:15.100
+And if they're coming from exactly the
+
+00:29:15.100 --> 00:29:16.540
+same distribution, then they'll
+
+00:29:16.540 --> 00:29:18.500
+converge to exactly the same value.
+
+00:29:19.680 --> 00:29:21.030
+Only if they come from different
+
+00:29:21.030 --> 00:29:22.790
+distributions would you possibly have a
+
+00:29:22.790 --> 00:29:24.250
+gap if you have infinite training
+
+00:29:24.250 --> 00:29:24.720
+samples.
+
+00:29:25.330 --> 00:29:27.133
+So we have these concepts of the test
+
+00:29:27.133 --> 00:29:27.411
+error.
+
+00:29:27.411 --> 00:29:29.253
+So that's the error on some samples
+
+00:29:29.253 --> 00:29:31.420
+that are not used for training that are
+
+00:29:31.420 --> 00:29:34.360
+randomly sampled from your distribution
+
+00:29:34.360 --> 00:29:35.020
+of data.
+
+00:29:35.020 --> 00:29:38.744
+The training error is the error on your
+
+00:29:38.744 --> 00:29:41.240
+training set that is used to optimize
+
+00:29:41.240 --> 00:29:43.458
+your model, and the generalization
+
+00:29:43.458 --> 00:29:46.803
+error is the gap between the test and
+
+00:29:46.803 --> 00:29:49.237
+the training error, so that the
+
+00:29:49.237 --> 00:29:51.672
+generalization error is your error due
+
+00:29:51.672 --> 00:29:55.386
+to due to like an imperfect model due
+
+00:29:55.386 --> 00:29:55.679
+to.
+
+00:29:55.750 --> 00:29:57.280
+To limited training samples.
+
+00:30:04.950 --> 00:30:05.650
+Question.
+
+00:30:07.940 --> 00:30:09.675
+So there's test error.
+
+00:30:09.675 --> 00:30:12.620
+So that's the I'll start with training.
+
+00:30:12.620 --> 00:30:14.070
+OK, so first there's training error.
+
+00:30:14.810 --> 00:30:17.610
+So training error is you fit, you fit a
+
+00:30:17.610 --> 00:30:19.010
+model on a training set, and then
+
+00:30:19.010 --> 00:30:20.540
+you're evaluating the error on the same
+
+00:30:20.540 --> 00:30:21.230
+training set.
+
+00:30:22.490 --> 00:30:24.620
+So if your model is really powerful,
+
+00:30:24.620 --> 00:30:27.282
+that training error might be 0, But if
+
+00:30:27.282 --> 00:30:29.220
+it's if it's more limited, like Naive
+
+00:30:29.220 --> 00:30:32.090
+Bayes, you'll often have nonzero error.
+
+00:30:32.950 --> 00:30:35.652
+And you since your loss is, since you
+
+00:30:35.652 --> 00:30:36.384
+have some.
+
+00:30:36.384 --> 00:30:38.580
+If you're optimizing a loss like the
+
+00:30:38.580 --> 00:30:41.160
+probability, then there's always room
+
+00:30:41.160 --> 00:30:42.870
+to improve that loss, so you'll always
+
+00:30:42.870 --> 00:30:45.430
+have like non like some loss on your
+
+00:30:45.430 --> 00:30:45.890
+training set.
+
+00:30:47.970 --> 00:30:50.120
+The test error is if you take that same
+
+00:30:50.120 --> 00:30:52.770
+model, but now you evaluate it on other
+
+00:30:52.770 --> 00:30:54.516
+samples from the distribution, other
+
+00:30:54.516 --> 00:30:56.040
+test samples, and you compute an
+
+00:30:56.040 --> 00:30:56.835
+expected error.
+
+00:30:56.835 --> 00:30:59.264
+The average error over those test
+
+00:30:59.264 --> 00:31:01.172
+samples, your test error.
+
+00:31:01.172 --> 00:31:03.330
+You always expect your test error to be
+
+00:31:03.330 --> 00:31:04.480
+higher than your training error.
+
+00:31:05.130 --> 00:31:06.400
+Because you're.
+
+00:31:06.490 --> 00:31:07.000
+Time.
+
+00:31:07.860 --> 00:31:10.140
+Because your test error was not used to
+
+00:31:10.140 --> 00:31:11.530
+optimize your model, but your training
+
+00:31:11.530 --> 00:31:12.000
+error was.
+
+00:31:13.140 --> 00:31:15.260
+In that gap between the test air and
+
+00:31:15.260 --> 00:31:16.260
+the training error is the
+
+00:31:16.260 --> 00:31:17.320
+generalization error.
+
+00:31:18.050 --> 00:31:20.560
+So that's how that's the error due to
+
+00:31:20.560 --> 00:31:23.680
+the challenge of making predictions
+
+00:31:23.680 --> 00:31:25.330
+about new samples that were not made in
+
+00:31:25.330 --> 00:31:25.710
+training.
+
+00:31:26.340 --> 00:31:27.510
+That were not seen in training.
+
+00:31:29.880 --> 00:31:30.260
+Question.
+
+00:31:33.240 --> 00:31:35.950
+So overfit means that.
+
+00:31:35.950 --> 00:31:37.920
+So this isn't the ideal plot for
+
+00:31:37.920 --> 00:31:38.610
+overfitting, but.
+
+00:31:39.500 --> 00:31:41.520
+Overfitting is that as your model gets
+
+00:31:41.520 --> 00:31:43.600
+more complicated, your training error
+
+00:31:43.600 --> 00:31:45.115
+will always should always go down.
+
+00:31:45.115 --> 00:31:48.510
+You would expect it to go down if you.
+
+00:31:49.070 --> 00:31:52.200
+If you, for example were to keep adding
+
+00:31:52.200 --> 00:31:55.040
+features to your model, then the same
+
+00:31:55.040 --> 00:31:57.030
+model should keep getting better on
+
+00:31:57.030 --> 00:31:58.550
+your training set because you've got
+
+00:31:58.550 --> 00:32:00.235
+more features with which to fit your
+
+00:32:00.235 --> 00:32:00.810
+training data.
+
+00:32:02.050 --> 00:32:04.430
+And maybe for a while your test error
+
+00:32:04.430 --> 00:32:06.320
+will also go down because you genuinely
+
+00:32:06.320 --> 00:32:07.350
+get a better predictor.
+
+00:32:08.190 --> 00:32:10.200
+But then at some point, as you continue
+
+00:32:10.200 --> 00:32:12.500
+to increase the complexity, the test
+
+00:32:12.500 --> 00:32:13.880
+error will start going up.
+
+00:32:13.880 --> 00:32:15.260
+Even though the training error keeps
+
+00:32:15.260 --> 00:32:17.540
+going down, the test error goes up, and
+
+00:32:17.540 --> 00:32:18.690
+that's the point at which you've
+
+00:32:18.690 --> 00:32:19.180
+overfit.
+
+00:32:19.920 --> 00:32:21.604
+So you can't.
+
+00:32:21.604 --> 00:32:22.165
+Really.
+
+00:32:22.165 --> 00:32:24.600
+Common, really common conceptual
+
+00:32:24.600 --> 00:32:27.500
+mistake that people make is to think
+
+00:32:27.500 --> 00:32:29.670
+that once you're training error is 0,
+
+00:32:29.670 --> 00:32:30.890
+then you've overfit.
+
+00:32:30.890 --> 00:32:32.060
+That's not overfitting.
+
+00:32:32.060 --> 00:32:32.515
+You can't.
+
+00:32:32.515 --> 00:32:33.930
+You can't look at your training error
+
+00:32:33.930 --> 00:32:35.789
+by itself to say that you've overfit.
+
+00:32:36.560 --> 00:32:38.430
+Overfitting is when your test error
+
+00:32:38.430 --> 00:32:40.480
+starts to go up after increasing the
+
+00:32:40.480 --> 00:32:41.190
+complexity.
+
+00:32:43.380 --> 00:32:44.950
+So in your homework 2.
+
+00:32:45.850 --> 00:32:47.778
+Trees are like a really good way to
+
+00:32:47.778 --> 00:32:49.235
+look at overfitting because the
+
+00:32:49.235 --> 00:32:51.280
+complexity is like the depth of the
+
+00:32:51.280 --> 00:32:52.983
+tree or the number of nodes in the
+
+00:32:52.983 --> 00:32:53.329
+tree.
+
+00:32:53.330 --> 00:32:56.530
+So in your in your homework two, you're
+
+00:32:56.530 --> 00:32:58.930
+going to look at overfitting and how
+
+00:32:58.930 --> 00:33:01.170
+the training and test error varies as
+
+00:33:01.170 --> 00:33:02.510
+you increase the complexity of your
+
+00:33:02.510 --> 00:33:03.080
+classifiers.
+
+00:33:04.230 --> 00:33:04.550
+Question.
+
+00:33:09.440 --> 00:33:09.880
+Right.
+
+00:33:09.880 --> 00:33:10.820
+Yeah, that's a good point.
+
+00:33:10.820 --> 00:33:13.380
+So increasing the sample size does not
+
+00:33:13.380 --> 00:33:15.610
+Causeway overfitting, but you will
+
+00:33:15.610 --> 00:33:21.280
+always get, you should expect to get a
+
+00:33:21.280 --> 00:33:24.070
+better fit to the true model, a closer
+
+00:33:24.070 --> 00:33:25.450
+fit to the true model as you increase
+
+00:33:25.450 --> 00:33:26.340
+the training size.
+
+00:33:26.340 --> 00:33:28.550
+The reason that I say I keep on saying
+
+00:33:28.550 --> 00:33:31.860
+expect and what that means is that if
+
+00:33:31.860 --> 00:33:34.416
+you were to resample this problem, like
+
+00:33:34.416 --> 00:33:36.430
+resample your data over and over again.
+
+00:33:36.590 --> 00:33:39.152
+Than on average this will happen, but
+
+00:33:39.152 --> 00:33:41.289
+in any particular scenario you can get
+
+00:33:41.290 --> 00:33:41.840
+unlucky.
+
+00:33:41.840 --> 00:33:44.270
+You could add like 5 training examples
+
+00:33:44.270 --> 00:33:46.490
+and they're really non representative
+
+00:33:46.490 --> 00:33:48.620
+by chance and they cause your model to
+
+00:33:48.620 --> 00:33:49.500
+get worse.
+
+00:33:49.500 --> 00:33:51.080
+So there's no guarantees.
+
+00:33:51.080 --> 00:33:53.365
+But you can say more easily what will
+
+00:33:53.365 --> 00:33:55.980
+happen in expectation, which means on
+
+00:33:55.980 --> 00:33:58.420
+average under the same kinds of
+
+00:33:58.420 --> 00:33:59.100
+situations.
+
+00:34:06.160 --> 00:34:10.527
+Alright, so I want to so a lot of a lot
+
+00:34:10.527 --> 00:34:13.120
+of people said that these a lot of
+
+00:34:13.120 --> 00:34:14.729
+respondents to the survey said that.
+
+00:34:16.090 --> 00:34:17.850
+Even when these concepts feel like they
+
+00:34:17.850 --> 00:34:20.910
+make sense abstractly or theoretically,
+
+00:34:20.910 --> 00:34:22.540
+it's not that easy to understand.
+
+00:34:22.540 --> 00:34:23.749
+How do you actually put it into
+
+00:34:23.750 --> 00:34:25.660
+practice and turn it into code?
+
+00:34:25.660 --> 00:34:27.750
+So I want to work through a particular
+
+00:34:27.750 --> 00:34:29.200
+example in some detail.
+
+00:34:30.090 --> 00:34:33.490
+And the example I choose is this
+
+00:34:33.490 --> 00:34:35.550
+Wisconsin breast cancer data set.
+
+00:34:36.450 --> 00:34:38.290
+So this data set was collected in the
+
+00:34:38.290 --> 00:34:39.360
+early 90s.
+
+00:34:40.440 --> 00:34:44.650
+The motivation is that is that doctors
+
+00:34:44.650 --> 00:34:46.800
+wanted to use this tool, called fine
+
+00:34:46.800 --> 00:34:50.410
+needle aspirates to diagnose whether a
+
+00:34:50.410 --> 00:34:52.660
+tumor is malignant or benign.
+
+00:34:53.900 --> 00:34:54.900
+And doctors.
+
+00:34:54.900 --> 00:34:57.040
+In some medical papers, doctors
+
+00:34:57.040 --> 00:35:01.360
+reported a 94% accuracy in making this
+
+00:35:01.360 --> 00:35:02.540
+diagnosis.
+
+00:35:02.540 --> 00:35:06.560
+But the authors of this study, the
+
+00:35:06.560 --> 00:35:08.520
+first author, is a medical doctor
+
+00:35:08.520 --> 00:35:08.980
+himself.
+
+00:35:11.150 --> 00:35:12.490
+Have like 2 concerns.
+
+00:35:12.490 --> 00:35:14.210
+One is that they want to see if you can
+
+00:35:14.210 --> 00:35:15.327
+get a better accuracy.
+
+00:35:15.327 --> 00:35:17.983
+They want two or three, maybe they want
+
+00:35:17.983 --> 00:35:19.560
+to reduce the amount of expertise
+
+00:35:19.560 --> 00:35:21.160
+that's needed in order to make a good
+
+00:35:21.160 --> 00:35:21.925
+diagnosis.
+
+00:35:21.925 --> 00:35:24.080
+And third, they suspect that these
+
+00:35:24.080 --> 00:35:26.620
+reports may be biased because there's a
+
+00:35:26.620 --> 00:35:29.065
+they note that there tends to be like a
+
+00:35:29.065 --> 00:35:30.900
+bias towards positive results that are.
+
+00:35:30.900 --> 00:35:34.638
+I mean, yeah, there tends to be a bias
+
+00:35:34.638 --> 00:35:36.879
+towards positive results and reports,
+
+00:35:36.880 --> 00:35:37.130
+right?
+
+00:35:37.990 --> 00:35:40.140
+People are more likely to report
+
+00:35:40.140 --> 00:35:41.436
+something if they think it's good, then
+
+00:35:41.436 --> 00:35:43.240
+if they get a disappointing outcome.
+
+00:35:44.810 --> 00:35:47.190
+So they want to create computer based
+
+00:35:47.190 --> 00:35:49.250
+tests that are less objective and
+
+00:35:49.250 --> 00:35:51.270
+provide an effective diagnostic tool.
+
+00:35:52.830 --> 00:35:55.350
+So they collected data from 569
+
+00:35:55.350 --> 00:35:58.660
+patients and then for developing the
+
+00:35:58.660 --> 00:36:00.584
+algorithm and doing their first tests
+
+00:36:00.584 --> 00:36:02.525
+and then they collected an additional
+
+00:36:02.525 --> 00:36:03.250
+54.
+
+00:36:03.960 --> 00:36:06.570
+Data from another 54 patients for their
+
+00:36:06.570 --> 00:36:07.290
+final tests.
+
+00:36:08.850 --> 00:36:13.080
+And so you can it's like important to
+
+00:36:13.080 --> 00:36:16.090
+understand like how painstaking this
+
+00:36:16.090 --> 00:36:18.340
+process is of collecting data.
+
+00:36:18.340 --> 00:36:18.740
+So.
+
+00:36:19.470 --> 00:36:21.620
+These are these are real people who
+
+00:36:21.620 --> 00:36:24.350
+have tumors and they take medical
+
+00:36:24.350 --> 00:36:26.660
+images of them and then they have some
+
+00:36:26.660 --> 00:36:28.730
+interface where somebody can go in and
+
+00:36:28.730 --> 00:36:31.176
+outline several of the cells, many of
+
+00:36:31.176 --> 00:36:32.530
+the cells that were detected.
+
+00:36:33.930 --> 00:36:35.836
+And then they have a.
+
+00:36:35.836 --> 00:36:38.220
+Then they do like an automated analysis
+
+00:36:38.220 --> 00:36:40.060
+of those outlines to compute different
+
+00:36:40.060 --> 00:36:42.100
+features, like how what is the radius
+
+00:36:42.100 --> 00:36:43.853
+of the cells and what's the area of the
+
+00:36:43.853 --> 00:36:45.250
+cells and what's the compactness.
+
+00:36:46.420 --> 00:36:47.350
+And then?
+
+00:36:47.450 --> 00:36:48.110
+
+
+00:36:48.860 --> 00:36:51.460
+As the final features, they look at
+
+00:36:51.460 --> 00:36:53.790
+these characteristics of the cells.
+
+00:36:53.790 --> 00:36:54.810
+They look at the average
+
+00:36:54.810 --> 00:36:57.162
+characteristic, the characteristic of
+
+00:36:57.162 --> 00:36:59.620
+the largest cell, the worst cell.
+
+00:37:00.340 --> 00:37:04.030
+And the and then the standard deviation
+
+00:37:04.030 --> 00:37:05.340
+of these characteristics.
+
+00:37:05.340 --> 00:37:06.730
+So they're looking at trying to look at
+
+00:37:06.730 --> 00:37:09.250
+like the distribution of these shape
+
+00:37:09.250 --> 00:37:11.680
+properties of the cells in order to
+
+00:37:11.680 --> 00:37:13.410
+determine if the cancerous cells are
+
+00:37:13.410 --> 00:37:14.390
+malignant or benign.
+
+00:37:15.880 --> 00:37:18.820
+So it's a pretty involved process to
+
+00:37:18.820 --> 00:37:19.620
+collect that data.
+
+00:37:22.080 --> 00:37:22.420
+
+
+00:38:00.720 --> 00:38:01.480
+Right.
+
+00:38:01.480 --> 00:38:04.120
+So what you would do?
+
+00:38:04.120 --> 00:38:08.160
+And if you go for any kinds of tests,
+
+00:38:08.160 --> 00:38:10.000
+you'll probably experience this to some
+
+00:38:10.000 --> 00:38:10.320
+extent.
+
+00:38:11.820 --> 00:38:13.870
+Like often, somebody will go, a
+
+00:38:13.870 --> 00:38:16.093
+technician will go in, they see some
+
+00:38:16.093 --> 00:38:17.710
+image, they take different measurements
+
+00:38:17.710 --> 00:38:18.350
+on the image.
+
+00:38:19.090 --> 00:38:22.410
+And then they can say then they may run
+
+00:38:22.410 --> 00:38:24.765
+this like through some data analysis,
+
+00:38:24.765 --> 00:38:27.650
+and either either they have rules in
+
+00:38:27.650 --> 00:38:29.640
+their head for like what are acceptable
+
+00:38:29.640 --> 00:38:32.715
+variations, or they run it through some
+
+00:38:32.715 --> 00:38:36.760
+analysis and they'll say, they might
+
+00:38:36.760 --> 00:38:39.110
+tell you have no cause for concern, or
+
+00:38:39.110 --> 00:38:41.474
+there's like some cause for concern, or
+
+00:38:41.474 --> 00:38:43.350
+like there's great cause for concern.
+
+00:38:44.140 --> 00:38:45.510
+But if you have an algorithm that it
+
+00:38:45.510 --> 00:38:47.100
+might tell you, in this case, for
+
+00:38:47.100 --> 00:38:49.630
+example, what's the probability that
+
+00:38:49.630 --> 00:38:51.850
+these cells are malignant versus
+
+00:38:51.850 --> 00:38:52.980
+benign?
+
+00:38:52.980 --> 00:38:55.595
+And then you might say, if there's a
+
+00:38:55.595 --> 00:38:57.730
+30% chance that it's malignant, then
+
+00:38:57.730 --> 00:38:59.210
+I'm going to recommend a biopsy.
+
+00:38:59.210 --> 00:39:02.160
+So you want to have some confidence
+
+00:39:02.160 --> 00:39:03.140
+with your prediction.
+
+00:39:04.210 --> 00:39:05.360
+So in this.
+
+00:39:06.760 --> 00:39:08.392
+In our analysis, we're not going to
+
+00:39:08.392 --> 00:39:11.020
+look at the confidences too much for
+
+00:39:11.020 --> 00:39:12.010
+simplicity.
+
+00:39:12.010 --> 00:39:15.457
+But in the study they also will look,
+
+00:39:15.457 --> 00:39:18.340
+they also look at the like specificity,
+
+00:39:18.340 --> 00:39:20.560
+like how often can you do you
+
+00:39:20.560 --> 00:39:22.406
+misdiagnose one way or the other and
+
+00:39:22.406 --> 00:39:24.155
+they can use the confidence as part of
+
+00:39:24.155 --> 00:39:24.860
+the recommendation.
+
+00:39:30.410 --> 00:39:35.273
+Alright, so I'm going to go into this
+
+00:39:35.273 --> 00:39:37.140
+and I think now is a good time to take
+
+00:39:37.140 --> 00:39:38.050
+a minute or two.
+
+00:39:38.050 --> 00:39:39.515
+You can think about this problem, how
+
+00:39:39.515 --> 00:39:40.250
+you would solve it.
+
+00:39:40.250 --> 00:39:42.130
+You've got 30 features, continuous
+
+00:39:42.130 --> 00:39:43.510
+features, and you're trying to predict
+
+00:39:43.510 --> 00:39:44.450
+malignant or benign.
+
+00:39:45.150 --> 00:39:48.480
+And also feel free to stretch your it.
+
+00:39:48.480 --> 00:39:51.920
+You need to prepare your mind for the
+
+00:39:51.920 --> 00:39:52.410
+next half.
+
+00:40:20.140 --> 00:40:20.570
+Question.
+
+00:40:36.560 --> 00:40:39.556
+Decision trees for example does that
+
+00:40:39.556 --> 00:40:42.250
+and neural networks will also do that.
+
+00:40:42.250 --> 00:40:44.940
+Or kernelized SVMS and nearest
+
+00:40:44.940 --> 00:40:45.374
+neighbor.
+
+00:40:45.374 --> 00:40:47.950
+They all they all depend jointly on the
+
+00:40:47.950 --> 00:40:48.560
+features.
+
+00:40:51.930 --> 00:40:52.700
+How does what?
+
+00:40:56.030 --> 00:40:58.985
+I guess because the distance is.
+
+00:40:58.985 --> 00:41:01.517
+That's a good point, yeah.
+
+00:41:01.517 --> 00:41:04.160
+The K&NI guess, it depends jointly on
+
+00:41:04.160 --> 00:41:05.790
+them, but it's independently
+
+00:41:05.790 --> 00:41:07.020
+considering those features.
+
+00:41:07.020 --> 00:41:08.180
+That's right, yeah.
+
+00:41:20.030 --> 00:41:23.680
+But it's nice if it's often hard to
+
+00:41:23.680 --> 00:41:25.810
+know what's relevant, and so it's nice.
+
+00:41:25.810 --> 00:41:27.510
+The ideal is that you can just collect
+
+00:41:27.510 --> 00:41:28.840
+a lot of things that you think might be
+
+00:41:28.840 --> 00:41:30.950
+relevant and feed it into the algorithm
+
+00:41:30.950 --> 00:41:34.578
+and not have to manually like manually
+
+00:41:34.578 --> 00:41:36.640
+like prune it and out.
+
+00:41:42.050 --> 00:41:45.256
+Yeah, so one is robust to irrelevant
+
+00:41:45.256 --> 00:41:47.780
+features, but if you do L2, it's not so
+
+00:41:47.780 --> 00:41:49.340
+robust to irrelevant features.
+
+00:41:49.340 --> 00:41:50.900
+So that's like another property of the
+
+00:41:50.900 --> 00:41:52.160
+algorithm is whether it has that
+
+00:41:52.160 --> 00:41:52.660
+robustness.
+
+00:41:57.120 --> 00:41:59.780
+Alright, so let me zoom in a little
+
+00:41:59.780 --> 00:42:00.280
+bit.
+
+00:42:03.050 --> 00:42:04.260
+I guess over here.
+
+00:42:10.690 --> 00:42:13.660
+So we've got this data set.
+
+00:42:13.660 --> 00:42:15.710
+Fortunately, in this case, I can load
+
+00:42:15.710 --> 00:42:17.900
+the data set from sklearn datasets.
+
+00:42:19.720 --> 00:42:22.300
+So here I have the initialization code
+
+00:42:22.300 --> 00:42:22.965
+and your homework.
+
+00:42:22.965 --> 00:42:24.790
+I provided this code to you as well
+
+00:42:24.790 --> 00:42:26.670
+that initially like loads the data and
+
+00:42:26.670 --> 00:42:28.480
+splits it up into different datasets.
+
+00:42:29.440 --> 00:42:32.010
+But here I've just got my libraries
+
+00:42:32.010 --> 00:42:33.470
+that I'm going to use.
+
+00:42:33.470 --> 00:42:37.960
+I load the data I this data comes in
+
+00:42:37.960 --> 00:42:39.260
+like a particular structure.
+
+00:42:39.260 --> 00:42:40.930
+So I take out the features which are
+
+00:42:40.930 --> 00:42:43.740
+capital X, the predictions which are Y.
+
+00:42:44.490 --> 00:42:45.940
+And it also gives me names of the
+
+00:42:45.940 --> 00:42:49.120
+features and names of the predictions
+
+00:42:49.120 --> 00:42:50.690
+which are good for visualization.
+
+00:42:51.740 --> 00:42:53.330
+So if I run this, it's going to start
+
+00:42:53.330 --> 00:42:55.328
+an instance on collabs and then it's
+
+00:42:55.328 --> 00:42:57.366
+going to download the data and print
+
+00:42:57.366 --> 00:42:59.900
+out the shape and the shape of Y.
+
+00:42:59.900 --> 00:43:02.950
+So I often like I print a lot of shapes
+
+00:43:02.950 --> 00:43:05.130
+of variables when I'm doing stuff
+
+00:43:05.130 --> 00:43:07.880
+because it helps me to make sure I
+
+00:43:07.880 --> 00:43:09.230
+understand exactly what I loaded.
+
+00:43:09.230 --> 00:43:11.679
+Like if I print out the shape and it's
+
+00:43:11.679 --> 00:43:14.006
+if the shape of X is 1 by something
+
+00:43:14.006 --> 00:43:15.660
+then I would be like maybe I took the
+
+00:43:15.660 --> 00:43:18.160
+wrong like values from this data
+
+00:43:18.160 --> 00:43:18.630
+structure.
+
+00:43:19.760 --> 00:43:23.580
+Alright, so I've got 569 data points.
+
+00:43:23.580 --> 00:43:26.950
+So remember that there were 569 samples
+
+00:43:26.950 --> 00:43:28.790
+that were drawn at first that were used
+
+00:43:28.790 --> 00:43:30.350
+for their training and algorithm
+
+00:43:30.350 --> 00:43:32.680
+development, and then another like 56
+
+00:43:32.680 --> 00:43:34.340
+or something that we use for testing.
+
+00:43:34.340 --> 00:43:36.380
+The 56 are not released, they're not
+
+00:43:36.380 --> 00:43:37.170
+part of this data set.
+
+00:43:38.230 --> 00:43:40.150
+And then there's 30 features, there's
+
+00:43:40.150 --> 00:43:41.300
+10 characteristics.
+
+00:43:41.970 --> 00:43:44.560
+That correspond to the like the worst
+
+00:43:44.560 --> 00:43:46.230
+case, the average case and the steering
+
+00:43:46.230 --> 00:43:46.760
+deviation.
+
+00:43:47.470 --> 00:43:50.034
+And I've got 569 labels, so number of
+
+00:43:50.034 --> 00:43:52.010
+labels equals number of data points, so
+
+00:43:52.010 --> 00:43:52.500
+that's good.
+
+00:43:54.430 --> 00:43:56.433
+Now I can print out.
+
+00:43:56.433 --> 00:43:58.960
+I usually will also like print out some
+
+00:43:58.960 --> 00:44:00.940
+examples just to make sure that there's
+
+00:44:00.940 --> 00:44:01.585
+nothing weird here.
+
+00:44:01.585 --> 00:44:04.125
+I don't have any nins or anything like
+
+00:44:04.125 --> 00:44:04.330
+that.
+
+00:44:05.190 --> 00:44:06.620
+So here are the different feature
+
+00:44:06.620 --> 00:44:08.060
+names.
+
+00:44:08.060 --> 00:44:11.080
+Here's I chose a few random example
+
+00:44:11.080 --> 00:44:11.760
+indices.
+
+00:44:12.430 --> 00:44:14.980
+And I can see, I can see some of the
+
+00:44:14.980 --> 00:44:15.740
+feature values.
+
+00:44:15.740 --> 00:44:18.530
+So there's no NANS or Memphis or
+
+00:44:18.530 --> 00:44:19.570
+anything like that in there.
+
+00:44:19.570 --> 00:44:20.400
+That's good.
+
+00:44:20.400 --> 00:44:22.320
+Also I can notice like.
+
+00:44:23.030 --> 00:44:25.974
+Some of some of their values are like
+
+00:44:25.974 --> 00:44:30.416
+1.2 E 2 or 11 E 3, so this is like
+
+00:44:30.416 --> 00:44:32.080
+1000, while some other ones are really
+
+00:44:32.080 --> 00:44:36.134
+small, like 1188 E -, 1.
+
+00:44:36.134 --> 00:44:37.910
+So that's something to consider.
+
+00:44:37.910 --> 00:44:39.340
+There's a pretty big range of the
+
+00:44:39.340 --> 00:44:40.230
+feature values here.
+
+00:44:43.520 --> 00:44:45.600
+So then another thing I'll do early is
+
+00:44:45.600 --> 00:44:48.050
+say how common is each class, because
+
+00:44:48.050 --> 00:44:50.120
+if like 99% of the examples are in one
+
+00:44:50.120 --> 00:44:51.745
+class, that's something I need to keep
+
+00:44:51.745 --> 00:44:53.840
+in mind versus a 5050 split.
+
+00:44:55.290 --> 00:44:56.650
+So in this case.
+
+00:44:56.750 --> 00:44:57.360
+
+
+00:44:58.700 --> 00:45:02.810
+37% of the examples have Class 0 and
+
+00:45:02.810 --> 00:45:04.600
+63% have Class 1.
+
+00:45:05.630 --> 00:45:10.190
+And if I think I printed the label
+
+00:45:10.190 --> 00:45:12.105
+names, yeah, so the label names.
+
+00:45:12.105 --> 00:45:14.750
+So 0 means malignant and one means
+
+00:45:14.750 --> 00:45:15.260
+benign.
+
+00:45:15.940 --> 00:45:20.190
+So in this sample, 37% are malignant
+
+00:45:20.190 --> 00:45:21.940
+and 63% are benign.
+
+00:45:24.410 --> 00:45:26.060
+Now I'm going to create a training and
+
+00:45:26.060 --> 00:45:27.160
+validation set.
+
+00:45:27.160 --> 00:45:29.410
+So I define the number of training
+
+00:45:29.410 --> 00:45:31.720
+samples 469.
+
+00:45:32.650 --> 00:45:35.845
+I use a random seed and that's because
+
+00:45:35.845 --> 00:45:38.360
+it might be that the training samples
+
+00:45:38.360 --> 00:45:40.141
+are stored in some structured way.
+
+00:45:40.141 --> 00:45:42.125
+Maybe they put all the examples with
+
+00:45:42.125 --> 00:45:44.260
+zero first, label zero first and then
+
+00:45:44.260 --> 00:45:45.280
+label one.
+
+00:45:45.280 --> 00:45:47.629
+Or maybe they were structured in some
+
+00:45:47.630 --> 00:45:49.910
+other way and I want it to be random,
+
+00:45:49.910 --> 00:45:51.800
+so randomness is not something you can
+
+00:45:51.800 --> 00:45:52.720
+leave to chance.
+
+00:45:52.720 --> 00:45:56.250
+You need to use some permutation to
+
+00:45:56.250 --> 00:45:58.450
+make sure that you get a random sample
+
+00:45:58.450 --> 00:45:59.040
+of the data.
+
+00:46:00.580 --> 00:46:03.319
+So I do a random permutation of the
+
+00:46:03.320 --> 00:46:05.840
+same length as the number of indices.
+
+00:46:05.840 --> 00:46:08.280
+I set a seed here because I just wanted
+
+00:46:08.280 --> 00:46:10.010
+this to be repeatable for the purpose
+
+00:46:10.010 --> 00:46:11.890
+of the class, and actually it's a good
+
+00:46:11.890 --> 00:46:14.310
+idea to set a seed anyway so that.
+
+00:46:16.450 --> 00:46:18.540
+Because takes out one source of
+
+00:46:18.540 --> 00:46:20.210
+variance for your debugging.
+
+00:46:21.980 --> 00:46:24.145
+So I split it into a training set.
+
+00:46:24.145 --> 00:46:25.770
+I took the first untrained.
+
+00:46:26.750 --> 00:46:29.290
+It's my X train and Y train and then I
+
+00:46:29.290 --> 00:46:32.420
+took all the rest as my X value, Y Val
+
+00:46:32.420 --> 00:46:34.410
+and by the 1st examples I mean the
+
+00:46:34.410 --> 00:46:36.060
+first ones that in this random
+
+00:46:36.060 --> 00:46:37.130
+permutation list.
+
+00:46:38.330 --> 00:46:41.580
+Now X train and Y train have.
+
+00:46:42.020 --> 00:46:47.790
+I have 469 examples so 469 by 30.
+
+00:46:48.680 --> 00:46:51.575
+And X value Y Val which is the second
+
+00:46:51.575 --> 00:46:53.310
+one has 100 examples.
+
+00:46:55.420 --> 00:46:58.375
+Sometimes the first thing I'll do is
+
+00:46:58.375 --> 00:47:01.360
+like a simple classifier just to see is
+
+00:47:01.360 --> 00:47:02.390
+this problem trivial.
+
+00:47:02.390 --> 00:47:04.125
+If I get like 0 error right away, then
+
+00:47:04.125 --> 00:47:06.780
+I can just like stop spend time on it.
+
+00:47:07.630 --> 00:47:10.909
+So I made a nearest neighbor
+
+00:47:10.910 --> 00:47:11.620
+classifier.
+
+00:47:11.620 --> 00:47:13.390
+So I have nearest neighbor.
+
+00:47:13.390 --> 00:47:15.600
+X train and Y train are fed in as well
+
+00:47:15.600 --> 00:47:16.340
+as X test.
+
+00:47:17.640 --> 00:47:21.470
+Pre initialize my predictions, so I do
+
+00:47:21.470 --> 00:47:23.560
+initialize it with zeros.
+
+00:47:23.560 --> 00:47:25.990
+For each test sample, I take the
+
+00:47:25.990 --> 00:47:27.540
+difference from the test sample and all
+
+00:47:27.540 --> 00:47:29.140
+the training samples.
+
+00:47:29.140 --> 00:47:30.940
+Under the hood, Numpy we'll do like
+
+00:47:30.940 --> 00:47:32.800
+broadcasting, which means it will copy
+
+00:47:32.800 --> 00:47:36.085
+this as necessary so that the X test
+
+00:47:36.085 --> 00:47:38.669
+will be a 1 by 30 and it will copy it
+
+00:47:38.669 --> 00:47:42.560
+so that it becomes a 469 by 30.
+
+00:47:43.860 --> 00:47:45.139
+Then I take the difference.
+
+00:47:45.140 --> 00:47:46.330
+It will be the difference of each
+
+00:47:46.330 --> 00:47:49.270
+element of the features and samples.
+
+00:47:49.960 --> 00:47:51.840
+Square it will be the square of each
+
+00:47:51.840 --> 00:47:54.660
+element and then I sum over axis one
+
+00:47:54.660 --> 00:47:55.920
+which is the 2nd axis.
+
+00:47:55.920 --> 00:47:57.210
+Zero is the first axis.
+
+00:47:58.110 --> 00:47:59.790
+So this will be the sum squared
+
+00:47:59.790 --> 00:48:00.830
+distance of the features.
+
+00:48:01.890 --> 00:48:02.770
+Euclidean distance.
+
+00:48:02.770 --> 00:48:04.390
+You would also take the square root,
+
+00:48:04.390 --> 00:48:05.857
+but I don't need to take the square
+
+00:48:05.857 --> 00:48:09.008
+root because the minimum of the square
+
+00:48:09.008 --> 00:48:11.104
+of a value is the same as the minimum
+
+00:48:11.104 --> 00:48:13.251
+of the square of the square of the
+
+00:48:13.251 --> 00:48:13.519
+value.
+
+00:48:13.680 --> 00:48:13.890
+Right.
+
+00:48:16.060 --> 00:48:19.780
+J is the argument distance, so I say J
+
+00:48:19.780 --> 00:48:21.495
+equals the argument and this distance.
+
+00:48:21.495 --> 00:48:23.130
+So this will give me the index that had
+
+00:48:23.130 --> 00:48:24.010
+the minimum distance.
+
+00:48:24.700 --> 00:48:26.420
+If I needed more than one, I could use
+
+00:48:26.420 --> 00:48:29.500
+argsort and then take like the first K
+
+00:48:29.500 --> 00:48:30.050
+indices.
+
+00:48:31.000 --> 00:48:33.386
+I assign the test to the training to
+
+00:48:33.386 --> 00:48:34.720
+the training sample that had the
+
+00:48:34.720 --> 00:48:36.500
+minimum distance and I returned it.
+
+00:48:36.500 --> 00:48:39.240
+So nearest neighbor is pretty simple.
+
+00:48:40.800 --> 00:48:43.980
+This like if you're a proficient coder,
+
+00:48:43.980 --> 00:48:46.410
+it's like a two minutes or whatever to
+
+00:48:46.410 --> 00:48:46.790
+decode it.
+
+00:48:48.690 --> 00:48:52.140
+Then I'm going to test it, so I then do
+
+00:48:52.140 --> 00:48:54.050
+the prediction on the validation set.
+
+00:48:54.050 --> 00:48:55.230
+Remember, nearest neighbor has no
+
+00:48:55.230 --> 00:48:56.870
+training, so I have no training code
+
+00:48:56.870 --> 00:48:58.105
+here, it's just really a prediction
+
+00:48:58.105 --> 00:48:58.430
+code.
+
+00:48:59.450 --> 00:49:02.320
+And now compute my average accuracy,
+
+00:49:02.320 --> 00:49:05.309
+which is why is the number of times the
+
+00:49:05.310 --> 00:49:08.500
+mean times that the validation label is
+
+00:49:08.500 --> 00:49:09.760
+equal to the prediction label.
+
+00:49:10.710 --> 00:49:12.230
+And then the error is 1 minus the
+
+00:49:12.230 --> 00:49:13.490
+accuracy, right?
+
+00:49:13.490 --> 00:49:14.040
+So let's run it.
+
+00:49:16.480 --> 00:49:21.550
+All right, so I got an error of 8% now.
+
+00:49:23.090 --> 00:49:24.060
+I could quit here.
+
+00:49:24.060 --> 00:49:26.840
+I could be like, OK, I'm done 8%, but I
+
+00:49:26.840 --> 00:49:28.150
+shouldn't really be satisfied with
+
+00:49:28.150 --> 00:49:29.080
+this, right?
+
+00:49:29.080 --> 00:49:32.400
+So the remember that in the study they
+
+00:49:32.400 --> 00:49:34.105
+said that doctors were reporting that
+
+00:49:34.105 --> 00:49:37.380
+they can get like 6% error, they had
+
+00:49:37.380 --> 00:49:38.810
+94% accuracy.
+
+00:49:39.530 --> 00:49:41.906
+And since I'm a machine learning
+
+00:49:41.906 --> 00:49:43.940
+machine learning engineer, I'm armed
+
+00:49:43.940 --> 00:49:44.800
+with data.
+
+00:49:44.800 --> 00:49:47.250
+I should be able to outperform a
+
+00:49:47.250 --> 00:49:49.190
+medical Doctor Who has years of
+
+00:49:49.190 --> 00:49:51.960
+experience on the same problem.
+
+00:49:54.860 --> 00:49:56.800
+Right, so all of his wits and
+
+00:49:56.800 --> 00:49:58.420
+experience is just bringing a knife to
+
+00:49:58.420 --> 00:49:59.300
+a gunfight.
+
+00:50:01.760 --> 00:50:02.410
+I'm just kidding.
+
+00:50:03.810 --> 00:50:05.670
+But seriously, like, I can probably do
+
+00:50:05.670 --> 00:50:06.130
+better, right?
+
+00:50:06.130 --> 00:50:07.190
+It's just my first attempt.
+
+00:50:07.900 --> 00:50:09.530
+So let's look at the data a little bit
+
+00:50:09.530 --> 00:50:11.440
+better, a little more in depth.
+
+00:50:12.340 --> 00:50:13.610
+So remember that one thing we noticed
+
+00:50:13.610 --> 00:50:15.145
+is that it looked like some feature
+
+00:50:15.145 --> 00:50:16.895
+values were a lot larger than other
+
+00:50:16.895 --> 00:50:18.540
+values, and nearest neighbor is not
+
+00:50:18.540 --> 00:50:19.716
+very robust to that.
+
+00:50:19.716 --> 00:50:22.830
+It might be like emphasizing the large
+
+00:50:22.830 --> 00:50:24.620
+values much more, which might not be
+
+00:50:24.620 --> 00:50:25.840
+the most important features.
+
+00:50:26.490 --> 00:50:28.390
+So here I have a print statement.
+
+00:50:28.390 --> 00:50:30.210
+The only thing fancy is that I use some
+
+00:50:30.210 --> 00:50:32.900
+spacing thing to make it like evenly
+
+00:50:32.900 --> 00:50:33.420
+spaced.
+
+00:50:34.040 --> 00:50:35.828
+And I'm printing the means of the
+
+00:50:35.828 --> 00:50:37.330
+features, the standard deviations of
+
+00:50:37.330 --> 00:50:39.710
+the features, the means of the features
+
+00:50:39.710 --> 00:50:42.413
+where y = 1 zero, and the means of the
+
+00:50:42.413 --> 00:50:43.599
+features were y = 1.
+
+00:50:44.340 --> 00:50:46.250
+So that can kind of tell me a couple
+
+00:50:46.250 --> 00:50:46.580
+things.
+
+00:50:46.580 --> 00:50:48.100
+One is like what is the scale that
+
+00:50:48.100 --> 00:50:49.530
+features by looking at the steering
+
+00:50:49.530 --> 00:50:50.310
+deviation and the mean.
+
+00:50:51.170 --> 00:50:54.050
+Also, are the features like predictive
+
+00:50:54.050 --> 00:50:54.338
+or not?
+
+00:50:54.338 --> 00:50:56.315
+If I have a good spread of the means of
+
+00:50:56.315 --> 00:50:59.095
+the two features, I mean of the of y =
+
+00:50:59.095 --> 00:51:01.749
+0 and y = 1, then it's predictive.
+
+00:51:01.750 --> 00:51:03.600
+But if I have a small spread compared
+
+00:51:03.600 --> 00:51:05.530
+to the steering deviation then it's not
+
+00:51:05.530 --> 00:51:06.240
+very predictive.
+
+00:51:07.350 --> 00:51:10.150
+Right, so for example, this feature
+
+00:51:10.150 --> 00:51:11.824
+here means smoothness.
+
+00:51:11.824 --> 00:51:15.584
+Mean is 1, standard deviation is 01,
+
+00:51:15.584 --> 00:51:19.947
+the mean of zero is 1, the mean of one
+
+00:51:19.947 --> 00:51:20.690
+is 09.
+
+00:51:20.690 --> 00:51:22.770
+And you know with three digits there
+
+00:51:22.770 --> 00:51:24.305
+might be look even closer.
+
+00:51:24.305 --> 00:51:26.092
+So obviously smoothness means
+
+00:51:26.092 --> 00:51:28.430
+smoothness is not a very good feature,
+
+00:51:28.430 --> 00:51:31.340
+it's not very predictive of the label.
+
+00:51:32.120 --> 00:51:35.050
+Where if I look at something like.
+
+00:51:35.140 --> 00:51:35.930
+
+
+00:51:37.780 --> 00:51:40.240
+If I look at something like this, just
+
+00:51:40.240 --> 00:51:42.125
+take the first one, the difference of
+
+00:51:42.125 --> 00:51:43.730
+the means is more than one steering
+
+00:51:43.730 --> 00:51:47.620
+deviation of the feature, and so mean
+
+00:51:47.620 --> 00:51:49.420
+radius is like fairly predictive.
+
+00:51:51.210 --> 00:51:53.395
+But the thing my take home from this is
+
+00:51:53.395 --> 00:51:56.480
+that some features have means and
+
+00:51:56.480 --> 00:51:58.950
+standard deviations that are sub one
+
+00:51:58.950 --> 00:51:59.730
+less than one.
+
+00:52:00.400 --> 00:52:03.340
+And others are in the hundreds, so not
+
+00:52:03.340 --> 00:52:04.540
+that's not good.
+
+00:52:04.540 --> 00:52:05.700
+So I want to do some kind of
+
+00:52:05.700 --> 00:52:06.590
+normalization.
+
+00:52:09.520 --> 00:52:11.857
+So I'm going to normalize by the mean
+
+00:52:11.857 --> 00:52:13.820
+and steering deviation, which means
+
+00:52:13.820 --> 00:52:16.537
+that I subtract the mean and divide by
+
+00:52:16.537 --> 00:52:17.880
+the standard deviation.
+
+00:52:17.880 --> 00:52:20.040
+Importantly, you want to compute the
+
+00:52:20.040 --> 00:52:22.138
+mean and the standard deviation once on
+
+00:52:22.138 --> 00:52:23.880
+the training set and then apply the
+
+00:52:23.880 --> 00:52:25.531
+same normalization to the training and
+
+00:52:25.531 --> 00:52:26.566
+the validation set.
+
+00:52:26.566 --> 00:52:28.580
+So you can't provide different
+
+00:52:28.580 --> 00:52:31.620
+normalizations to different sets, or
+
+00:52:31.620 --> 00:52:33.080
+else you're going to your features will
+
+00:52:33.080 --> 00:52:35.030
+not be comparable and you'll it's a
+
+00:52:35.030 --> 00:52:35.640
+bug.
+
+00:52:35.640 --> 00:52:37.360
+It's so it won't work.
+
+00:52:38.650 --> 00:52:40.240
+OK, so I compute the mean compute
+
+00:52:40.240 --> 00:52:41.720
+steering, aviation take the difference,
+
+00:52:41.720 --> 00:52:43.160
+divide by zero and aviation do the same
+
+00:52:43.160 --> 00:52:44.220
+thing on my valve set.
+
+00:52:44.990 --> 00:52:46.430
+And there's nothing to print here, but
+
+00:52:46.430 --> 00:52:47.430
+I need to run it.
+
+00:52:47.430 --> 00:52:48.000
+Whoops.
+
+00:52:51.250 --> 00:52:52.380
+All right, so now I'm going to repeat
+
+00:52:52.380 --> 00:52:53.150
+my nearest neighbor.
+
+00:52:53.920 --> 00:52:54.866
+OK, 4%.
+
+00:52:54.866 --> 00:52:57.336
+So there was a lot better before I got
+
+00:52:57.336 --> 00:53:01.206
+12%, I think 8%, yeah, so before I got
+
+00:53:01.206 --> 00:53:01.500
+8%.
+
+00:53:02.130 --> 00:53:03.200
+Now it's 4%.
+
+00:53:04.050 --> 00:53:04.720
+So that's good.
+
+00:53:05.380 --> 00:53:07.040
+But I still don't know if like nearest
+
+00:53:07.040 --> 00:53:07.850
+neighbor is the best.
+
+00:53:07.850 --> 00:53:09.240
+So I shouldn't just try like 1
+
+00:53:09.240 --> 00:53:11.140
+algorithm and then assume that's the
+
+00:53:11.140 --> 00:53:11.910
+best I should get.
+
+00:53:11.910 --> 00:53:14.620
+I should try other algorithms and try
+
+00:53:14.620 --> 00:53:16.280
+to see if I can improve things further.
+
+00:53:17.510 --> 00:53:18.110
+Question.
+
+00:53:24.670 --> 00:53:25.550
+So the yes.
+
+00:53:25.550 --> 00:53:26.940
+So the question is why did the error
+
+00:53:26.940 --> 00:53:28.170
+rate get better?
+
+00:53:28.170 --> 00:53:30.950
+And I think it's because under the
+
+00:53:30.950 --> 00:53:33.920
+original features, these features like
+
+00:53:33.920 --> 00:53:38.000
+mean area that have a huge range are
+
+00:53:38.000 --> 00:53:40.690
+going to dominate the distances.
+
+00:53:40.690 --> 00:53:42.420
+All of these features concavity,
+
+00:53:42.420 --> 00:53:45.470
+compactness, concave point, symmetry at
+
+00:53:45.470 --> 00:53:48.730
+mostly we'll add a distance of .1 or
+
+00:53:48.730 --> 00:53:51.010
+something like that where this mean
+
+00:53:51.010 --> 00:53:53.887
+area is going to tend to add distances
+
+00:53:53.887 --> 00:53:54.430
+of.
+
+00:53:54.490 --> 00:53:54.960
+Hundreds.
+
+00:53:55.580 --> 00:53:58.620
+And so if I don't normalize it, that
+
+00:53:58.620 --> 00:54:00.100
+means that essentially I'm seeing the
+
+00:54:00.100 --> 00:54:01.728
+bigger the feature values, the more
+
+00:54:01.728 --> 00:54:02.990
+important they are, or the more
+
+00:54:02.990 --> 00:54:04.307
+variants and the feature values, the
+
+00:54:04.307 --> 00:54:05.049
+more important they are.
+
+00:54:05.670 --> 00:54:07.340
+And that's not based on any like
+
+00:54:07.340 --> 00:54:08.480
+knowledge of the problem.
+
+00:54:08.480 --> 00:54:09.970
+That was just because that's how the
+
+00:54:09.970 --> 00:54:10.720
+data turned out.
+
+00:54:10.720 --> 00:54:12.560
+And so I don't really trust that kind
+
+00:54:12.560 --> 00:54:14.210
+of decision.
+
+00:54:16.270 --> 00:54:16.650
+Go ahead.
+
+00:54:18.070 --> 00:54:18.350
+OK.
+
+00:54:19.290 --> 00:54:20.240
+You had a question?
+
+00:54:29.700 --> 00:54:32.490
+So I compute the mean and this is
+
+00:54:32.490 --> 00:54:34.615
+computing the mean over the first axis.
+
+00:54:34.615 --> 00:54:36.640
+So it means that for every feature
+
+00:54:36.640 --> 00:54:38.700
+value I compute the mean over all the
+
+00:54:38.700 --> 00:54:39.320
+examples.
+
+00:54:40.110 --> 00:54:42.680
+Of the training features XTR.
+
+00:54:43.450 --> 00:54:45.560
+So I computed the mean, the expectation
+
+00:54:45.560 --> 00:54:49.370
+or the arithmetic average of each
+
+00:54:49.370 --> 00:54:50.010
+feature.
+
+00:54:50.990 --> 00:54:53.330
+Over all the training samples, and then
+
+00:54:53.330 --> 00:54:56.500
+I compute this stern deviation of each
+
+00:54:56.500 --> 00:54:58.140
+feature over all the examples.
+
+00:54:58.140 --> 00:54:58.960
+So that's the.
+
+00:55:00.570 --> 00:55:00.940
+Right.
+
+00:55:03.150 --> 00:55:07.200
+So remember that X train has this shape
+
+00:55:07.200 --> 00:55:11.920
+469 by 30, so if I go down the first
+
+00:55:11.920 --> 00:55:14.480
+axis then I'm changing the example.
+
+00:55:14.480 --> 00:55:17.330
+So 0123 et cetera are different
+
+00:55:17.330 --> 00:55:18.100
+examples.
+
+00:55:18.100 --> 00:55:20.363
+And if I go down the second axis then
+
+00:55:20.363 --> 00:55:22.470
+I'm going into different feature
+
+00:55:22.470 --> 00:55:22.960
+columns.
+
+00:55:23.680 --> 00:55:25.760
+And so I want to take the mean over the
+
+00:55:25.760 --> 00:55:27.524
+examples for each feature.
+
+00:55:27.524 --> 00:55:30.113
+And so I say access equals zero for the
+
+00:55:30.113 --> 00:55:31.870
+mean to take the mean over samples.
+
+00:55:31.870 --> 00:55:34.774
+Otherwise I'll end up with a 1 by 30
+
+00:55:34.774 --> 00:55:38.480
+where I mean with a 469 by 1 where I've
+
+00:55:38.480 --> 00:55:39.850
+taken the average feature for each
+
+00:55:39.850 --> 00:55:40.380
+example.
+
+00:55:46.980 --> 00:55:49.390
+So if I say X is equals zero, it means
+
+00:55:49.390 --> 00:55:51.000
+it will take the mean over all the
+
+00:55:51.000 --> 00:55:52.400
+remaining dimensions.
+
+00:55:52.750 --> 00:55:53.320
+And.
+
+00:55:54.040 --> 00:55:55.590
+Averaging over the first dimension.
+
+00:56:02.380 --> 00:56:04.870
+So then this will be a 30 dimensional
+
+00:56:04.870 --> 00:56:06.080
+vector X MU.
+
+00:56:07.050 --> 00:56:11.230
+It will be the mean of each feature
+
+00:56:11.230 --> 00:56:12.060
+over the samples.
+
+00:56:12.930 --> 00:56:14.540
+And this is also a 30 dimensional
+
+00:56:14.540 --> 00:56:15.880
+vector standard deviation.
+
+00:56:17.170 --> 00:56:19.300
+And then I'm subtracting off the mean
+
+00:56:19.300 --> 00:56:21.185
+and dividing by the standard deviation.
+
+00:56:21.185 --> 00:56:24.150
+And Numpy is nice that even though X
+
+00:56:24.150 --> 00:56:28.355
+train is 469 by 30 and X mu is 30, is
+
+00:56:28.355 --> 00:56:28.840
+30.
+
+00:56:29.030 --> 00:56:32.370
+Numpy is smart, and it says you're
+
+00:56:32.370 --> 00:56:35.390
+doing a 469 by 30 -, A thirty.
+
+00:56:35.390 --> 00:56:39.060
+So I need to copy that 3469 times to
+
+00:56:39.060 --> 00:56:39.810
+take the difference.
+
+00:56:41.550 --> 00:56:42.790
+And same for the divide.
+
+00:56:42.790 --> 00:56:44.990
+This is an element wise divide so it's
+
+00:56:44.990 --> 00:56:45.800
+important to know.
+
+00:56:46.500 --> 00:56:48.340
+There you can have like a matrix
+
+00:56:48.340 --> 00:56:50.710
+multiplication or matrix inverse or you
+
+00:56:50.710 --> 00:56:53.006
+can have an element wise multiplication
+
+00:56:53.006 --> 00:56:53.759
+or inverse.
+
+00:56:54.570 --> 00:56:57.070
+Usually like the simple operators are
+
+00:56:57.070 --> 00:56:58.320
+element wise in Python.
+
+00:56:58.970 --> 00:57:01.485
+So this means that for every element of
+
+00:57:01.485 --> 00:57:04.796
+this matrix, I'm going to divide by the
+
+00:57:04.796 --> 00:57:06.940
+standard deviation the corresponding
+
+00:57:06.940 --> 00:57:07.680
+standard deviation.
+
+00:57:09.390 --> 00:57:10.690
+And then I do the same thing for the
+
+00:57:10.690 --> 00:57:11.640
+validation set.
+
+00:57:11.640 --> 00:57:12.960
+And what was your question?
+
+00:57:22.780 --> 00:57:23.490
+Yeah.
+
+00:57:32.420 --> 00:57:37.550
+So L1 used L1 regularization for linear
+
+00:57:37.550 --> 00:57:40.183
+logistic regression and that will that
+
+00:57:40.183 --> 00:57:43.110
+will like put that will like select
+
+00:57:43.110 --> 00:57:44.030
+features for.
+
+00:57:44.030 --> 00:57:46.110
+You could also use L1 nearest neighbor
+
+00:57:46.110 --> 00:57:47.720
+distance which would be less sensitive
+
+00:57:47.720 --> 00:57:48.110
+to this.
+
+00:57:49.700 --> 00:57:52.150
+But with this range of like .1 versus
+
+00:57:52.150 --> 00:57:54.590
+like 500, it will still be that the
+
+00:57:54.590 --> 00:57:55.820
+larger features will dominate.
+
+00:57:57.180 --> 00:57:57.430
+Yep.
+
+00:57:59.850 --> 00:58:03.560
+All right, so after I normalized, now
+
+00:58:03.560 --> 00:58:06.550
+note that I'm passing in X train N,
+
+00:58:06.550 --> 00:58:08.670
+which is for stands for norm for me.
+
+00:58:09.450 --> 00:58:10.380
+In X Val north.
+
+00:58:10.380 --> 00:58:12.240
+Now I get lower error.
+
+00:58:12.830 --> 00:58:14.220
+Alright, so now let's try a different
+
+00:58:14.220 --> 00:58:14.885
+classifier.
+
+00:58:14.885 --> 00:58:17.340
+Let's do Naive Bayes, and I'm going to
+
+00:58:17.340 --> 00:58:21.055
+assume that each feature value given
+
+00:58:21.055 --> 00:58:23.399
+the class is a Gaussian.
+
+00:58:23.399 --> 00:58:27.480
+So given that y = 0, Y equals one.
+
+00:58:27.480 --> 00:58:30.232
+Then my probability of the feature is a
+
+00:58:30.232 --> 00:58:31.770
+Gaussian with some mean and some
+
+00:58:31.770 --> 00:58:32.680
+standard deviation.
+
+00:58:33.410 --> 00:58:35.640
+Now for nibs I need a training and
+
+00:58:35.640 --> 00:58:36.610
+prediction function.
+
+00:58:37.590 --> 00:58:40.560
+So I'm going to pass in my training
+
+00:58:40.560 --> 00:58:41.430
+data X&Y.
+
+00:58:42.300 --> 00:58:44.760
+App says some like I'm going to use
+
+00:58:44.760 --> 00:58:46.864
+that as like a prior to add it to the
+
+00:58:46.864 --> 00:58:48.390
+variance so that even if my feature
+
+00:58:48.390 --> 00:58:50.340
+value has no variance in training, I'm
+
+00:58:50.340 --> 00:58:52.175
+going to have some minimal variance so
+
+00:58:52.175 --> 00:58:54.450
+that I don't have like a divide by zero
+
+00:58:54.450 --> 00:58:56.610
+essentially where I'm not like over
+
+00:58:56.610 --> 00:59:00.600
+relying on the variance that I observe.
+
+00:59:02.080 --> 00:59:03.960
+All right, so initialize my MU and my
+
+00:59:03.960 --> 00:59:06.988
+Sigma to be the number of features by
+
+00:59:06.988 --> 00:59:08.880
+two, and the two is because there's two
+
+00:59:08.880 --> 00:59:10.360
+classes, so I'm going to estimate this
+
+00:59:10.360 --> 00:59:10.960
+for each class.
+
+00:59:12.250 --> 00:59:14.988
+I compute my probability of the label
+
+00:59:14.988 --> 00:59:17.870
+to be just the mean of y = 0.
+
+00:59:17.870 --> 00:59:19.180
+So this is a probability that the label
+
+00:59:19.180 --> 00:59:20.000
+is equal to 0.
+
+00:59:21.530 --> 00:59:23.820
+And then for each feature so range,
+
+00:59:23.820 --> 00:59:25.650
+you'll be 0 to the number of features.
+
+00:59:26.510 --> 00:59:30.100
+I compute the mean over the cases where
+
+00:59:30.100 --> 00:59:31.330
+the label equals 0.
+
+00:59:32.660 --> 00:59:34.770
+And the mean over the case where the
+
+00:59:34.770 --> 00:59:36.450
+labels equals one.
+
+00:59:36.450 --> 00:59:37.990
+And I could do this as like a
+
+00:59:37.990 --> 00:59:40.260
+vectorized operation like over an axis,
+
+00:59:40.260 --> 00:59:41.970
+but for clarity I did it this way.
+
+00:59:42.700 --> 00:59:43.350
+With the four loop.
+
+00:59:45.040 --> 00:59:47.990
+Compute their stern deviation where y =
+
+00:59:47.990 --> 00:59:50.827
+0 and the stereo deviation where y = 1
+
+00:59:50.827 --> 00:59:52.520
+and again like this epsilon will be
+
+00:59:52.520 --> 00:59:55.600
+some small number that will just like
+
+00:59:55.600 --> 00:59:57.260
+make sure that my variance isn't zero.
+
+00:59:57.260 --> 00:59:59.810
+Or like says that like I think there
+
+00:59:59.810 --> 01:00:01.030
+might be a little bit more variance
+
+01:00:01.030 --> 01:00:01.740
+than I observe.
+
+01:00:03.080 --> 01:00:03.600
+And.
+
+01:00:04.420 --> 01:00:05.090
+That's it.
+
+01:00:05.090 --> 01:00:07.570
+So then I'll return my mean steering
+
+01:00:07.570 --> 01:00:09.150
+deviation and the probability of the
+
+01:00:09.150 --> 01:00:10.010
+label question.
+
+01:00:12.500 --> 01:00:12.760
+Sorry.
+
+01:00:21.950 --> 01:00:24.952
+Because X shape one, so X shape zero is
+
+01:00:24.952 --> 01:00:26.505
+the number of samples and X shape one
+
+01:00:26.505 --> 01:00:27.840
+is the number of features.
+
+01:00:27.840 --> 01:00:30.810
+And there's a mean for every mean
+
+01:00:30.810 --> 01:00:33.273
+estimate for every feature, not for
+
+01:00:33.273 --> 01:00:34.050
+every sample.
+
+01:00:35.780 --> 01:00:37.840
+So this will be a number of features by
+
+01:00:37.840 --> 01:00:38.230
+two.
+
+01:00:43.510 --> 01:00:44.720
+Alright, and then I'm going to do
+
+01:00:44.720 --> 01:00:45.380
+prediction.
+
+01:00:45.380 --> 01:00:48.200
+So now I'll write my prediction code.
+
+01:00:48.200 --> 01:00:50.080
+I now need to pass in the thing that I
+
+01:00:50.080 --> 01:00:50.930
+want to predict for.
+
+01:00:51.620 --> 01:00:53.720
+That means in the steering deviations
+
+01:00:53.720 --> 01:00:55.840
+and the P0 that I estimated from my
+
+01:00:55.840 --> 01:00:56.670
+training function.
+
+01:00:57.640 --> 01:01:00.450
+And I'm going to compute the log
+
+01:01:00.450 --> 01:01:04.460
+probability of X given of X&Y, not the
+
+01:01:04.460 --> 01:01:05.390
+probability of X&Y.
+
+01:01:06.130 --> 01:01:07.889
+And the reason for that is that if I
+
+01:01:07.890 --> 01:01:09.960
+multiply a lot of small probabilities
+
+01:01:09.960 --> 01:01:11.706
+together then I get a really small
+
+01:01:11.706 --> 01:01:11.972
+number.
+
+01:01:11.972 --> 01:01:13.955
+And if I have a lot of features like
+
+01:01:13.955 --> 01:01:16.418
+you do for MNIST for example, then that
+
+01:01:16.418 --> 01:01:18.470
+small number will eventually become
+
+01:01:18.470 --> 01:01:21.820
+zero and like in terms of floating
+
+01:01:21.820 --> 01:01:23.889
+point operations or it will become like
+
+01:01:23.890 --> 01:01:26.470
+unwieldly small.
+
+01:01:26.470 --> 01:01:28.160
+So you want to compute the log
+
+01:01:28.160 --> 01:01:29.460
+probability, not the probability.
+
+01:01:30.460 --> 01:01:33.100
+And minimizing the OR maximizing the
+
+01:01:33.100 --> 01:01:34.602
+log probability is the same as
+
+01:01:34.602 --> 01:01:35.660
+maximizing the probability.
+
+01:01:36.860 --> 01:01:38.560
+So for each feature.
+
+01:01:39.350 --> 01:01:43.388
+I add the log probability of the
+
+01:01:43.388 --> 01:01:46.726
+feature given y = 0 or the feature
+
+01:01:46.726 --> 01:01:47.739
+given y = 1.
+
+01:01:48.960 --> 01:01:53.265
+And this is this is the log of the
+
+01:01:53.265 --> 01:01:54.000
+Gaussian function.
+
+01:01:54.000 --> 01:01:56.340
+Just ignoring the constant multiplier
+
+01:01:56.340 --> 01:01:58.540
+in the Gaussian function because that
+
+01:01:58.540 --> 01:02:01.300
+won't be any different whether y = 0
+
+01:02:01.300 --> 01:02:03.059
+one there one over square root, square
+
+01:02:03.059 --> 01:02:04.310
+root 2π is Sigma.
+
+01:02:06.200 --> 01:02:12.750
+So this minus mean minus X ^2 divided
+
+01:02:12.750 --> 01:02:14.140
+by Sigma squared.
+
+01:02:14.140 --> 01:02:15.930
+That's like in the exponent of the
+
+01:02:15.930 --> 01:02:16.490
+Gaussian.
+
+01:02:16.490 --> 01:02:18.530
+So when I take the log of it, I've just
+
+01:02:18.530 --> 01:02:19.860
+got that exponent there.
+
+01:02:20.820 --> 01:02:25.040
+So I'm adding that to my score of log
+
+01:02:25.040 --> 01:02:29.630
+PX y = 0 and log pxy equals one.
+
+01:02:32.780 --> 01:02:35.721
+Then I'm adding my prior so to my 0
+
+01:02:35.721 --> 01:02:38.204
+score I add the log probability of y =
+
+01:02:38.204 --> 01:02:38.479
+0.
+
+01:02:38.480 --> 01:02:41.440
+Into my one score, I add the log
+
+01:02:41.440 --> 01:02:44.230
+probability of y = 1, which is just one
+
+01:02:44.230 --> 01:02:45.729
+minus the probability of y = 0.
+
+01:02:46.780 --> 01:02:48.540
+And then I take the argmax to get my
+
+01:02:48.540 --> 01:02:50.899
+prediction and I'm taking the argmax
+
+01:02:50.900 --> 01:02:53.910
+over axis one because that was my label
+
+01:02:53.910 --> 01:02:54.380
+axis.
+
+01:02:55.170 --> 01:02:55.720
+So.
+
+01:02:56.860 --> 01:02:58.875
+So here the first axis is the number of
+
+01:02:58.875 --> 01:03:00.915
+test samples, the second axis is the
+
+01:03:00.915 --> 01:03:01.860
+number of labels.
+
+01:03:01.860 --> 01:03:04.470
+I take the argmax over the labels to
+
+01:03:04.470 --> 01:03:07.820
+get my maximum my most likely
+
+01:03:07.820 --> 01:03:09.510
+prediction for every test sample.
+
+01:03:13.750 --> 01:03:15.930
+And then finally the code to call this
+
+01:03:15.930 --> 01:03:18.334
+so I call Gaussian train NI Bayes
+
+01:03:18.334 --> 01:03:21.650
+Gaussian train and I use this as my as
+
+01:03:21.650 --> 01:03:23.800
+like my prior on the variance my
+
+01:03:23.800 --> 01:03:24.290
+epsilon.
+
+01:03:25.400 --> 01:03:29.310
+And then I'd call predict and I pass in
+
+01:03:29.310 --> 01:03:30.240
+the validation data.
+
+01:03:31.200 --> 01:03:32.510
+And then I measure my error.
+
+01:03:33.400 --> 01:03:35.130
+And I'm going to do this.
+
+01:03:35.130 --> 01:03:36.970
+So here's a question.
+
+01:03:36.970 --> 01:03:39.338
+Do you think that here I'm doing it on
+
+01:03:39.338 --> 01:03:41.219
+the non normalized features and here
+
+01:03:41.219 --> 01:03:43.182
+I'm doing it on the normalized
+
+01:03:43.182 --> 01:03:43.509
+features?
+
+01:03:44.380 --> 01:03:47.160
+Do you think that those results will be
+
+01:03:47.160 --> 01:03:48.800
+different or the same?
+
+01:03:48.800 --> 01:03:50.510
+So how many people think that these
+
+01:03:50.510 --> 01:03:52.260
+will be the same if I?
+
+01:03:52.960 --> 01:03:56.930
+Do not have bays on rescaled and mean
+
+01:03:56.930 --> 01:04:00.130
+normalized features versus normalized.
+
+01:04:01.370 --> 01:04:02.790
+So how many people think it will be the
+
+01:04:02.790 --> 01:04:03.640
+same result?
+
+01:04:05.470 --> 01:04:07.060
+OK, how many people think it will be a
+
+01:04:07.060 --> 01:04:07.610
+different result?
+
+01:04:10.570 --> 01:04:12.250
+About 5050.
+
+01:04:12.250 --> 01:04:13.510
+Alright, so let's see.
+
+01:04:13.510 --> 01:04:14.820
+Let's see how it turns out.
+
+01:04:18.860 --> 01:04:20.980
+So it's exactly the same, and it's
+
+01:04:20.980 --> 01:04:22.855
+actually guaranteed to be exactly the
+
+01:04:22.855 --> 01:04:25.350
+same in this case because.
+
+01:04:27.190 --> 01:04:28.790
+Because if I scale or shift the
+
+01:04:28.790 --> 01:04:30.910
+features, all it's going to do is
+
+01:04:30.910 --> 01:04:32.320
+change my mean invariance.
+
+01:04:32.960 --> 01:04:34.420
+But it will change it the same way for
+
+01:04:34.420 --> 01:04:36.500
+each class, so the probability of the
+
+01:04:36.500 --> 01:04:38.450
+features given the data given the label
+
+01:04:38.450 --> 01:04:40.540
+doesn't change at all when I shift them
+
+01:04:40.540 --> 01:04:42.050
+or scale them according to a Gaussian
+
+01:04:42.050 --> 01:04:42.990
+distribution.
+
+01:04:42.990 --> 01:04:45.080
+So that's why the feature normalization
+
+01:04:45.080 --> 01:04:46.790
+isn't really necessary here for Naive
+
+01:04:46.790 --> 01:04:47.060
+Bayes.
+
+01:04:48.890 --> 01:04:50.605
+But it wasn't didn't do great.
+
+01:04:50.605 --> 01:04:51.790
+It doesn't usually.
+
+01:04:51.790 --> 01:04:52.870
+So not a big surprise.
+
+01:04:54.240 --> 01:04:56.697
+So then finally, let's do.
+
+01:04:56.697 --> 01:04:58.500
+Let's put in a logistic there.
+
+01:04:58.500 --> 01:05:00.100
+Let's do linear and logistic
+
+01:05:00.100 --> 01:05:03.060
+regression, and I'm going to use the
+
+01:05:03.060 --> 01:05:03.770
+model here.
+
+01:05:04.510 --> 01:05:06.700
+So C = 1 is the default that's Lambda
+
+01:05:06.700 --> 01:05:07.650
+equals one.
+
+01:05:07.650 --> 01:05:09.410
+I'll give it plenty of iterations, just
+
+01:05:09.410 --> 01:05:10.750
+make sure it can converge.
+
+01:05:10.750 --> 01:05:12.350
+I fit it on the training data.
+
+01:05:13.230 --> 01:05:15.310
+Test it on the validation data.
+
+01:05:15.310 --> 01:05:17.270
+And here I'm going to compare for if I
+
+01:05:17.270 --> 01:05:19.230
+don't normalize versus I normalize.
+
+01:05:23.690 --> 01:05:27.037
+And so in this case I got 3% error when
+
+01:05:27.037 --> 01:05:29.907
+I didn't normalize and I got 0% error
+
+01:05:29.907 --> 01:05:31.350
+when I normalized.
+
+01:05:33.670 --> 01:05:34.990
+So the normalization.
+
+01:05:34.990 --> 01:05:36.470
+The reason it makes a difference in
+
+01:05:36.470 --> 01:05:39.070
+this linear model is that I have some
+
+01:05:39.070 --> 01:05:40.100
+regularization weight.
+
+01:05:40.770 --> 01:05:43.420
+So if I set this to something really
+
+01:05:43.420 --> 01:05:46.780
+big, SK learn is a little awkward and
+
+01:05:46.780 --> 01:05:48.620
+that C is the inverse of Lambda.
+
+01:05:48.620 --> 01:05:50.970
+So the higher this value is, the less
+
+01:05:50.970 --> 01:05:51.970
+the regularization.
+
+01:05:58.010 --> 01:06:00.710
+I thought they would do something, but
+
+01:06:00.710 --> 01:06:01.240
+it didn't.
+
+01:06:03.440 --> 01:06:05.290
+That's not going to make a difference.
+
+01:06:06.730 --> 01:06:07.790
+That's interesting actually.
+
+01:06:07.790 --> 01:06:08.970
+I don't know why.
+
+01:06:09.730 --> 01:06:11.180
+Maybe I maybe I got.
+
+01:06:11.180 --> 01:06:13.510
+Let's see, let's make it really small
+
+01:06:13.510 --> 01:06:13.980
+instead.
+
+01:06:24.460 --> 01:06:24.920
+What's what?
+
+01:06:29.290 --> 01:06:32.130
+So that definitely changed things, but
+
+01:06:32.130 --> 01:06:33.620
+it made the normalization worse.
+
+01:06:33.620 --> 01:06:34.500
+That's interesting.
+
+01:06:34.500 --> 01:06:36.420
+OK, I cannot explain that off the dot
+
+01:06:36.420 --> 01:06:37.200
+my head.
+
+01:06:38.070 --> 01:06:41.200
+But another thing is that if I do 0.
+
+01:06:42.740 --> 01:06:44.095
+Wait, actually zero.
+
+01:06:44.095 --> 01:06:46.425
+I don't remember again if which way?
+
+01:06:46.425 --> 01:06:47.710
+I have to, yeah.
+
+01:06:48.470 --> 01:06:48.990
+So.
+
+01:06:50.650 --> 01:06:52.340
+You need like you need some
+
+01:06:52.340 --> 01:06:53.280
+regularization.
+
+01:06:54.220 --> 01:06:55.780
+Or else you get errors like that.
+
+01:06:58.220 --> 01:07:01.460
+They're not regularizing is not info.
+
+01:07:02.560 --> 01:07:05.650
+Not regularizing is usually not an
+
+01:07:05.650 --> 01:07:05.980
+option.
+
+01:07:05.980 --> 01:07:07.070
+OK, never mind, all right.
+
+01:07:08.140 --> 01:07:10.723
+Yeah, you guys can play with it if you
+
+01:07:10.723 --> 01:07:10.859
+want.
+
+01:07:10.860 --> 01:07:11.323
+I'm going to.
+
+01:07:11.323 --> 01:07:12.910
+I just, I don't want to get stuck there
+
+01:07:12.910 --> 01:07:15.340
+as getting too much into the weeds.
+
+01:07:16.530 --> 01:07:20.235
+The normalization helped in the case of
+
+01:07:20.235 --> 01:07:22.370
+the default regularization.
+
+01:07:24.010 --> 01:07:27.120
+I can also plot a.
+
+01:07:27.790 --> 01:07:29.590
+I can also do like other ways of
+
+01:07:29.590 --> 01:07:31.360
+looking at the data.
+
+01:07:31.360 --> 01:07:32.550
+Let's look at.
+
+01:07:32.550 --> 01:07:34.390
+I'm going to change this since it was
+
+01:07:34.390 --> 01:07:35.520
+kind of boring.
+
+01:07:37.500 --> 01:07:38.410
+Let me just.
+
+01:07:38.500 --> 01:07:39.190
+
+
+01:07:41.150 --> 01:07:41.510
+Whoops.
+
+01:07:42.630 --> 01:07:44.430
+I don't it's not very interesting to
+
+01:07:44.430 --> 01:07:46.340
+look at an Roc curve if you get perfect
+
+01:07:46.340 --> 01:07:46.910
+prediction.
+
+01:07:48.670 --> 01:07:50.290
+So let me just change this a little
+
+01:07:50.290 --> 01:07:50.640
+bit.
+
+01:07:52.040 --> 01:07:54.870
+So I'm going to look at the one where I
+
+01:07:54.870 --> 01:07:56.380
+did not perfect prediction.
+
+01:07:57.840 --> 01:07:58.650
+
+
+01:08:00.300 --> 01:08:00.830
+Mexican.
+
+01:08:03.700 --> 01:08:07.390
+Right, so this arc curve shows me given
+
+01:08:07.390 --> 01:08:09.320
+if I choose different thresholds on my
+
+01:08:09.320 --> 01:08:10.000
+confidence.
+
+01:08:10.870 --> 01:08:13.535
+By default, you choose a confidence at
+
+01:08:13.535 --> 01:08:14.050
+5:00.
+
+01:08:14.050 --> 01:08:15.810
+If probability is greater than five,
+
+01:08:15.810 --> 01:08:17.810
+then you assign it to the class that
+
+01:08:17.810 --> 01:08:19.069
+had that greater probability.
+
+01:08:19.700 --> 01:08:21.440
+But you can say for example if the
+
+01:08:21.440 --> 01:08:23.820
+probability is greater than .3 then I'm
+
+01:08:23.820 --> 01:08:27.030
+going to say it's like malignant and
+
+01:08:27.030 --> 01:08:28.150
+otherwise it's benign.
+
+01:08:28.150 --> 01:08:29.740
+So you can choose different thresholds.
+
+01:08:30.450 --> 01:08:31.990
+Especially if there's a different
+
+01:08:31.990 --> 01:08:33.440
+consequence to getting either one
+
+01:08:33.440 --> 01:08:36.100
+wrong, like which there is for
+
+01:08:36.100 --> 01:08:37.260
+malignant versus benign.
+
+01:08:38.080 --> 01:08:40.530
+So you can look at this arc curve which
+
+01:08:40.530 --> 01:08:42.260
+shows you the true positive rate and
+
+01:08:42.260 --> 01:08:43.990
+the false positive rate for different
+
+01:08:43.990 --> 01:08:44.700
+thresholds.
+
+01:08:45.460 --> 01:08:48.710
+So I can choose a value such that L
+
+01:08:48.710 --> 01:08:50.170
+never have a.
+
+01:08:50.940 --> 01:08:52.910
+Where here I define true positive as y
+
+01:08:52.910 --> 01:08:53.510
+= 0.
+
+01:08:54.220 --> 01:08:56.190
+So I can choose a threshold where.
+
+01:08:57.010 --> 01:08:59.930
+I will get every single malign case
+
+01:08:59.930 --> 01:09:02.380
+correct, but I'll have like 20% false
+
+01:09:02.380 --> 01:09:03.450
+positives.
+
+01:09:03.450 --> 01:09:05.870
+Or I can choose a case where I'll
+
+01:09:05.870 --> 01:09:07.360
+sometimes make mistakes.
+
+01:09:07.360 --> 01:09:10.110
+Thinking I'm malignant is not
+
+01:09:10.110 --> 01:09:11.040
+malignant.
+
+01:09:11.040 --> 01:09:15.360
+But when it's benign, like 9099% of the
+
+01:09:15.360 --> 01:09:16.570
+time I'll think it's benign.
+
+01:09:16.570 --> 01:09:18.815
+So you can choose like you can kind of
+
+01:09:18.815 --> 01:09:19.450
+choose your errors.
+
+01:09:25.800 --> 01:09:30.690
+So this is so this like given some
+
+01:09:30.690 --> 01:09:33.080
+point on this curve, it tells me the
+
+01:09:33.080 --> 01:09:35.120
+true positive rate is the percent of
+
+01:09:35.120 --> 01:09:37.775
+times that I correctly classify equals
+
+01:09:37.775 --> 01:09:39.379
+zero as y = 0.
+
+01:09:40.330 --> 01:09:42.020
+And the false positive rate is the
+
+01:09:42.020 --> 01:09:43.660
+percent of times that I.
+
+01:09:45.460 --> 01:09:46.790
+Classify.
+
+01:09:48.160 --> 01:09:50.400
+Y = 1 as y = 0.
+
+01:09:54.870 --> 01:09:57.410
+Alright, so I can also look at the
+
+01:09:57.410 --> 01:09:58.350
+feature importance.
+
+01:09:58.350 --> 01:10:01.450
+So if I do L1, so here I trained one
+
+01:10:01.450 --> 01:10:04.230
+model with L1 logistic regression or
+
+01:10:04.230 --> 01:10:06.586
+this is L2 and one with L1 logistic
+
+01:10:06.586 --> 01:10:06.930
+regression?
+
+01:10:07.740 --> 01:10:08.860
+And that makes me use a different
+
+01:10:08.860 --> 01:10:10.000
+solver if it's L1.
+
+01:10:11.270 --> 01:10:13.980
+So I can see the errors.
+
+01:10:14.070 --> 01:10:14.730
+
+
+01:10:18.090 --> 01:10:19.505
+A little weird but that error.
+
+01:10:19.505 --> 01:10:24.588
+But OK, I can see the errors and I can
+
+01:10:24.588 --> 01:10:26.780
+see the feature values.
+
+01:10:29.290 --> 01:10:32.870
+So with L2 I get lots of low weights,
+
+01:10:32.870 --> 01:10:34.222
+but none of them are zero.
+
+01:10:34.222 --> 01:10:37.750
+With L1 I get lots of 0 weights in a
+
+01:10:37.750 --> 01:10:39.160
+few larger weights.
+
+01:10:43.420 --> 01:10:44.910
+And then I can also do some further
+
+01:10:44.910 --> 01:10:46.400
+analysis looking at the tree.
+
+01:10:48.090 --> 01:10:50.090
+So first I'll train a full tree.
+
+01:10:51.060 --> 01:10:53.010
+And then next I'll train a tree with
+
+01:10:53.010 --> 01:10:54.370
+Max depth equals 2.
+
+01:10:56.680 --> 01:11:00.006
+So with the full tree I got error of
+
+01:11:00.006 --> 01:11:00.403
+4%.
+
+01:11:00.403 --> 01:11:05.106
+So it was as good as the OR was not as
+
+01:11:05.106 --> 01:11:06.590
+good as logistic regressor but pretty
+
+01:11:06.590 --> 01:11:06.930
+decent.
+
+01:11:08.220 --> 01:11:09.500
+But this tree is kind of hard to
+
+01:11:09.500 --> 01:11:09.940
+interpret.
+
+01:11:09.940 --> 01:11:11.410
+You wouldn't be able to give it to a
+
+01:11:11.410 --> 01:11:13.415
+technician and say like use this tree
+
+01:11:13.415 --> 01:11:14.330
+to make your decision.
+
+01:11:15.050 --> 01:11:17.020
+The short tree had higher error, but
+
+01:11:17.020 --> 01:11:18.730
+it's a lot simpler, so I can see its
+
+01:11:18.730 --> 01:11:20.530
+first splitting on the perimeter of the
+
+01:11:20.530 --> 01:11:21.240
+largest cells.
+
+01:11:25.000 --> 01:11:27.510
+And then finally, after doing all this
+
+01:11:27.510 --> 01:11:30.010
+analysis, I'm going to do tenfold cross
+
+01:11:30.010 --> 01:11:32.780
+validation using my best model.
+
+01:11:33.370 --> 01:11:35.590
+So here I'll just compare L1 logistic
+
+01:11:35.590 --> 01:11:38.240
+regression and nearest neighbor.
+
+01:11:39.160 --> 01:11:41.345
+I am doing tenfold, so I'm going to do
+
+01:11:41.345 --> 01:11:45.126
+10 estimates I do for each split.
+
+01:11:45.126 --> 01:11:48.490
+So the split will be after permutation.
+
+01:11:48.490 --> 01:11:53.120
+The first split will take indices 01020
+
+01:11:53.120 --> 01:11:56.414
+or yeah, 0102030, et cetera.
+
+01:11:56.414 --> 01:12:00.540
+The second split will take 11121, the
+
+01:12:00.540 --> 01:12:03.840
+third will take 21222, et cetera.
+
+01:12:04.830 --> 01:12:07.050
+Every time I use 90% of the data to
+
+01:12:07.050 --> 01:12:09.400
+train and the remaining data to test.
+
+01:12:10.520 --> 01:12:12.510
+And I'm doing that by just specifying
+
+01:12:12.510 --> 01:12:13.990
+the data that I'm using to test and
+
+01:12:13.990 --> 01:12:15.930
+then subtracting those indices to get
+
+01:12:15.930 --> 01:12:17.100
+the data that I used to train.
+
+01:12:18.080 --> 01:12:21.396
+Every time I normalize based on the
+
+01:12:21.396 --> 01:12:23.140
+training data, normalize both my
+
+01:12:23.140 --> 01:12:24.554
+training and validation data based on
+
+01:12:24.554 --> 01:12:26.180
+the same training data for the current
+
+01:12:26.180 --> 01:12:26.540
+split.
+
+01:12:27.600 --> 01:12:29.340
+Then I train and evaluate my nearest
+
+01:12:29.340 --> 01:12:31.870
+neighbor and logistic regressor.
+
+01:12:38.000 --> 01:12:39.230
+So that was fast.
+
+01:12:40.850 --> 01:12:41.103
+Right.
+
+01:12:41.103 --> 01:12:43.950
+And so then I have my errors.
+
+01:12:43.950 --> 01:12:46.970
+So one thing to note is that my even
+
+01:12:46.970 --> 01:12:48.250
+though in that one case I was
+
+01:12:48.250 --> 01:12:50.310
+evaluating before that one split, my
+
+01:12:50.310 --> 01:12:52.190
+logistic regression error was zero,
+
+01:12:52.190 --> 01:12:53.670
+it's not 0 every time.
+
+01:12:53.670 --> 01:12:56.984
+It ranges from zero to 5.3.
+
+01:12:56.984 --> 01:12:59.906
+And my nearest neighbor accuracy ranges
+
+01:12:59.906 --> 01:13:02.980
+from zero to 8 or 8.7 depending on the
+
+01:13:02.980 --> 01:13:03.330
+split.
+
+01:13:04.300 --> 01:13:06.085
+So different samples of your training
+
+01:13:06.085 --> 01:13:08.592
+and test data will give you different
+
+01:13:08.592 --> 01:13:09.866
+error measurement errors.
+
+01:13:09.866 --> 01:13:11.950
+And so that's why like cross validation
+
+01:13:11.950 --> 01:13:14.300
+can be a nice tool to give you not only
+
+01:13:14.300 --> 01:13:16.870
+an expected error, but some variance on
+
+01:13:16.870 --> 01:13:18.140
+the estimate of that error.
+
+01:13:19.000 --> 01:13:19.500
+So.
+
+01:13:20.410 --> 01:13:23.330
+My standard error of my estimate of the
+
+01:13:23.330 --> 01:13:26.195
+mean, which is the stair deviation of
+
+01:13:26.195 --> 01:13:28.390
+my error estimates divided by the
+
+01:13:28.390 --> 01:13:29.720
+square of the number of samples.
+
+01:13:30.680 --> 01:13:35.420
+Is 09 for nearest neighbor and six for
+
+01:13:35.420 --> 01:13:36.500
+logistic regression.
+
+01:13:37.500 --> 01:13:39.270
+And I can also use that to compute a
+
+01:13:39.270 --> 01:13:41.540
+confidence interval by multiplying that
+
+01:13:41.540 --> 01:13:45.410
+standard error by I forgot 1.96.
+
+01:13:46.280 --> 01:13:49.330
+So I can say like I'm 95% confident
+
+01:13:49.330 --> 01:13:51.930
+that my logistic regression error is
+
+01:13:51.930 --> 01:13:56.440
+somewhere between 12 and 34 or three.
+
+01:13:56.440 --> 01:14:00.040
+Sorry, 1.2% and 34%.
+
+01:14:02.360 --> 01:14:04.615
+And my nearest neighbor error is higher
+
+01:14:04.615 --> 01:14:06.620
+and I have like a bigger confidence
+
+01:14:06.620 --> 01:14:07.020
+interval.
+
+01:14:09.360 --> 01:14:14.360
+Now let's just compare very briefly how
+
+01:14:14.360 --> 01:14:14.860
+that.
+
+01:14:15.610 --> 01:14:19.660
+How the original paper did on this same
+
+01:14:19.660 --> 01:14:20.110
+problem?
+
+01:14:23.320 --> 01:14:25.480
+I just have one more slide, so don't
+
+01:14:25.480 --> 01:14:27.950
+worry, we will finish.
+
+01:14:28.690 --> 01:14:30.360
+Within a minute or so of runtime.
+
+01:14:31.200 --> 01:14:33.610
+Alright, so in the paper they use an
+
+01:14:33.610 --> 01:14:36.300
+MSM tree, which is that you have a
+
+01:14:36.300 --> 01:14:37.820
+linear classifier.
+
+01:14:37.820 --> 01:14:39.240
+Essentially that's used to do each
+
+01:14:39.240 --> 01:14:40.140
+split of the tree.
+
+01:14:41.090 --> 01:14:42.720
+But at the end of the day they choose
+
+01:14:42.720 --> 01:14:44.550
+only one split, so it ends up being a
+
+01:14:44.550 --> 01:14:45.380
+linear classifier.
+
+01:14:46.300 --> 01:14:49.633
+There they are trying to minimize the
+
+01:14:49.633 --> 01:14:51.520
+number of features as well as the
+
+01:14:51.520 --> 01:14:53.900
+number of splitting planes in order to
+
+01:14:53.900 --> 01:14:55.550
+improve generalization and make a
+
+01:14:55.550 --> 01:14:57.090
+simple interpretable function.
+
+01:14:57.800 --> 01:14:59.370
+So at the end of the day, they choose
+
+01:14:59.370 --> 01:15:01.105
+just three features, mean texture,
+
+01:15:01.105 --> 01:15:02.780
+worst area and worst smoothness.
+
+01:15:03.520 --> 01:15:04.420
+And.
+
+01:15:05.930 --> 01:15:08.610
+They used tenfold cross validation and
+
+01:15:08.610 --> 01:15:11.770
+they got an error of 3% within a
+
+01:15:11.770 --> 01:15:15.570
+confidence interval or minus 15%.
+
+01:15:15.570 --> 01:15:17.120
+So pretty similar to what we got.
+
+01:15:17.120 --> 01:15:18.960
+We got slightly lower error but we were
+
+01:15:18.960 --> 01:15:20.560
+using more features in the logistic
+
+01:15:20.560 --> 01:15:21.090
+regressor.
+
+01:15:21.910 --> 01:15:23.694
+And then they tested it on their held
+
+01:15:23.694 --> 01:15:26.475
+out set and they got a perfect accuracy
+
+01:15:26.475 --> 01:15:27.730
+on the held out set.
+
+01:15:28.550 --> 01:15:29.849
+Now that doesn't mean that their
+
+01:15:29.850 --> 01:15:31.670
+accuracy is perfect because they're
+
+01:15:31.670 --> 01:15:34.350
+cross validation if anything, is a
+
+01:15:34.350 --> 01:15:37.315
+biased towards a underestimating the
+
+01:15:37.315 --> 01:15:37.570
+error.
+
+01:15:37.570 --> 01:15:40.440
+So I would say their error is like
+
+01:15:40.440 --> 01:15:43.870
+roughly 15 to 45%, which is what they
+
+01:15:43.870 --> 01:15:45.180
+correctly report in the paper.
+
+01:15:46.950 --> 01:15:47.290
+Right.
+
+01:15:47.290 --> 01:15:51.030
+So we performed fairly similarly to the
+
+01:15:51.030 --> 01:15:51.705
+analysis.
+
+01:15:51.705 --> 01:15:53.670
+The nice thing is that now I can do
+
+01:15:53.670 --> 01:15:56.900
+this like in under an hour if I want.
+
+01:15:56.900 --> 01:15:59.140
+Well at that time it would be a lot
+
+01:15:59.140 --> 01:16:01.380
+more work to do that kind of analysis.
+
+01:16:02.330 --> 01:16:04.490
+But they also need to obviously want to
+
+01:16:04.490 --> 01:16:06.410
+be a lot more careful and do careful
+
+01:16:06.410 --> 01:16:07.780
+analysis and make sure that this is
+
+01:16:07.780 --> 01:16:10.240
+going to be like a useful tool for.
+
+01:16:10.320 --> 01:16:12.180
+That guy's diagnosis.
+
+01:16:14.130 --> 01:16:14.870
+Hey.
+
+01:16:14.870 --> 01:16:16.400
+So hopefully that was helpful.
+
+01:16:16.400 --> 01:16:19.700
+And next week I am going to talk about
+
+01:16:19.700 --> 01:16:20.150
+or not.
+
+01:16:20.150 --> 01:16:21.750
+Next week it's only Tuesday.
+
+01:16:21.750 --> 01:16:23.550
+On Thursday I'm going to talk about.
+
+01:16:23.550 --> 01:16:24.962
+No, wait, what day is it?
+
+01:16:24.962 --> 01:16:25.250
+Thursday.
+
+01:16:25.250 --> 01:16:25.868
+OK, good.
+
+01:16:25.868 --> 01:16:27.020
+It is next week.
+
+01:16:27.020 --> 01:16:28.810
+Yeah, at least chat with time.
+
+01:16:30.520 --> 01:16:33.300
+Next week I'll talk about ensembles and
+
+01:16:33.300 --> 01:16:35.310
+SVM and stochastic gradient descent.
+
+01:16:35.310 --> 01:16:35.780
+Thanks.
+
+01:16:35.780 --> 01:16:36.690
+Have a good weekend.
+
+01:16:38.360 --> 01:16:40.130
+And remember that homework one is due
+
+01:16:40.130 --> 01:16:40.830
+Monday.
+
+01:16:41.650 --> 01:16:42.760
+For those asking question.
+