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+WEBVTT Kind: captions; Language: en-US
+
+NOTE
+Created on 2024-02-07T20:51:27.1993072Z by ClassTranscribe
+
+00:01:22.450 --> 00:01:23.720
+Good morning, everybody.
+
+00:01:25.160 --> 00:01:25.690
+Morning.
+
+00:01:29.980 --> 00:01:31.830
+Alright, so I'm going to get started.
+
+00:01:31.830 --> 00:01:33.590
+Just a note.
+
+00:01:33.590 --> 00:01:37.980
+So I'll generally start at 9:31
+
+00:01:37.980 --> 00:01:38.590
+exactly.
+
+00:01:38.590 --> 00:01:42.600
+So I give a minute of slack and.
+
+00:01:43.360 --> 00:01:44.640
+At the end of the class, I'll make it
+
+00:01:44.640 --> 00:01:45.056
+pretty clear.
+
+00:01:45.056 --> 00:01:46.640
+When class is over, just wait till I
+
+00:01:46.640 --> 00:01:47.945
+say thank you or something.
+
+00:01:47.945 --> 00:01:49.580
+That kind of indicates that class is
+
+00:01:49.580 --> 00:01:50.659
+over before you pack up.
+
+00:01:50.660 --> 00:01:52.684
+Because otherwise like when students
+
+00:01:52.684 --> 00:01:56.080
+start to pack up, like if I get to the
+
+00:01:56.080 --> 00:01:57.507
+last slide and then students start to
+
+00:01:57.507 --> 00:01:59.170
+pack up, it makes quite a lot of noise
+
+00:01:59.170 --> 00:02:01.590
+if like couple 100 people are packing
+
+00:02:01.590 --> 00:02:02.260
+up at the same time.
+
+00:02:03.490 --> 00:02:05.930
+Right, so by the way these are I forgot
+
+00:02:05.930 --> 00:02:08.210
+to mention that brain image is an image
+
+00:02:08.210 --> 00:02:09.600
+that's created by Dolly.
+
+00:02:09.600 --> 00:02:10.770
+You might have heard of that.
+
+00:02:10.770 --> 00:02:14.580
+It's a AI like image generation method
+
+00:02:14.580 --> 00:02:17.440
+that can take an image, take a text and
+
+00:02:17.440 --> 00:02:19.210
+then generate an image that matches a
+
+00:02:19.210 --> 00:02:19.480
+text.
+
+00:02:20.320 --> 00:02:22.470
+This is also an image that's created by
+
+00:02:22.470 --> 00:02:22.950
+Dolly.
+
+00:02:24.430 --> 00:02:26.280
+I forget exactly what the prompt was on
+
+00:02:26.280 --> 00:02:26.720
+this one.
+
+00:02:26.720 --> 00:02:28.854
+It was it didn't exactly match the
+
+00:02:28.854 --> 00:02:29.028
+prompt.
+
+00:02:29.028 --> 00:02:30.660
+I think it was like, I think I said
+
+00:02:30.660 --> 00:02:32.170
+something like a bunch of animals
+
+00:02:32.170 --> 00:02:32.960
+somewhere ring.
+
+00:02:33.970 --> 00:02:36.580
+Orange vests and somewhere in green
+
+00:02:36.580 --> 00:02:38.090
+vests standing in a line.
+
+00:02:38.090 --> 00:02:39.956
+It has some trouble, like associating
+
+00:02:39.956 --> 00:02:41.900
+the right words with the right objects,
+
+00:02:41.900 --> 00:02:44.030
+but I still think it's pretty fitting
+
+00:02:44.030 --> 00:02:44.780
+for nearest neighbor.
+
+00:02:46.130 --> 00:02:47.775
+I like how there's like that one guy
+
+00:02:47.775 --> 00:02:49.700
+that is like standing out.
+
+00:02:54.930 --> 00:02:58.120
+So today I'm going to talk about two
+
+00:02:58.120 --> 00:02:58.860
+things really.
+
+00:02:58.860 --> 00:03:01.249
+So one is talking a bit more about the
+
+00:03:01.250 --> 00:03:03.540
+basic process of supervised machine
+
+00:03:03.540 --> 00:03:06.320
+learning, and the other is about the K
+
+00:03:06.320 --> 00:03:07.945
+nearest neighbor algorithm, which is
+
+00:03:07.945 --> 00:03:10.330
+one of the kind of like fundamental
+
+00:03:10.330 --> 00:03:11.800
+algorithms and machine learning.
+
+00:03:12.560 --> 00:03:15.635
+And I'll also talk about how we what
+
+00:03:15.635 --> 00:03:17.160
+are the sources of error.
+
+00:03:17.160 --> 00:03:18.270
+So why is it a?
+
+00:03:18.270 --> 00:03:19.939
+What are the different reasons that a
+
+00:03:19.940 --> 00:03:21.460
+machine learning algorithm will make
+
+00:03:21.460 --> 00:03:24.390
+test error even after it's fit the
+
+00:03:24.390 --> 00:03:24.970
+training set?
+
+00:03:25.640 --> 00:03:28.650
+And I'll talk about a couple of
+
+00:03:28.650 --> 00:03:29.979
+applications, so I'll talk about
+
+00:03:29.980 --> 00:03:32.344
+homework, one which has a couple of
+
+00:03:32.344 --> 00:03:32.940
+applications in it.
+
+00:03:33.540 --> 00:03:36.410
+And I'll also talk about the deep face
+
+00:03:36.410 --> 00:03:37.210
+algorithm.
+
+00:03:41.160 --> 00:03:43.620
+So a machine learning model is
+
+00:03:43.620 --> 00:03:46.539
+something that maps from features to
+
+00:03:46.540 --> 00:03:47.430
+prediction.
+
+00:03:47.430 --> 00:03:51.040
+So in this notation I've got F of X is
+
+00:03:51.040 --> 00:03:53.700
+mapping to YX are the features, F is
+
+00:03:53.700 --> 00:03:55.460
+some function that we'll have some
+
+00:03:55.460 --> 00:03:56.150
+parameters.
+
+00:03:56.800 --> 00:03:59.120
+And why is the prediction?
+
+00:04:00.050 --> 00:04:01.450
+So for example you could have a
+
+00:04:01.450 --> 00:04:03.810
+classification problem like is this a
+
+00:04:03.810 --> 00:04:04.530
+dog or a cat?
+
+00:04:04.530 --> 00:04:06.660
+And it might be based on image features
+
+00:04:06.660 --> 00:04:10.263
+or image pixels and so then X are the
+
+00:04:10.263 --> 00:04:13.985
+image pixels, Y is yes or no, or it
+
+00:04:13.985 --> 00:04:15.460
+could be dog or cat depending on how
+
+00:04:15.460 --> 00:04:15.920
+you frame it.
+
+00:04:16.940 --> 00:04:20.200
+Or if the problem is this e-mail spam
+
+00:04:20.200 --> 00:04:23.210
+or not, then the features might be like
+
+00:04:23.210 --> 00:04:25.440
+some summary of the words in the
+
+00:04:25.440 --> 00:04:27.680
+document and the words in the subject
+
+00:04:27.680 --> 00:04:31.430
+and the sender and the output is like
+
+00:04:31.430 --> 00:04:33.420
+true or false or one or zero.
+
+00:04:34.600 --> 00:04:36.450
+You could also have regression tests,
+
+00:04:36.450 --> 00:04:38.144
+for example, what will the stock price
+
+00:04:38.144 --> 00:04:39.572
+be of NVIDIA tomorrow?
+
+00:04:39.572 --> 00:04:42.260
+And then the features might be the
+
+00:04:42.260 --> 00:04:44.530
+historic stock prices, maybe some
+
+00:04:44.530 --> 00:04:45.960
+features about what's trending on
+
+00:04:45.960 --> 00:04:47.610
+Twitter, I don't know anything you
+
+00:04:47.610 --> 00:04:48.070
+want.
+
+00:04:48.070 --> 00:04:50.780
+And then the prediction would be the
+
+00:04:50.780 --> 00:04:53.236
+numerical value of the stock price
+
+00:04:53.236 --> 00:04:53.619
+tomorrow.
+
+00:04:54.360 --> 00:04:55.640
+When you're training something like
+
+00:04:55.640 --> 00:04:57.150
+that, you've got like a whole bunch of
+
+00:04:57.150 --> 00:04:58.020
+historical data.
+
+00:04:58.020 --> 00:04:59.710
+So you try to learn a model that can
+
+00:04:59.710 --> 00:05:01.780
+predict based, predict the historical
+
+00:05:01.780 --> 00:05:04.140
+stock prices given the preceding ones,
+
+00:05:04.140 --> 00:05:05.579
+and then you would hope that when you
+
+00:05:05.580 --> 00:05:08.830
+apply it to today's data that it would
+
+00:05:08.830 --> 00:05:10.520
+be able to predict the price tomorrow.
+
+00:05:12.140 --> 00:05:13.390
+Likewise, what will be the high
+
+00:05:13.390 --> 00:05:14.410
+temperature tomorrow?
+
+00:05:14.410 --> 00:05:16.297
+Features might be other temperatures,
+
+00:05:16.297 --> 00:05:17.900
+temperatures in other locations, other
+
+00:05:17.900 --> 00:05:21.410
+kinds of barometric data, and the
+
+00:05:21.410 --> 00:05:23.530
+output is some temperature.
+
+00:05:24.410 --> 00:05:25.600
+Or you could have a structured
+
+00:05:25.600 --> 00:05:27.630
+prediction task where you're outputting
+
+00:05:27.630 --> 00:05:29.295
+not just one number, but a whole bunch
+
+00:05:29.295 --> 00:05:31.025
+of numbers that are somehow related to
+
+00:05:31.025 --> 00:05:31.690
+each other.
+
+00:05:31.690 --> 00:05:33.420
+For example, what is the pose of this
+
+00:05:33.420 --> 00:05:33.925
+person?
+
+00:05:33.925 --> 00:05:36.767
+You would output positions of each of
+
+00:05:36.767 --> 00:05:38.520
+the key points on the person's body.
+
+00:05:40.140 --> 00:05:40.440
+Right.
+
+00:05:40.440 --> 00:05:42.313
+All of these though are just mapping a
+
+00:05:42.313 --> 00:05:45.315
+set of features to some labeler to some
+
+00:05:45.315 --> 00:05:46.170
+set of labels.
+
+00:05:48.630 --> 00:05:50.720
+The machine learning has three stages.
+
+00:05:50.720 --> 00:05:52.870
+There's a training stage which is when
+
+00:05:52.870 --> 00:05:54.580
+you optimize the model parameters.
+
+00:05:55.620 --> 00:05:58.260
+There is a validation stage, which is
+
+00:05:58.260 --> 00:06:00.820
+when you evaluate some model that's
+
+00:06:00.820 --> 00:06:03.357
+been optimized and use the validation
+
+00:06:03.357 --> 00:06:06.317
+to select among possible models or to
+
+00:06:06.317 --> 00:06:08.720
+select among some parameters that you
+
+00:06:08.720 --> 00:06:09.900
+set for those models.
+
+00:06:10.520 --> 00:06:13.380
+So the training is purely optimizing
+
+00:06:13.380 --> 00:06:15.530
+your some model design that you have on
+
+00:06:15.530 --> 00:06:16.590
+the training data.
+
+00:06:16.590 --> 00:06:18.480
+The validation is saying whether that
+
+00:06:18.480 --> 00:06:19.800
+was a good model design.
+
+00:06:20.420 --> 00:06:23.150
+And so you might iterate between the
+
+00:06:23.150 --> 00:06:25.290
+training and the validation many times.
+
+00:06:25.290 --> 00:06:27.290
+At the end of that, you'll pick what
+
+00:06:27.290 --> 00:06:29.290
+you think is the most effective model,
+
+00:06:29.290 --> 00:06:30.680
+and then ideally that should be
+
+00:06:30.680 --> 00:06:33.710
+evaluated only once on the test data as
+
+00:06:33.710 --> 00:06:35.440
+a measure of the final performance.
+
+00:06:39.330 --> 00:06:43.010
+So training is fitting the data to
+
+00:06:43.010 --> 00:06:46.190
+minimize some loss or maximize some
+
+00:06:46.190 --> 00:06:47.115
+objective function.
+
+00:06:47.115 --> 00:06:49.490
+So there's kind of a lot to unpack in
+
+00:06:49.490 --> 00:06:51.180
+this one little equation.
+
+00:06:51.180 --> 00:06:54.290
+So first the Theta here are the
+
+00:06:54.290 --> 00:06:56.405
+parameters of the model, so that's what
+
+00:06:56.405 --> 00:06:57.610
+would be optimized.
+
+00:06:57.610 --> 00:06:59.566
+And here I'm writing it as minimizing
+
+00:06:59.566 --> 00:07:01.650
+some loss, which is the most common way
+
+00:07:01.650 --> 00:07:02.280
+you would see it.
+
+00:07:03.350 --> 00:07:06.020
+Theta star is the Theta that minimizes
+
+00:07:06.020 --> 00:07:06.920
+that loss.
+
+00:07:07.290 --> 00:07:10.080
+The loss I'll get to it can be
+
+00:07:10.080 --> 00:07:11.440
+different different definitions.
+
+00:07:11.440 --> 00:07:13.209
+It could be, for example, a 01
+
+00:07:13.210 --> 00:07:15.220
+classification loss or a cross entropy
+
+00:07:15.220 --> 00:07:15.620
+loss.
+
+00:07:15.620 --> 00:07:18.070
+That's evaluating the likelihood of the
+
+00:07:18.070 --> 00:07:19.820
+ground truth labels given the data.
+
+00:07:21.330 --> 00:07:23.427
+You've got your model F, you've got
+
+00:07:23.427 --> 00:07:24.840
+your features X.
+
+00:07:25.850 --> 00:07:28.430
+Those errors are slightly off and your
+
+00:07:28.430 --> 00:07:29.510
+ground truth prediction.
+
+00:07:29.510 --> 00:07:31.580
+So Capital X, capital Y here are the
+
+00:07:31.580 --> 00:07:34.230
+training data and they're those are
+
+00:07:34.230 --> 00:07:36.980
+pairs of examples or examples, meaning
+
+00:07:36.980 --> 00:07:38.920
+that you've got pairs of features and
+
+00:07:38.920 --> 00:07:40.250
+then what you're supposed to predict
+
+00:07:40.250 --> 00:07:41.020
+from those features.
+
+00:07:43.820 --> 00:07:45.750
+So here's one example.
+
+00:07:45.750 --> 00:07:48.040
+Let's say that we want to learn to
+
+00:07:48.040 --> 00:07:49.590
+predict the next day's temperature
+
+00:07:49.590 --> 00:07:51.410
+given the preceding day temperatures.
+
+00:07:51.410 --> 00:07:53.520
+So the way that you would commonly
+
+00:07:53.520 --> 00:07:55.000
+formulate this is you'd have some
+
+00:07:55.000 --> 00:07:56.810
+matrix of features this X.
+
+00:07:56.810 --> 00:08:00.000
+So in Python you just have a 2D Numpy
+
+00:08:00.000 --> 00:08:00.400
+of A.
+
+00:08:01.110 --> 00:08:04.462
+And you would often store it as that
+
+00:08:04.462 --> 00:08:06.330
+you have one row per example.
+
+00:08:06.330 --> 00:08:07.970
+So each one of these rows.
+
+00:08:07.970 --> 00:08:10.716
+Here is a different example, and if you
+
+00:08:10.716 --> 00:08:12.850
+have 1000 training examples, you'd have
+
+00:08:12.850 --> 00:08:13.510
+1000 rows.
+
+00:08:14.410 --> 00:08:16.090
+And then you have one column per
+
+00:08:16.090 --> 00:08:16.840
+feature.
+
+00:08:16.840 --> 00:08:19.730
+So this might be the temperature of the
+
+00:08:19.730 --> 00:08:21.650
+preceding day, the temperature of two
+
+00:08:21.650 --> 00:08:23.415
+days ago, three days ago, four days
+
+00:08:23.415 --> 00:08:23.740
+ago.
+
+00:08:23.740 --> 00:08:25.530
+And this training data would probably
+
+00:08:25.530 --> 00:08:27.390
+be based on, like, historical data
+
+00:08:27.390 --> 00:08:28.170
+that's available.
+
+00:08:29.840 --> 00:08:32.505
+And then Y is what you need to predict.
+
+00:08:32.505 --> 00:08:35.275
+So the goal is to predict, for example
+
+00:08:35.275 --> 00:08:38.840
+50.5 based on these numbers here, to
+
+00:08:38.840 --> 00:08:41.025
+predict 473 from these numbers here,
+
+00:08:41.025 --> 00:08:43.290
+and so on South you'll have the same
+
+00:08:43.290 --> 00:08:45.640
+number of rows and your Y as you have
+
+00:08:45.640 --> 00:08:48.040
+in your X, but X will have a number of
+
+00:08:48.040 --> 00:08:50.677
+columns that corresponds to the number
+
+00:08:50.677 --> 00:08:51.570
+of features.
+
+00:08:51.570 --> 00:08:53.890
+And if Y is just you're just predicting
+
+00:08:53.890 --> 00:08:55.250
+a single number, then you will only
+
+00:08:55.250 --> 00:08:56.100
+have one column.
+
+00:08:58.790 --> 00:09:00.270
+So for this problem, it might be
+
+00:09:00.270 --> 00:09:03.240
+natural to use a squared loss, which is
+
+00:09:03.240 --> 00:09:06.620
+that we're going to say that the.
+
+00:09:07.360 --> 00:09:09.330
+We want to minimize the squared
+
+00:09:09.330 --> 00:09:11.710
+difference between each prediction F of
+
+00:09:11.710 --> 00:09:13.580
+XI given Theta.
+
+00:09:14.400 --> 00:09:17.630
+Is a prediction on the ith training
+
+00:09:17.630 --> 00:09:20.900
+features given the parameters Theta.
+
+00:09:21.730 --> 00:09:24.810
+And I want to make that as close as
+
+00:09:24.810 --> 00:09:27.387
+possible to the correct value Yi and
+
+00:09:27.387 --> 00:09:29.973
+I'm going to I'm going to say close as
+
+00:09:29.973 --> 00:09:32.040
+possible is defined by a squared
+
+00:09:32.040 --> 00:09:32.990
+difference.
+
+00:09:35.410 --> 00:09:37.470
+And I might say for this I'm going to
+
+00:09:37.470 --> 00:09:39.720
+use a linear model, so we'll talk about
+
+00:09:39.720 --> 00:09:42.720
+linear models in more detail next
+
+00:09:42.720 --> 00:09:45.385
+Thursday, but it's pretty intuitive.
+
+00:09:45.385 --> 00:09:47.850
+You just have a set for each of your
+
+00:09:47.850 --> 00:09:48.105
+features.
+
+00:09:48.105 --> 00:09:49.710
+You have some coefficient that's
+
+00:09:49.710 --> 00:09:51.800
+multiplied by those features, you sum
+
+00:09:51.800 --> 00:09:53.099
+them up, and then you have some
+
+00:09:53.100 --> 00:09:53.980
+constant term.
+
+00:09:55.170 --> 00:09:56.829
+And then if we wanted to optimize this
+
+00:09:56.830 --> 00:09:58.900
+model, we could optimize it using
+
+00:09:58.900 --> 00:10:00.390
+ordinary least squares regression,
+
+00:10:00.390 --> 00:10:01.610
+which again we'll talk about next
+
+00:10:01.610 --> 00:10:02.300
+Thursday.
+
+00:10:02.300 --> 00:10:03.980
+So the details of this aren't
+
+00:10:03.980 --> 00:10:06.170
+important, but the example is just to
+
+00:10:06.170 --> 00:10:08.820
+give you a sense of what the training
+
+00:10:08.820 --> 00:10:09.710
+process involves.
+
+00:10:09.710 --> 00:10:11.770
+You have a feature matrix X.
+
+00:10:11.770 --> 00:10:13.789
+You have a prediction vector a matrix
+
+00:10:13.790 --> 00:10:14.120
+Y.
+
+00:10:14.950 --> 00:10:16.550
+You have to define a loss, define a
+
+00:10:16.550 --> 00:10:18.130
+model and figure out how you're going
+
+00:10:18.130 --> 00:10:18.895
+to optimize it.
+
+00:10:18.895 --> 00:10:20.350
+And then you would actually perform the
+
+00:10:20.350 --> 00:10:22.420
+optimization, get the parameters, and
+
+00:10:22.420 --> 00:10:23.110
+that's training.
+
+00:10:25.480 --> 00:10:28.050
+So often you'll have a bunch of design
+
+00:10:28.050 --> 00:10:29.470
+decisions when you're faced with some
+
+00:10:29.470 --> 00:10:30.782
+kind of machine learning problem.
+
+00:10:30.782 --> 00:10:33.660
+So you might say, well, maybe that
+
+00:10:33.660 --> 00:10:35.520
+temperature prediction problem, maybe a
+
+00:10:35.520 --> 00:10:38.450
+linear regressor is good enough.
+
+00:10:38.450 --> 00:10:40.493
+Maybe I need a neural network.
+
+00:10:40.493 --> 00:10:42.370
+Maybe I should use a decision tree.
+
+00:10:42.370 --> 00:10:44.066
+So you might have different algorithms
+
+00:10:44.066 --> 00:10:45.610
+that you're considering trying.
+
+00:10:46.240 --> 00:10:48.460
+And even for each of those algorithms,
+
+00:10:48.460 --> 00:10:50.320
+there might be different parameters
+
+00:10:50.320 --> 00:10:51.925
+that you're considering, like what's
+
+00:10:51.925 --> 00:10:53.280
+the depth of the tree that I should
+
+00:10:53.280 --> 00:10:53.580
+use.
+
+00:10:55.190 --> 00:10:58.160
+And so you so it's important to have
+
+00:10:58.160 --> 00:11:00.450
+some kind of validation set that you
+
+00:11:00.450 --> 00:11:01.960
+can use to.
+
+00:11:02.990 --> 00:11:05.022
+That you can use to determine how good
+
+00:11:05.022 --> 00:11:07.020
+the model is that you chose, or what
+
+00:11:07.020 --> 00:11:08.755
+how good the design parameters of that
+
+00:11:08.755 --> 00:11:09.160
+model are.
+
+00:11:09.920 --> 00:11:12.766
+So for each one of the different kind
+
+00:11:12.766 --> 00:11:13.940
+of model designs that you're
+
+00:11:13.940 --> 00:11:15.592
+considering, you would train your model
+
+00:11:15.592 --> 00:11:16.980
+and then you evaluate it on a
+
+00:11:16.980 --> 00:11:19.300
+validation set and then you choose the
+
+00:11:19.300 --> 00:11:20.210
+best of those.
+
+00:11:21.100 --> 00:11:23.390
+The best of those models as you're like
+
+00:11:23.390 --> 00:11:24.160
+final model.
+
+00:11:25.280 --> 00:11:28.296
+So in some if you're doing, like if
+
+00:11:28.296 --> 00:11:30.900
+you're getting data sets from online,
+
+00:11:30.900 --> 00:11:32.460
+sometimes data sets.
+
+00:11:32.460 --> 00:11:35.050
+They'll almost always have a train and
+
+00:11:35.050 --> 00:11:37.200
+a test set that is designated for you.
+
+00:11:37.200 --> 00:11:38.620
+Which means that you can do all the
+
+00:11:38.620 --> 00:11:39.980
+training on the train set, but you
+
+00:11:39.980 --> 00:11:41.400
+shouldn't look at the test set until
+
+00:11:41.400 --> 00:11:42.500
+you're ready to do your final
+
+00:11:42.500 --> 00:11:43.210
+evaluation.
+
+00:11:44.090 --> 00:11:45.790
+They don't always have a trained and
+
+00:11:45.790 --> 00:11:47.900
+Val split, so sometimes you need to
+
+00:11:47.900 --> 00:11:49.680
+separate out a portion of the training
+
+00:11:49.680 --> 00:11:51.240
+data and use it for validation.
+
+00:11:52.820 --> 00:11:55.750
+So the reason that this is important
+
+00:11:55.750 --> 00:11:59.680
+because otherwise you will end up over
+
+00:11:59.680 --> 00:12:01.050
+optimizing for your test set.
+
+00:12:01.050 --> 00:12:03.120
+If you evaluate 1000 different models
+
+00:12:03.120 --> 00:12:04.820
+and you choose the best one for
+
+00:12:04.820 --> 00:12:08.401
+testing, then you don't really know if
+
+00:12:08.401 --> 00:12:09.759
+that test performance is really
+
+00:12:09.760 --> 00:12:12.080
+reflecting the performance that you
+
+00:12:12.080 --> 00:12:13.510
+would see with another random set of
+
+00:12:13.510 --> 00:12:15.250
+test examples because you've optimized
+
+00:12:15.250 --> 00:12:17.120
+your model selection for that test set.
+
+00:12:20.220 --> 00:12:22.440
+And then the final stages is evaluation
+
+00:12:22.440 --> 00:12:23.570
+or testing.
+
+00:12:23.570 --> 00:12:26.090
+And here you have some held out test
+
+00:12:26.090 --> 00:12:28.220
+held out set of examples that are not
+
+00:12:28.220 --> 00:12:29.340
+used in training.
+
+00:12:29.340 --> 00:12:30.890
+Because you want to make sure that your
+
+00:12:30.890 --> 00:12:33.370
+model does not only work well on the
+
+00:12:33.370 --> 00:12:35.580
+things that it fit to, but it will also
+
+00:12:35.580 --> 00:12:36.999
+work well if you give it some new
+
+00:12:37.000 --> 00:12:37.610
+example.
+
+00:12:37.610 --> 00:12:39.445
+Because you're not really interested in
+
+00:12:39.445 --> 00:12:41.045
+making predictions for the data where
+
+00:12:41.045 --> 00:12:42.740
+you already know the value of the
+
+00:12:42.740 --> 00:12:44.370
+prediction, you're interested in making
+
+00:12:44.370 --> 00:12:44.870
+new predictions.
+
+00:12:44.870 --> 00:12:46.955
+You want to predict tomorrow's
+
+00:12:46.955 --> 00:12:48.650
+temperature, even though nobody knows
+
+00:12:48.650 --> 00:12:50.090
+tomorrow's temperature or tomorrow's
+
+00:12:50.090 --> 00:12:50.680
+stock price.
+
+00:12:52.790 --> 00:12:55.255
+Though the term held out means that
+
+00:12:55.255 --> 00:12:57.440
+it's not used at all in the training
+
+00:12:57.440 --> 00:13:00.337
+process, and that should mean that it's
+
+00:13:00.337 --> 00:13:00.690
+not.
+
+00:13:00.690 --> 00:13:02.123
+You don't even look at it, you're not
+
+00:13:02.123 --> 00:13:04.380
+even aware of what those values are.
+
+00:13:04.380 --> 00:13:07.335
+So in the most clean setups, the test,
+
+00:13:07.335 --> 00:13:10.660
+the test data is on some evaluation
+
+00:13:10.660 --> 00:13:13.090
+server that people cannot access if
+
+00:13:13.090 --> 00:13:13.530
+they're doing.
+
+00:13:13.530 --> 00:13:15.830
+If there's some kind of benchmark,
+
+00:13:15.830 --> 00:13:16.900
+research, benchmark.
+
+00:13:17.610 --> 00:13:19.720
+And in many setups you're not allowed
+
+00:13:19.720 --> 00:13:22.690
+to even evaluate your method more than
+
+00:13:22.690 --> 00:13:25.185
+once a week so that you to make sure
+
+00:13:25.185 --> 00:13:27.325
+that people are not like trying out
+
+00:13:27.325 --> 00:13:28.695
+many different things and then choosing
+
+00:13:28.695 --> 00:13:30.140
+the best one based on the test set.
+
+00:13:31.830 --> 00:13:33.180
+So I'm not going to go through these
+
+00:13:33.180 --> 00:13:34.580
+performance measures, but there's lots
+
+00:13:34.580 --> 00:13:36.369
+of different performance measures that
+
+00:13:36.370 --> 00:13:37.340
+people could use.
+
+00:13:37.340 --> 00:13:39.390
+The most common for classification is
+
+00:13:39.390 --> 00:13:41.410
+just the classification classification
+
+00:13:41.410 --> 00:13:43.740
+error, which is the percent of times
+
+00:13:43.740 --> 00:13:46.680
+that your classifier is wrong.
+
+00:13:46.680 --> 00:13:48.200
+Obviously you want that to be low.
+
+00:13:49.020 --> 00:13:50.850
+Accuracy is just one minus the error.
+
+00:13:51.660 --> 00:13:54.835
+And then for regression you might use
+
+00:13:54.835 --> 00:13:56.780
+like a root mean squared error, which
+
+00:13:56.780 --> 00:13:59.725
+is like your average more or less your
+
+00:13:59.725 --> 00:14:02.410
+average distance from prediction to.
+
+00:14:03.930 --> 00:14:08.370
+To true value or like a residual R2
+
+00:14:08.370 --> 00:14:10.060
+which is like how much of the variance
+
+00:14:10.060 --> 00:14:11.380
+does your aggressor explain?
+
+00:14:14.400 --> 00:14:15.190
+So.
+
+00:14:15.300 --> 00:14:15.900
+
+
+00:14:16.730 --> 00:14:18.470
+If you're doing machine learning,
+
+00:14:18.470 --> 00:14:19.190
+research.
+
+00:14:20.060 --> 00:14:21.890
+Usually the way the data is collected
+
+00:14:21.890 --> 00:14:23.700
+is that the somebody collects like a
+
+00:14:23.700 --> 00:14:26.010
+big pool of data and then they randomly
+
+00:14:26.010 --> 00:14:28.750
+sample from that one pool of data to
+
+00:14:28.750 --> 00:14:30.520
+get their training and test splits.
+
+00:14:31.300 --> 00:14:33.790
+And that means that those training and
+
+00:14:33.790 --> 00:14:36.930
+test samples are sampled from the same
+
+00:14:36.930 --> 00:14:37.350
+distribution.
+
+00:14:37.350 --> 00:14:40.300
+They're what's called IID, which means
+
+00:14:40.300 --> 00:14:41.610
+independent and identically
+
+00:14:41.610 --> 00:14:43.695
+distributed, and it just means that
+
+00:14:43.695 --> 00:14:44.975
+they're coming from the same
+
+00:14:44.975 --> 00:14:45.260
+distribution.
+
+00:14:46.290 --> 00:14:48.000
+In the real world, though, that's often
+
+00:14:48.000 --> 00:14:48.840
+not the case.
+
+00:14:48.840 --> 00:14:50.640
+So a lot of a lot of machine learning
+
+00:14:50.640 --> 00:14:52.080
+theory is predicated.
+
+00:14:52.080 --> 00:14:55.990
+It depends on the assumption that the
+
+00:14:55.990 --> 00:14:57.540
+training and test data are coming from
+
+00:14:57.540 --> 00:15:00.205
+the same distribution but in the real
+
+00:15:00.205 --> 00:15:00.500
+world.
+
+00:15:01.550 --> 00:15:03.120
+Often they're different distributions.
+
+00:15:03.120 --> 00:15:07.330
+For example, you might be, you might,
+
+00:15:07.330 --> 00:15:11.272
+you might be trying to like categorize
+
+00:15:11.272 --> 00:15:14.980
+images, but the images that you collect
+
+00:15:14.980 --> 00:15:17.680
+in your for training are going to be
+
+00:15:17.680 --> 00:15:19.240
+different than what the user is provide
+
+00:15:19.240 --> 00:15:20.220
+to your system.
+
+00:15:20.220 --> 00:15:21.740
+Or you might be trying to recognize
+
+00:15:21.740 --> 00:15:23.650
+faces, but you don't have access to all
+
+00:15:23.650 --> 00:15:24.900
+the faces in the world.
+
+00:15:24.900 --> 00:15:26.830
+You have access to faces of people that
+
+00:15:26.830 --> 00:15:28.490
+volunteer to give you your data, which
+
+00:15:28.490 --> 00:15:29.955
+may be a different distribution than
+
+00:15:29.955 --> 00:15:30.960
+the end users.
+
+00:15:31.190 --> 00:15:32.200
+Of your application.
+
+00:15:33.440 --> 00:15:34.760
+Or it may be that things change
+
+00:15:34.760 --> 00:15:37.490
+overtime and so the distribution
+
+00:15:37.490 --> 00:15:37.970
+changes.
+
+00:15:39.350 --> 00:15:41.180
+So yes, go ahead.
+
+00:15:47.900 --> 00:15:52.190
+So if the distribution changes, the.
+
+00:15:54.170 --> 00:15:55.660
+So this is kind of where it gets
+
+00:15:55.660 --> 00:15:57.908
+different between research and
+
+00:15:57.908 --> 00:16:00.679
+practice, because in practice the
+
+00:16:00.680 --> 00:16:02.580
+distribution changes and you don't
+
+00:16:02.580 --> 00:16:02.976
+know.
+
+00:16:02.976 --> 00:16:05.570
+Like you have to then collect another
+
+00:16:05.570 --> 00:16:08.210
+test set based on your users data and
+
+00:16:08.210 --> 00:16:08.980
+annotate it.
+
+00:16:08.980 --> 00:16:10.810
+And then you could evaluate how you're
+
+00:16:10.810 --> 00:16:12.740
+actually doing on user data, but then
+
+00:16:12.740 --> 00:16:14.635
+it might change again because things in
+
+00:16:14.635 --> 00:16:16.345
+the world change and your users change
+
+00:16:16.345 --> 00:16:16.620
+so.
+
+00:16:17.660 --> 00:16:19.270
+So you have like this kind of
+
+00:16:19.270 --> 00:16:21.480
+intrinsically unknown thing about what
+
+00:16:21.480 --> 00:16:23.460
+is the true test distribution in
+
+00:16:23.460 --> 00:16:24.020
+practice.
+
+00:16:24.810 --> 00:16:28.835
+In an experiment, if somebody if you
+
+00:16:28.835 --> 00:16:30.816
+have like some domain what's called a
+
+00:16:30.816 --> 00:16:33.579
+domain shift where the test, test, test
+
+00:16:33.580 --> 00:16:34.780
+distribution is different than
+
+00:16:34.780 --> 00:16:35.450
+training.
+
+00:16:35.450 --> 00:16:37.033
+For example, in a driving application
+
+00:16:37.033 --> 00:16:41.014
+you could say you have to train it on,
+
+00:16:41.014 --> 00:16:44.575
+you have to train it on nice weather
+
+00:16:44.575 --> 00:16:46.240
+days, but it could be tested on foggy
+
+00:16:46.240 --> 00:16:46.580
+days.
+
+00:16:47.440 --> 00:16:49.970
+And then you kind of can know what the
+
+00:16:49.970 --> 00:16:52.230
+distribution shift is, and sometimes
+
+00:16:52.230 --> 00:16:54.135
+you're allowed to take that test data
+
+00:16:54.135 --> 00:16:56.591
+and learn unsupervised to adapt to that
+
+00:16:56.591 --> 00:16:58.970
+test data, and you can evaluate how you
+
+00:16:58.970 --> 00:16:59.390
+did.
+
+00:16:59.390 --> 00:17:01.800
+So in the research world, we're like
+
+00:17:01.800 --> 00:17:03.590
+all the tests and training data is
+
+00:17:03.590 --> 00:17:04.470
+known up front.
+
+00:17:04.470 --> 00:17:06.070
+You still have like a lot more control
+
+00:17:06.070 --> 00:17:07.630
+and a lot more knowledge than you often
+
+00:17:07.630 --> 00:17:09.090
+do in application scenario.
+
+00:17:16.920 --> 00:17:20.800
+So this is a recap of the training and
+
+00:17:20.800 --> 00:17:21.920
+evaluation procedure.
+
+00:17:22.700 --> 00:17:25.790
+You have you start with some, ideally
+
+00:17:25.790 --> 00:17:27.500
+some training data, some validation
+
+00:17:27.500 --> 00:17:28.750
+data, some test data.
+
+00:17:29.900 --> 00:17:33.400
+You have some model training and design
+
+00:17:33.400 --> 00:17:35.060
+phase, so you.
+
+00:17:36.270 --> 00:17:39.670
+You have some idea of what kind of what
+
+00:17:39.670 --> 00:17:41.370
+different models might be that you want
+
+00:17:41.370 --> 00:17:42.060
+to evaluate.
+
+00:17:42.060 --> 00:17:44.260
+You have an algorithm to train those
+
+00:17:44.260 --> 00:17:44.790
+models.
+
+00:17:44.790 --> 00:17:47.003
+So you take the training data, apply it
+
+00:17:47.003 --> 00:17:48.503
+to that design, you get some
+
+00:17:48.503 --> 00:17:49.935
+parameters, that's your model.
+
+00:17:49.935 --> 00:17:52.180
+Evaluate those parameters on the
+
+00:17:52.180 --> 00:17:55.730
+validation set and the model validation
+
+00:17:55.730 --> 00:17:55.970
+there.
+
+00:17:56.590 --> 00:17:59.160
+And then you might look at those
+
+00:17:59.160 --> 00:18:01.160
+results and be like, I think I can do
+
+00:18:01.160 --> 00:18:01.510
+better.
+
+00:18:01.510 --> 00:18:03.390
+So you go back to the drawing board,
+
+00:18:03.390 --> 00:18:05.880
+redo your designs and then you repeat
+
+00:18:05.880 --> 00:18:08.642
+that process until finally you say now
+
+00:18:08.642 --> 00:18:10.830
+I think the best model that I can
+
+00:18:10.830 --> 00:18:12.790
+possibly get, and then you evaluate it
+
+00:18:12.790 --> 00:18:13.560
+on your test set.
+
+00:18:19.970 --> 00:18:21.640
+So any other questions about that
+
+00:18:21.640 --> 00:18:23.170
+before I actually get into one of the
+
+00:18:23.170 --> 00:18:25.520
+algorithms, the KNN?
+
+00:18:28.100 --> 00:18:30.635
+OK, this obviously like this is going
+
+00:18:30.635 --> 00:18:32.530
+to feel second nature to you by the end
+
+00:18:32.530 --> 00:18:34.090
+of the course because it's what you use
+
+00:18:34.090 --> 00:18:35.440
+for every single machine learning
+
+00:18:35.440 --> 00:18:35.890
+algorithm.
+
+00:18:35.890 --> 00:18:39.660
+So even if it seems like a little
+
+00:18:39.660 --> 00:18:42.030
+abstract or foggy right now, I'm sure
+
+00:18:42.030 --> 00:18:42.490
+it will not.
+
+00:18:43.290 --> 00:18:44.120
+Before too long.
+
+00:18:46.020 --> 00:18:49.050
+All right, so first see if you can
+
+00:18:49.050 --> 00:18:52.070
+apply your own machine learning, I
+
+00:18:52.070 --> 00:18:52.340
+guess.
+
+00:18:53.350 --> 00:18:55.470
+So let's say I've got two classes here.
+
+00:18:55.470 --> 00:18:58.704
+I've got O's and I've got X's.
+
+00:18:58.704 --> 00:19:01.430
+So and plus is a new test sample.
+
+00:19:01.430 --> 00:19:03.930
+So what class do you think the black
+
+00:19:03.930 --> 00:19:05.460
+plus corresponds to?
+
+00:19:09.830 --> 00:19:11.300
+Alright, so I'll do a vote.
+
+00:19:11.300 --> 00:19:13.040
+How many people think it's an X?
+
+00:19:14.940 --> 00:19:16.480
+How many people think it's a no?
+
+00:19:18.550 --> 00:19:23.014
+So it's about 90 maybe like 99.5% think
+
+00:19:23.014 --> 00:19:25.990
+it's an X and about .5% think it's a
+
+00:19:25.990 --> 00:19:27.410
+no.
+
+00:19:27.410 --> 00:19:27.755
+All right.
+
+00:19:27.755 --> 00:19:28.830
+So why is it an X?
+
+00:19:29.630 --> 00:19:30.020
+Yeah.
+
+00:19:42.250 --> 00:19:45.860
+That's like a Matthew way to put it,
+
+00:19:45.860 --> 00:19:46.902
+but that's right, yeah.
+
+00:19:46.902 --> 00:19:49.137
+So one reason you might think it's an X
+
+00:19:49.137 --> 00:19:51.988
+is that it's closest to X.
+
+00:19:51.988 --> 00:19:54.716
+That's the closest example to it is an
+
+00:19:54.716 --> 00:19:55.069
+X, right?
+
+00:19:55.790 --> 00:19:57.240
+Are there any other reasons that you
+
+00:19:57.240 --> 00:19:58.160
+think it might be next?
+
+00:19:58.160 --> 00:19:58.360
+Yeah.
+
+00:20:01.500 --> 00:20:02.370
+It looks like what?
+
+00:20:03.330 --> 00:20:04.360
+It looks like an X.
+
+00:20:06.090 --> 00:20:07.220
+I guess that's true.
+
+00:20:08.290 --> 00:20:08.630
+Yeah.
+
+00:20:09.960 --> 00:20:10.500
+Any other?
+
+00:20:24.830 --> 00:20:25.143
+OK.
+
+00:20:25.143 --> 00:20:27.410
+And then this one was, if you think
+
+00:20:27.410 --> 00:20:29.120
+about like drawing, trying to draw a
+
+00:20:29.120 --> 00:20:31.917
+line between the X's and the O's, then
+
+00:20:31.917 --> 00:20:34.660
+the best line you could draw the plus
+
+00:20:34.660 --> 00:20:36.710
+would be on the X side of the line.
+
+00:20:37.940 --> 00:20:39.530
+So those are all good answers.
+
+00:20:39.530 --> 00:20:41.150
+And actually there, so there's like.
+
+00:20:41.920 --> 00:20:43.840
+There's basically like 3 different ways
+
+00:20:43.840 --> 00:20:45.920
+that you can solve this problem.
+
+00:20:45.920 --> 00:20:48.220
+One is nearest neighbor, which is what
+
+00:20:48.220 --> 00:20:50.440
+I'll talk about, which is when you say
+
+00:20:50.440 --> 00:20:52.423
+it's closest to the X, so therefore
+
+00:20:52.423 --> 00:20:53.020
+it's an X.
+
+00:20:53.020 --> 00:20:55.086
+Or most of the points that are.
+
+00:20:55.086 --> 00:20:57.070
+Most of the known points that are close
+
+00:20:57.070 --> 00:20:59.299
+to it are X's, so therefore it's an X.
+
+00:20:59.300 --> 00:21:01.440
+That's an instant space method.
+
+00:21:01.440 --> 00:21:03.990
+Another method is a linear method where
+
+00:21:03.990 --> 00:21:06.120
+you draw a line and you say, well it's
+
+00:21:06.120 --> 00:21:07.706
+on the UX side of the line, so
+
+00:21:07.706 --> 00:21:08.519
+therefore it's an X.
+
+00:21:09.230 --> 00:21:11.360
+And the third method is a probabilistic
+
+00:21:11.360 --> 00:21:13.056
+method where you fit some probabilities
+
+00:21:13.056 --> 00:21:14.935
+to the O's into the X's.
+
+00:21:14.935 --> 00:21:16.830
+And you say given those probabilities,
+
+00:21:16.830 --> 00:21:18.510
+it's more likely to be an X than a no.
+
+00:21:19.170 --> 00:21:21.629
+There's a really like all the different
+
+00:21:21.630 --> 00:21:23.833
+methods that you can use, and the
+
+00:21:23.833 --> 00:21:25.210
+different algorithms are just different
+
+00:21:25.210 --> 00:21:26.520
+ways of parameterizing those
+
+00:21:26.520 --> 00:21:27.070
+approaches.
+
+00:21:28.610 --> 00:21:30.089
+Or different ways of solving them or
+
+00:21:30.090 --> 00:21:31.460
+putting constraints on them.
+
+00:21:34.430 --> 00:21:36.990
+So this is the key principle of machine
+
+00:21:36.990 --> 00:21:40.460
+learning that given some feature target
+
+00:21:40.460 --> 00:21:44.660
+pairs X1Y1TO XNN.
+
+00:21:44.660 --> 00:21:49.570
+If XI is similar to XJ, then Yi is
+
+00:21:49.570 --> 00:21:50.850
+probably similar to YJ.
+
+00:21:51.450 --> 00:21:53.115
+In other words, if the features are
+
+00:21:53.115 --> 00:21:55.100
+similar, then the targets are also
+
+00:21:55.100 --> 00:21:55.900
+probably similar.
+
+00:21:57.020 --> 00:21:57.790
+And this is.
+
+00:21:58.440 --> 00:21:59.586
+This is kind of the.
+
+00:21:59.586 --> 00:22:01.220
+This is, I would say, an assumption of
+
+00:22:01.220 --> 00:22:02.720
+every single machine learning algorithm
+
+00:22:02.720 --> 00:22:03.810
+that I can think of.
+
+00:22:03.810 --> 00:22:05.500
+If it's not the case, things get really
+
+00:22:05.500 --> 00:22:06.010
+complicated.
+
+00:22:06.010 --> 00:22:07.210
+I don't know how you would possibly
+
+00:22:07.210 --> 00:22:10.250
+solve it if XI if there's no.
+
+00:22:11.430 --> 00:22:13.750
+If XI being similar to XJ tells you
+
+00:22:13.750 --> 00:22:17.390
+nothing about how Yi and YJ relate to
+
+00:22:17.390 --> 00:22:19.310
+each other, then it seems like you
+
+00:22:19.310 --> 00:22:20.320
+can't do better than chance.
+
+00:22:21.960 --> 00:22:23.920
+So with variations on how you define
+
+00:22:23.920 --> 00:22:24.790
+the similarity.
+
+00:22:24.790 --> 00:22:26.330
+So what does it mean for XI to be
+
+00:22:26.330 --> 00:22:27.570
+similar to XJ?
+
+00:22:27.570 --> 00:22:29.650
+And also, if you've got a bunch of
+
+00:22:29.650 --> 00:22:31.520
+similar points, how you combine those
+
+00:22:31.520 --> 00:22:32.830
+similarities to make a final
+
+00:22:32.830 --> 00:22:33.500
+prediction.
+
+00:22:33.500 --> 00:22:36.010
+Those differences are what distinguish
+
+00:22:36.010 --> 00:22:37.340
+the different algorithms from each
+
+00:22:37.340 --> 00:22:39.050
+other, but they're all based on this
+
+00:22:39.050 --> 00:22:41.063
+idea that if the features are similar,
+
+00:22:41.063 --> 00:22:42.609
+the predictions are also similar.
+
+00:22:45.500 --> 00:22:46.940
+So this brings us to the nearest
+
+00:22:46.940 --> 00:22:47.810
+neighbor algorithm.
+
+00:22:48.780 --> 00:22:50.960
+Probably the simplest, but also one of
+
+00:22:50.960 --> 00:22:52.600
+the most useful machine learning
+
+00:22:52.600 --> 00:22:53.170
+algorithms.
+
+00:22:54.210 --> 00:22:56.760
+And it kind of encodes that simple
+
+00:22:56.760 --> 00:22:58.540
+intuition most directly.
+
+00:22:58.540 --> 00:23:02.339
+So for a given set of test features,
+
+00:23:02.339 --> 00:23:05.365
+assign the label or target value to the
+
+00:23:05.365 --> 00:23:07.505
+most similar training features.
+
+00:23:07.505 --> 00:23:11.170
+And if you say, you can sometimes say
+
+00:23:11.170 --> 00:23:13.910
+how many of these similar examples
+
+00:23:13.910 --> 00:23:15.200
+you're going to consider.
+
+00:23:15.200 --> 00:23:17.814
+The default is often KK equals one.
+
+00:23:17.814 --> 00:23:20.193
+So the most similar single example, you
+
+00:23:20.193 --> 00:23:23.460
+assign its label to the test data.
+
+00:23:24.140 --> 00:23:25.530
+So here's the algorithm.
+
+00:23:25.530 --> 00:23:27.730
+It's pretty short.
+
+00:23:28.860 --> 00:23:30.620
+You compute the distance of each of
+
+00:23:30.620 --> 00:23:32.030
+your training samples to the test
+
+00:23:32.030 --> 00:23:32.530
+sample.
+
+00:23:33.510 --> 00:23:35.870
+Take the index of the training sample
+
+00:23:35.870 --> 00:23:37.810
+with the minimum distance and then you
+
+00:23:37.810 --> 00:23:38.600
+get that label.
+
+00:23:38.600 --> 00:23:39.505
+That's it.
+
+00:23:39.505 --> 00:23:41.780
+I can literally like code it faster
+
+00:23:41.780 --> 00:23:43.830
+than I can look up how you would use
+
+00:23:43.830 --> 00:23:45.770
+some library to for the nearest
+
+00:23:45.770 --> 00:23:46.440
+neighbor algorithm.
+
+00:23:46.440 --> 00:23:47.420
+It's like a few lines.
+
+00:23:49.320 --> 00:23:50.290
+So.
+
+00:23:51.460 --> 00:23:54.450
+And then within this, so there's just a
+
+00:23:54.450 --> 00:23:56.520
+couple of designs.
+
+00:23:56.520 --> 00:23:58.720
+One is what distance measure do you
+
+00:23:58.720 --> 00:24:00.780
+use, another is like how many nearest
+
+00:24:00.780 --> 00:24:01.870
+neighbors do you consider?
+
+00:24:02.500 --> 00:24:04.160
+And then often if you're applying this
+
+00:24:04.160 --> 00:24:06.390
+algorithm, you might want to apply some
+
+00:24:06.390 --> 00:24:08.020
+kind of transformation to the input
+
+00:24:08.020 --> 00:24:08.600
+features.
+
+00:24:09.380 --> 00:24:11.343
+So that they behave better according
+
+00:24:11.343 --> 00:24:13.690
+according to your similarity measure.
+
+00:24:14.430 --> 00:24:16.060
+The simplest distance function we can
+
+00:24:16.060 --> 00:24:18.946
+use is the L2 distance.
+
+00:24:18.946 --> 00:24:24.030
+So L2 means like the two norm or the
+
+00:24:24.030 --> 00:24:25.510
+Euclidian distance.
+
+00:24:25.510 --> 00:24:28.570
+It's the linear distance in like in
+
+00:24:28.570 --> 00:24:29.605
+space basically.
+
+00:24:29.605 --> 00:24:31.930
+So usually if you think of a distance
+
+00:24:31.930 --> 00:24:33.819
+intuitively, you're thinking of the L2.
+
+00:24:37.810 --> 00:24:41.040
+So we can try to so K nearest neighbor
+
+00:24:41.040 --> 00:24:42.820
+is just the generalization of nearest
+
+00:24:42.820 --> 00:24:44.060
+neighbor where you allow there to be
+
+00:24:44.060 --> 00:24:45.996
+more than 1 sample, so you can look at
+
+00:24:45.996 --> 00:24:47.340
+the K closest samples.
+
+00:24:49.110 --> 00:24:50.500
+So we'll try it with these.
+
+00:24:50.500 --> 00:24:53.840
+So let's say for this plus up here my
+
+00:24:53.840 --> 00:24:55.632
+pointer is not working for this one
+
+00:24:55.632 --> 00:24:55.950
+here.
+
+00:24:55.950 --> 00:24:57.700
+If you do one nearest neighbor, what
+
+00:24:57.700 --> 00:24:58.920
+would be the closest?
+
+00:25:00.360 --> 00:25:03.190
+Yeah, I'd say X and for the other one.
+
+00:25:05.760 --> 00:25:06.940
+Right.
+
+00:25:06.940 --> 00:25:08.766
+So for one nearest neighbor that the
+
+00:25:08.766 --> 00:25:11.010
+plus on the left would probably be X
+
+00:25:11.010 --> 00:25:12.610
+and the plus on the right would be O.
+
+00:25:13.940 --> 00:25:16.930
+And I should clarify here that the plus
+
+00:25:16.930 --> 00:25:19.690
+symbol itself is not really relevant,
+
+00:25:19.690 --> 00:25:21.810
+it's just the position.
+
+00:25:21.810 --> 00:25:24.251
+So here I've got 2 features X1 and X2,
+
+00:25:24.251 --> 00:25:28.880
+and I've got two classes O and, but the
+
+00:25:28.880 --> 00:25:31.360
+shapes of them are not are just
+
+00:25:31.360 --> 00:25:34.480
+abstract ways of representing some
+
+00:25:34.480 --> 00:25:34.990
+class.
+
+00:25:36.400 --> 00:25:37.830
+In these examples.
+
+00:25:38.740 --> 00:25:40.930
+So three nearest neighbor.
+
+00:25:40.930 --> 00:25:42.200
+Then you would look at the three
+
+00:25:42.200 --> 00:25:42.600
+nearest neighbors.
+
+00:25:42.600 --> 00:25:44.280
+So now one of the labels would flip in
+
+00:25:44.280 --> 00:25:44.985
+this case.
+
+00:25:44.985 --> 00:25:47.760
+So these circles are not meant to
+
+00:25:47.760 --> 00:25:49.800
+indicate like the region of influence.
+
+00:25:49.800 --> 00:25:51.953
+They're just circling the three nearest
+
+00:25:51.953 --> 00:25:52.346
+neighbors.
+
+00:25:52.346 --> 00:25:53.100
+They're ovals.
+
+00:25:54.010 --> 00:25:58.520
+So this one now has 2O's closer to it
+
+00:25:58.520 --> 00:26:00.405
+and so it's label would flip.
+
+00:26:00.405 --> 00:26:02.733
+It's most likely label would flip flip
+
+00:26:02.733 --> 00:26:04.840
+to O and if you wanted to you could
+
+00:26:04.840 --> 00:26:06.700
+output some confidence that says.
+
+00:26:08.030 --> 00:26:10.650
+You could say 2/3 of them are close to
+
+00:26:10.650 --> 00:26:12.470
+O, so I think it's a 2/3 chance that
+
+00:26:12.470 --> 00:26:13.160
+it's a no.
+
+00:26:13.160 --> 00:26:15.130
+It would be a pretty crude like
+
+00:26:15.130 --> 00:26:17.440
+probability estimate, but maybe better
+
+00:26:17.440 --> 00:26:18.220
+than nothing.
+
+00:26:18.220 --> 00:26:20.400
+Another way that you could get
+
+00:26:20.400 --> 00:26:21.760
+confidence if you were doing one
+
+00:26:21.760 --> 00:26:23.090
+nearest neighbor is to look at the
+
+00:26:23.090 --> 00:26:26.025
+ratio of the distances between the
+
+00:26:26.025 --> 00:26:28.832
+closest example and the closest example
+
+00:26:28.832 --> 00:26:30.310
+from the from another class.
+
+00:26:32.310 --> 00:26:33.980
+And then likewise I could do 5 nearest
+
+00:26:33.980 --> 00:26:36.430
+neighbor, so K could be anything.
+
+00:26:36.430 --> 00:26:38.590
+Typically it's not too large though.
+
+00:26:39.350 --> 00:26:40.030
+And.
+
+00:26:41.490 --> 00:26:43.940
+And classification is the most common
+
+00:26:43.940 --> 00:26:45.530
+case is K = 1.
+
+00:26:45.530 --> 00:26:48.130
+But you'll see in regression it can be
+
+00:26:48.130 --> 00:26:50.020
+kind of helpful to have a larger K.
+
+00:26:52.480 --> 00:26:52.800
+Right.
+
+00:26:52.800 --> 00:26:55.080
+So then what distance function do we
+
+00:26:55.080 --> 00:26:58.150
+use for K&N?
+
+00:26:59.750 --> 00:27:01.990
+We we've got a few choices.
+
+00:27:01.990 --> 00:27:03.360
+There's actually many choices, of
+
+00:27:03.360 --> 00:27:05.170
+course, but these are the most common.
+
+00:27:05.170 --> 00:27:06.980
+One is Euclidian, so I just put the
+
+00:27:06.980 --> 00:27:07.722
+equation there.
+
+00:27:07.722 --> 00:27:08.870
+It's the it's.
+
+00:27:08.870 --> 00:27:11.540
+You don't even need root if you're just
+
+00:27:11.540 --> 00:27:14.090
+trying to find the closest, because
+
+00:27:14.090 --> 00:27:15.540
+square root is monotonic.
+
+00:27:15.540 --> 00:27:15.880
+So.
+
+00:27:16.630 --> 00:27:19.790
+If a if the squared distance is
+
+00:27:19.790 --> 00:27:21.732
+minimized, then the square of the
+
+00:27:21.732 --> 00:27:23.010
+square distance is also minimize.
+
+00:27:24.710 --> 00:27:26.910
+And but so you've got Euclidian
+
+00:27:26.910 --> 00:27:28.130
+distance there, summer squared
+
+00:27:28.130 --> 00:27:30.890
+differences, city block which is sum of
+
+00:27:30.890 --> 00:27:32.210
+absolute distances.
+
+00:27:33.250 --> 00:27:34.740
+Mahalanobis distance.
+
+00:27:34.740 --> 00:27:37.290
+This is the most complicated where you
+
+00:27:37.290 --> 00:27:39.080
+have where you first like do what's
+
+00:27:39.080 --> 00:27:41.430
+called whitening, which is when you
+
+00:27:41.430 --> 00:27:45.630
+just put a inverse variance matrix.
+
+00:27:46.400 --> 00:27:50.225
+In between the product and.
+
+00:27:50.225 --> 00:27:52.340
+So basically this makes it so that if
+
+00:27:52.340 --> 00:27:54.670
+some features have a lot more variance,
+
+00:27:54.670 --> 00:27:56.510
+a lot more like spread than other
+
+00:27:56.510 --> 00:27:57.070
+features.
+
+00:27:57.760 --> 00:28:00.260
+Then they 1st at first reduces that
+
+00:28:00.260 --> 00:28:02.280
+spread so that they all have about the
+
+00:28:02.280 --> 00:28:03.560
+same amount of spreads so that the
+
+00:28:03.560 --> 00:28:05.770
+distance functions are like normalized,
+
+00:28:05.770 --> 00:28:06.520
+more comparable.
+
+00:28:07.600 --> 00:28:09.687
+Between the different features and it
+
+00:28:09.687 --> 00:28:10.925
+will also rotate.
+
+00:28:10.925 --> 00:28:13.870
+It will also like rotate the data to
+
+00:28:13.870 --> 00:28:15.660
+find the major axis.
+
+00:28:15.660 --> 00:28:18.020
+We'll talk about that more later.
+
+00:28:18.020 --> 00:28:19.940
+I don't want to get too much into the
+
+00:28:19.940 --> 00:28:22.436
+distance metric, just be aware of like
+
+00:28:22.436 --> 00:28:23.610
+that it's there and what it is.
+
+00:28:25.650 --> 00:28:28.830
+So of these measures L2.
+
+00:28:30.060 --> 00:28:32.600
+Kind of assumes implicitly assumes that
+
+00:28:32.600 --> 00:28:34.660
+all the dimensions are equally scaled,
+
+00:28:34.660 --> 00:28:37.740
+because if you have a distance of three
+
+00:28:37.740 --> 00:28:40.140
+for one feature and a distance of three
+
+00:28:40.140 --> 00:28:41.579
+for another feature, it'll it'll
+
+00:28:41.580 --> 00:28:43.580
+contribute the same to the distance.
+
+00:28:43.580 --> 00:28:46.400
+But it could be that one feature is
+
+00:28:46.400 --> 00:28:48.400
+height and one feature is income, and
+
+00:28:48.400 --> 00:28:49.930
+then the scales are totally different.
+
+00:28:50.770 --> 00:28:52.510
+And if you were to compute nearest
+
+00:28:52.510 --> 00:28:55.447
+neighbor, where your data is like the
+
+00:28:55.447 --> 00:28:57.057
+height of a person and their income,
+
+00:28:57.057 --> 00:28:58.396
+and you're trying to predict, predict
+
+00:28:58.396 --> 00:29:01.490
+their age, then the income is obviously
+
+00:29:01.490 --> 00:29:03.250
+going to dominate those distances.
+
+00:29:03.250 --> 00:29:04.850
+Because the height distances, if you
+
+00:29:04.850 --> 00:29:06.970
+don't normalize, are going to be at
+
+00:29:06.970 --> 00:29:10.570
+most like one or two depending on your
+
+00:29:10.570 --> 00:29:10.980
+units.
+
+00:29:11.780 --> 00:29:16.120
+And the income differences could be in
+
+00:29:16.120 --> 00:29:17.210
+the thousands or millions.
+
+00:29:18.980 --> 00:29:23.890
+So a city block is kind of similar, you
+
+00:29:23.890 --> 00:29:25.970
+just taking the absolute instead of the
+
+00:29:25.970 --> 00:29:26.960
+squared differences.
+
+00:29:27.700 --> 00:29:28.870
+And the main difference between
+
+00:29:28.870 --> 00:29:30.826
+Euclidean and city block is that city
+
+00:29:30.826 --> 00:29:33.937
+block will be less sensitive to the
+
+00:29:33.937 --> 00:29:35.880
+biggest differences, biggest
+
+00:29:35.880 --> 00:29:37.060
+dimensional differences.
+
+00:29:37.930 --> 00:29:41.360
+So with Euclidian, if you have say 5
+
+00:29:41.360 --> 00:29:43.601
+features and four of them have a
+
+00:29:43.601 --> 00:29:45.895
+distance of one and one of them has a
+
+00:29:45.895 --> 00:29:47.926
+distance of 1000, then your total
+
+00:29:47.926 --> 00:29:50.990
+distance is going to be like a million,
+
+00:29:50.990 --> 00:29:54.649
+roughly a million and four your total
+
+00:29:54.650 --> 00:29:55.420
+square distance.
+
+00:29:56.120 --> 00:29:58.910
+And so that 1000 totally dominates, or
+
+00:29:58.910 --> 00:30:00.480
+even if that one is 10.
+
+00:30:00.480 --> 00:30:02.920
+Let's say you have 4 distances of 1 and
+
+00:30:02.920 --> 00:30:05.965
+a distance of 10, then your total is
+
+00:30:05.965 --> 00:30:08.010
+104 once you square them and sum them.
+
+00:30:09.600 --> 00:30:13.250
+But with city block, if you have 4
+
+00:30:13.250 --> 00:30:15.564
+distances that are one and one distance
+
+00:30:15.564 --> 00:30:17.724
+that is 10, then the city block
+
+00:30:17.724 --> 00:30:19.877
+distance is 14 because it's one plus
+
+00:30:19.877 --> 00:30:21.340
+one 4 * + 10.
+
+00:30:22.010 --> 00:30:24.460
+So city block is less sensitive to like
+
+00:30:24.460 --> 00:30:26.916
+the biggest feature dimension, the
+
+00:30:26.916 --> 00:30:27.980
+biggest feature difference.
+
+00:30:29.730 --> 00:30:32.010
+And then Mahalanobis does not assume
+
+00:30:32.010 --> 00:30:33.360
+that all the features are already
+
+00:30:33.360 --> 00:30:35.020
+scaled for it will rescale them.
+
+00:30:35.020 --> 00:30:37.290
+So if you were to do this thing with,
+
+00:30:37.290 --> 00:30:39.260
+you're trying to predict somebody's age
+
+00:30:39.260 --> 00:30:41.090
+given income and height.
+
+00:30:41.730 --> 00:30:43.770
+Then after you apply your inverse
+
+00:30:43.770 --> 00:30:46.420
+covariance matrix, it will rescale the
+
+00:30:46.420 --> 00:30:48.970
+heights and the ages so that they both
+
+00:30:48.970 --> 00:30:49.750
+follow some.
+
+00:30:50.950 --> 00:30:54.000
+Unit norm distribution or normalized
+
+00:30:54.000 --> 00:30:57.240
+distribution where the variance is now
+
+00:30:57.240 --> 00:30:58.840
+one in each of those dimensions.
+
+00:31:05.200 --> 00:31:07.790
+So with K&N, if you're doing
+
+00:31:07.790 --> 00:31:10.720
+classification, then the prediction is
+
+00:31:10.720 --> 00:31:12.470
+usually just the most common class.
+
+00:31:13.430 --> 00:31:15.520
+If you're doing regression and you get
+
+00:31:15.520 --> 00:31:17.510
+the K nearest neighbors, then the
+
+00:31:17.510 --> 00:31:19.290
+prediction is usually the average of
+
+00:31:19.290 --> 00:31:21.406
+the labels of those K nearest
+
+00:31:21.406 --> 00:31:21.869
+neighbors.
+
+00:31:21.870 --> 00:31:23.820
+So for classification, if you're doing
+
+00:31:23.820 --> 00:31:26.026
+digit classification and you're 3
+
+00:31:26.026 --> 00:31:29.100
+nearest neighbors are 992, you would
+
+00:31:29.100 --> 00:31:29.760
+predict 9.
+
+00:31:30.980 --> 00:31:32.210
+If your.
+
+00:31:32.630 --> 00:31:38.850
+Say trying to how aesthetic people
+
+00:31:38.850 --> 00:31:41.170
+would think in images on a score on a
+
+00:31:41.170 --> 00:31:43.680
+scale of zero to 10 and your returns
+
+00:31:43.680 --> 00:31:45.850
+are 992, then you would take the
+
+00:31:45.850 --> 00:31:47.670
+average of those most likely so it
+
+00:31:47.670 --> 00:31:48.769
+would be 20 / 3.
+
+00:31:52.440 --> 00:31:54.710
+So let's just do another example.
+
+00:31:55.040 --> 00:31:55.700
+
+
+00:31:56.920 --> 00:31:58.130
+So let's say that we're doing
+
+00:31:58.130 --> 00:31:58.960
+classification.
+
+00:31:58.960 --> 00:32:00.470
+I just kind of randomly found some
+
+00:32:00.470 --> 00:32:03.000
+scatter plot on the Internet links down
+
+00:32:03.000 --> 00:32:03.380
+there.
+
+00:32:03.380 --> 00:32:05.640
+And let's say that we're trying to
+
+00:32:05.640 --> 00:32:07.890
+predict the sex, male or female, from
+
+00:32:07.890 --> 00:32:09.370
+standing and sitting heights.
+
+00:32:09.370 --> 00:32:11.032
+So we've got this standing height on
+
+00:32:11.032 --> 00:32:13.320
+the X dimension and the sitting height
+
+00:32:13.320 --> 00:32:14.845
+on the Y dimension.
+
+00:32:14.845 --> 00:32:19.035
+The circles are female, the males are
+
+00:32:19.035 --> 00:32:19.370
+male.
+
+00:32:20.320 --> 00:32:22.590
+And let's say that I want to predict
+
+00:32:22.590 --> 00:32:26.240
+for the X is it a male or a female and
+
+00:32:26.240 --> 00:32:28.060
+I'm doing 1 nearest neighbor.
+
+00:32:28.060 --> 00:32:29.890
+So what would what would the answer be?
+
+00:32:31.770 --> 00:32:34.580
+Right, the answer would be female
+
+00:32:34.580 --> 00:32:37.290
+because the closest circle is a female.
+
+00:32:37.290 --> 00:32:38.580
+And what if I do three nearest
+
+00:32:38.580 --> 00:32:38.990
+neighbor?
+
+00:32:41.270 --> 00:32:41.540
+Right.
+
+00:32:41.540 --> 00:32:42.490
+Also female.
+
+00:32:42.490 --> 00:32:46.665
+I need to get super large K before it's
+
+00:32:46.665 --> 00:32:48.710
+even plausible that it could be male.
+
+00:32:48.710 --> 00:32:50.570
+Maybe even like K would have to be the
+
+00:32:50.570 --> 00:32:52.070
+whole data set, and that would only
+
+00:32:52.070 --> 00:32:53.180
+work if there's more males than
+
+00:32:53.180 --> 00:32:53.600
+females.
+
+00:32:54.720 --> 00:32:55.926
+And what about the plus?
+
+00:32:55.926 --> 00:32:58.760
+If I do if I do 1 N, is it male or
+
+00:32:58.760 --> 00:32:59.190
+female?
+
+00:33:00.850 --> 00:33:01.095
+OK.
+
+00:33:01.095 --> 00:33:02.560
+And what if I do three and north?
+
+00:33:04.950 --> 00:33:08.386
+Right, female, because now the out of
+
+00:33:08.386 --> 00:33:10.770
+the five closest neighbor out of the
+
+00:33:10.770 --> 00:33:12.600
+most relevant out of the three closest
+
+00:33:12.600 --> 00:33:14.060
+neighbors, two of them are female and
+
+00:33:14.060 --> 00:33:14.630
+one is male.
+
+00:33:15.970 --> 00:33:17.740
+What about the circle, male or female?
+
+00:33:19.450 --> 00:33:21.220
+Right, it will be mail for.
+
+00:33:22.060 --> 00:33:23.070
+Virtually any K.
+
+00:33:24.350 --> 00:33:24.740
+All right.
+
+00:33:24.740 --> 00:33:26.010
+So that's classification.
+
+00:33:27.880 --> 00:33:29.450
+And now let's say we want to do
+
+00:33:29.450 --> 00:33:30.540
+regression.
+
+00:33:30.540 --> 00:33:32.530
+So we want to predict the sitting
+
+00:33:32.530 --> 00:33:35.104
+height given the standing height.
+
+00:33:35.104 --> 00:33:37.360
+The standing height is on the X axis.
+
+00:33:38.020 --> 00:33:39.720
+And I want to predict this sitting
+
+00:33:39.720 --> 00:33:40.410
+height.
+
+00:33:41.670 --> 00:33:43.730
+So it might be hard to see if you're
+
+00:33:43.730 --> 00:33:44.060
+far away.
+
+00:33:44.060 --> 00:33:47.300
+It might be kind of hard to see it very
+
+00:33:47.300 --> 00:33:51.150
+clearly but for this height, so that I
+
+00:33:51.150 --> 00:33:52.850
+don't know exactly what the value is,
+
+00:33:52.850 --> 00:33:56.360
+but whatever, 100 and 4144 or
+
+00:33:56.360 --> 00:33:56.790
+something.
+
+00:33:57.530 --> 00:33:59.750
+What would be the sitting height?
+
+00:34:00.620 --> 00:34:01.360
+Roughly.
+
+00:34:05.400 --> 00:34:08.050
+So it would be whatever this is here
+
+00:34:08.050 --> 00:34:10.630
+let me use my, I'll use my cursor.
+
+00:34:12.500 --> 00:34:14.760
+So it would be whatever this point is
+
+00:34:14.760 --> 00:34:16.200
+here it would be the sitting height.
+
+00:34:17.100 --> 00:34:18.716
+And notice that if I moved a little bit
+
+00:34:18.716 --> 00:34:20.750
+to the left it would drop quite a lot,
+
+00:34:20.750 --> 00:34:22.390
+and if I move a little bit to the right
+
+00:34:22.390 --> 00:34:23.685
+then this would be the closest point
+
+00:34:23.685 --> 00:34:24.660
+and then drop a little.
+
+00:34:25.380 --> 00:34:28.110
+So the so it's kind of unstable if I'm
+
+00:34:28.110 --> 00:34:30.677
+doing one and what if I were doing 3
+
+00:34:30.677 --> 00:34:33.830
+and N then would it be higher than One
+
+00:34:33.830 --> 00:34:35.000
+North or lower?
+
+00:34:39.130 --> 00:34:41.030
+Yes, it would be lower because if I
+
+00:34:41.030 --> 00:34:42.720
+were doing 3 N then it would be the
+
+00:34:42.720 --> 00:34:44.883
+average of this point and this point
+
+00:34:44.883 --> 00:34:47.820
+and this point which is lower than the
+
+00:34:47.820 --> 00:34:48.310
+center point.
+
+00:34:50.130 --> 00:34:51.670
+And now let's look at this One South.
+
+00:34:51.670 --> 00:34:54.329
+Now this one.
+
+00:34:54.330 --> 00:34:56.090
+What is the setting height roughly?
+
+00:34:56.730 --> 00:34:57.890
+If I do one and north.
+
+00:35:02.740 --> 00:35:04.570
+So it's this guy up here.
+
+00:35:04.570 --> 00:35:07.700
+So it would be around 84 and what is it
+
+00:35:07.700 --> 00:35:09.990
+roughly if I do three and north?
+
+00:35:17.040 --> 00:35:19.556
+So it's probably around here.
+
+00:35:19.556 --> 00:35:22.955
+So I'd say around like 81 maybe, but
+
+00:35:22.955 --> 00:35:25.110
+it's a big drop because these guys,
+
+00:35:25.110 --> 00:35:27.625
+these three points here are the are the
+
+00:35:27.625 --> 00:35:28.820
+three nearest neighbors.
+
+00:35:30.010 --> 00:35:32.100
+And if I am doing one nearest neighbor
+
+00:35:32.100 --> 00:35:34.020
+and I were to plot the regressed
+
+00:35:34.020 --> 00:35:36.390
+height, it would be like jumping all
+
+00:35:36.390 --> 00:35:37.280
+over the place, right?
+
+00:35:37.280 --> 00:35:38.900
+Because every time it only depends on
+
+00:35:38.900 --> 00:35:40.410
+that one nearest neighbor.
+
+00:35:40.410 --> 00:35:42.335
+So it gives us a really, it can give us
+
+00:35:42.335 --> 00:35:44.580
+a really unintuitive, bly jumpy
+
+00:35:44.580 --> 00:35:46.180
+regression value.
+
+00:35:46.180 --> 00:35:48.006
+But if I do three or five nearest
+
+00:35:48.006 --> 00:35:49.340
+neighbor, it's going to end up being
+
+00:35:49.340 --> 00:35:51.230
+much smoother as I move from left to
+
+00:35:51.230 --> 00:35:51.380
+right.
+
+00:35:52.330 --> 00:35:53.350
+And then this is like.
+
+00:35:54.440 --> 00:35:56.080
+This happens to be showing a linear
+
+00:35:56.080 --> 00:35:57.970
+regression of justice all the data.
+
+00:35:57.970 --> 00:36:00.060
+We'll talk about linear regression next
+
+00:36:00.060 --> 00:36:01.920
+Thursday, but that's kind of the
+
+00:36:01.920 --> 00:36:02.860
+smoothest estimate.
+
+00:36:05.470 --> 00:36:07.830
+Alright, I'll show.
+
+00:36:07.830 --> 00:36:09.075
+Actually, I want to.
+
+00:36:09.075 --> 00:36:10.380
+I know it's kind of.
+
+00:36:11.770 --> 00:36:14.200
+Let's see 93935.
+
+00:36:15.450 --> 00:36:17.830
+So about in the middle of the class, I
+
+00:36:17.830 --> 00:36:19.480
+want to like give everyone a chance to
+
+00:36:19.480 --> 00:36:20.880
+like stand up and.
+
+00:36:22.090 --> 00:36:23.625
+Check your e-mail or phone or whatever,
+
+00:36:23.625 --> 00:36:24.670
+because I think it's hard to
+
+00:36:24.670 --> 00:36:27.040
+concentrate for an hour and 15 minutes
+
+00:36:27.040 --> 00:36:27.480
+in a row.
+
+00:36:27.480 --> 00:36:29.020
+It's easy for me because I'm teaching,
+
+00:36:29.020 --> 00:36:30.120
+but harder.
+
+00:36:30.120 --> 00:36:31.400
+I would not be able to do it if I were
+
+00:36:31.400 --> 00:36:32.280
+sitting in your seats.
+
+00:36:32.280 --> 00:36:33.980
+So I'm going to take a break for like
+
+00:36:33.980 --> 00:36:34.580
+one minute.
+
+00:36:34.580 --> 00:36:36.660
+So feel free to stand up and stretch,
+
+00:36:36.660 --> 00:36:39.500
+check your e-mail, whatever you want,
+
+00:36:39.500 --> 00:36:41.640
+and then I'll show you these demos.
+
+00:38:28.140 --> 00:38:29.990
+Alright, I'm going to pick up again.
+
+00:38:38.340 --> 00:38:39.740
+Alright, I'm going to start again.
+
+00:38:41.070 --> 00:38:43.830
+Sorry, I know I'm interrupting a lot of
+
+00:38:43.830 --> 00:38:44.860
+conversations.
+
+00:38:44.860 --> 00:38:49.488
+So here's the first demo here.
+
+00:38:49.488 --> 00:38:50.570
+It's kind of simple.
+
+00:38:50.570 --> 00:38:52.600
+It's a KCNN demo actually.
+
+00:38:52.600 --> 00:38:53.820
+They're both CNN demos.
+
+00:38:53.820 --> 00:38:54.510
+Obviously.
+
+00:38:54.510 --> 00:38:57.810
+The thing I like about this demo is, I
+
+00:38:57.810 --> 00:38:59.070
+guess first I'll explain what it's
+
+00:38:59.070 --> 00:38:59.380
+doing.
+
+00:38:59.380 --> 00:39:00.958
+So it's got some red points here.
+
+00:39:00.958 --> 00:39:01.881
+This is one class.
+
+00:39:01.881 --> 00:39:03.289
+It's got some blue points.
+
+00:39:03.290 --> 00:39:04.310
+That's another class.
+
+00:39:04.310 --> 00:39:07.035
+The red area are all the areas that
+
+00:39:07.035 --> 00:39:09.026
+will be classified as red, and the blue
+
+00:39:09.026 --> 00:39:10.614
+areas are all the areas that will be
+
+00:39:10.614 --> 00:39:11.209
+classified as blue.
+
+00:39:11.930 --> 00:39:15.344
+And you can change K and you can change
+
+00:39:15.344 --> 00:39:16.610
+the distance measure.
+
+00:39:16.610 --> 00:39:19.090
+And then if I click somewhere here, it
+
+00:39:19.090 --> 00:39:21.390
+shows me which point is determining the
+
+00:39:21.390 --> 00:39:22.560
+classification.
+
+00:39:22.560 --> 00:39:26.073
+So I'm clicking on the center point and
+
+00:39:26.073 --> 00:39:28.190
+then it's drawing a connecting line and
+
+00:39:28.190 --> 00:39:29.949
+radius that correspond to the one
+
+00:39:29.950 --> 00:39:31.465
+nearest neighbor because this is set to
+
+00:39:31.465 --> 00:39:31.670
+1.
+
+00:39:33.160 --> 00:39:35.640
+So one thing I'll note I'll do is just
+
+00:39:35.640 --> 00:39:36.116
+change.
+
+00:39:36.116 --> 00:39:38.750
+KK is almost always odd because if it's
+
+00:39:38.750 --> 00:39:40.400
+even then you have like a split
+
+00:39:40.400 --> 00:39:41.560
+decision a lot of times.
+
+00:39:42.770 --> 00:39:45.310
+So if I have K = 3, just notice how the
+
+00:39:45.310 --> 00:39:47.790
+boundary changes as I increase K.
+
+00:39:50.120 --> 00:39:52.370
+It becomes simpler and simpler, right?
+
+00:39:52.370 --> 00:39:54.300
+It just becomes like eventually it
+
+00:39:54.300 --> 00:39:55.710
+should become well.
+
+00:39:57.440 --> 00:39:59.990
+Got got bigger than the data, so in K =
+
+00:39:59.990 --> 00:40:01.770
+23 I think there's probably 23 points,
+
+00:40:01.770 --> 00:40:03.250
+so it's just the most common class.
+
+00:40:04.790 --> 00:40:07.450
+And then it kind of becomes more like a
+
+00:40:07.450 --> 00:40:09.880
+straight line with a very high K.
+
+00:40:10.190 --> 00:40:10.720
+
+
+00:40:16.330 --> 00:40:18.820
+Then if I change the distance measure,
+
+00:40:18.820 --> 00:40:19.915
+I've got Manhattan.
+
+00:40:19.915 --> 00:40:22.610
+Manhattan is that L1 distance, so it
+
+00:40:22.610 --> 00:40:24.800
+becomes like a little bit more.
+
+00:40:24.890 --> 00:40:25.470
+
+
+00:40:26.300 --> 00:40:27.590
+A little bit more like.
+
+00:40:28.360 --> 00:40:30.720
+Vertical horizontal lines in the
+
+00:40:30.720 --> 00:40:33.410
+decision boundary compared to.
+
+00:40:33.530 --> 00:40:34.060
+
+
+00:40:34.830 --> 00:40:37.120
+Compared to the Euclidian distance.
+
+00:40:39.280 --> 00:40:40.780
+
+
+00:40:41.460 --> 00:40:45.023
+And then this is showing this box is
+
+00:40:45.023 --> 00:40:47.945
+showing like the box that contains all
+
+00:40:47.945 --> 00:40:51.970
+the points within the where K7 the
+
+00:40:51.970 --> 00:40:53.800
+seven nearest neighbors according to
+
+00:40:53.800 --> 00:40:55.100
+Manhattan distance.
+
+00:40:55.100 --> 00:40:57.504
+So you can see that it's kind of like a
+
+00:40:57.504 --> 00:40:59.436
+weird in some ways it feels like a
+
+00:40:59.436 --> 00:41:00.440
+weird distance measure.
+
+00:41:00.440 --> 00:41:02.910
+Another thing that I should bring up.
+
+00:41:02.910 --> 00:41:05.950
+I decide not to go into too much detail
+
+00:41:05.950 --> 00:41:07.803
+in this today because I think it's like
+
+00:41:07.803 --> 00:41:10.890
+a more of a not as central of a point
+
+00:41:10.890 --> 00:41:11.710
+as the things that I am.
+
+00:41:11.850 --> 00:41:12.210
+Talking about.
+
+00:41:12.920 --> 00:41:16.990
+But our intuition for high dimensions
+
+00:41:16.990 --> 00:41:17.730
+is really bad.
+
+00:41:18.370 --> 00:41:21.325
+So everything I visualize, almost
+
+00:41:21.325 --> 00:41:23.090
+everything is in two dimensions because
+
+00:41:23.090 --> 00:41:25.110
+that's all I can put on a piece of
+
+00:41:25.110 --> 00:41:26.060
+paper or screen.
+
+00:41:27.700 --> 00:41:30.620
+I can't visualize 1000 dimensions, but
+
+00:41:30.620 --> 00:41:32.167
+things behave kind of differently in
+
+00:41:32.167 --> 00:41:33.790
+1000 dimensions in two dimensions.
+
+00:41:33.790 --> 00:41:37.280
+So for example, if I randomly sample a
+
+00:41:37.280 --> 00:41:39.197
+whole bunch of points in a unit cube
+
+00:41:39.197 --> 00:41:41.944
+and 1000 dimensions, almost all the
+
+00:41:41.944 --> 00:41:44.082
+points lie like right on the surface of
+
+00:41:44.082 --> 00:41:46.219
+that cube, and they'll all lie if I
+
+00:41:46.220 --> 00:41:47.025
+have some epsilon.
+
+00:41:47.025 --> 00:41:48.750
+If Epsilon is like really really tiny,
+
+00:41:48.750 --> 00:41:50.420
+they'll still all be like right on the
+
+00:41:50.420 --> 00:41:51.170
+surface of that cube.
+
+00:41:51.880 --> 00:41:54.400
+And in high dimensional spaces it takes
+
+00:41:54.400 --> 00:41:56.510
+like tons and tons of data to populate
+
+00:41:56.510 --> 00:41:59.320
+that space, and so every point tends to
+
+00:41:59.320 --> 00:42:00.890
+be pretty far away from every other
+
+00:42:00.890 --> 00:42:02.269
+point in a high dimensional space.
+
+00:42:04.440 --> 00:42:06.639
+They're just worth being aware of that
+
+00:42:06.640 --> 00:42:08.560
+limitation of our minds that we don't
+
+00:42:08.560 --> 00:42:11.200
+think well in high dimensions, but I'll
+
+00:42:11.200 --> 00:42:12.680
+probably talk about it in more detail
+
+00:42:12.680 --> 00:42:13.910
+at some later time.
+
+00:42:14.500 --> 00:42:17.290
+So this demo I like even more.
+
+00:42:17.290 --> 00:42:19.260
+This is another nearest neighbor demo.
+
+00:42:19.260 --> 00:42:21.280
+Again, I get to choose the metric, I'll
+
+00:42:21.280 --> 00:42:22.820
+leave it at L2.
+
+00:42:23.550 --> 00:42:25.360
+It's that one nearest neighbor I can
+
+00:42:25.360 --> 00:42:26.700
+choose the number of points.
+
+00:42:27.470 --> 00:42:31.110
+And I'll do three classes.
+
+00:42:32.390 --> 00:42:33.050
+So.
+
+00:42:35.540 --> 00:42:36.480
+Let's see.
+
+00:42:39.720 --> 00:42:41.800
+Alright, so one thing I wanted to point
+
+00:42:41.800 --> 00:42:45.600
+out is that one nearest neighbor can be
+
+00:42:45.600 --> 00:42:48.006
+pretty sensitive to an individual
+
+00:42:48.006 --> 00:42:48.423
+point.
+
+00:42:48.423 --> 00:42:50.670
+So let's say I take this one green
+
+00:42:50.670 --> 00:42:52.150
+point and I drag it around.
+
+00:42:54.460 --> 00:42:56.770
+It can make a really big impact on the
+
+00:42:56.770 --> 00:42:58.810
+decision boundary all by itself.
+
+00:43:00.470 --> 00:43:02.200
+Right, because only that point matters.
+
+00:43:02.200 --> 00:43:03.920
+There's nothing else in this space, so
+
+00:43:03.920 --> 00:43:05.620
+it gets to claim the entire space by
+
+00:43:05.620 --> 00:43:06.070
+itself.
+
+00:43:07.220 --> 00:43:09.600
+Another thing to note about CNN is that
+
+00:43:09.600 --> 00:43:12.660
+for one N, if you create a veroni
+
+00:43:12.660 --> 00:43:15.690
+diagram which is, you split this into
+
+00:43:15.690 --> 00:43:18.380
+different cells where each cell,
+
+00:43:18.380 --> 00:43:20.250
+everything within each cell is closest
+
+00:43:20.250 --> 00:43:21.390
+to a single point.
+
+00:43:22.160 --> 00:43:23.500
+That's kind of that's the decision
+
+00:43:23.500 --> 00:43:24.550
+boundary of the cannon.
+
+00:43:26.750 --> 00:43:29.460
+So it's pretty sensitive if I change it
+
+00:43:29.460 --> 00:43:30.740
+to three and north.
+
+00:43:31.850 --> 00:43:34.760
+It's not going to be as sensitive this
+
+00:43:34.760 --> 00:43:36.310
+they're making white because it's a 3
+
+00:43:36.310 --> 00:43:36.840
+way tie.
+
+00:43:38.430 --> 00:43:40.910
+So it's still somewhat sensitive, but
+
+00:43:40.910 --> 00:43:42.960
+now if this guy invades the red zone,
+
+00:43:42.960 --> 00:43:45.213
+he doesn't really have any impact.
+
+00:43:45.213 --> 00:43:48.220
+If he's off by himself, he has a little
+
+00:43:48.220 --> 00:43:49.510
+impact, but there has to be like
+
+00:43:49.510 --> 00:43:51.795
+another green that is also close.
+
+00:43:51.795 --> 00:43:54.569
+So this guy is a supporting guy, so if
+
+00:43:54.570 --> 00:43:55.310
+I take him away.
+
+00:43:55.970 --> 00:43:57.400
+Then this guy is not going to have too
+
+00:43:57.400 --> 00:43:58.380
+much effect out here.
+
+00:43:59.460 --> 00:44:02.280
+And obviously as I increase K that.
+
+00:44:02.730 --> 00:44:06.350
+Happens even more so now this has
+
+00:44:06.350 --> 00:44:08.240
+relatively little influence.
+
+00:44:08.310 --> 00:44:08.890
+
+
+00:44:10.540 --> 00:44:12.510
+A single point by itself can't do too
+
+00:44:12.510 --> 00:44:14.670
+much if you have K = 5.
+
+00:44:17.270 --> 00:44:19.740
+And then as I change again, you'll see
+
+00:44:19.740 --> 00:44:21.760
+that the decision boundary becomes a
+
+00:44:21.760 --> 00:44:22.430
+lot smoother.
+
+00:44:22.430 --> 00:44:23.599
+So here's K = 1.
+
+00:44:23.600 --> 00:44:24.890
+Notice how there's like little blue
+
+00:44:24.890 --> 00:44:25.520
+islands.
+
+00:44:26.550 --> 00:44:29.549
+K = 3 the islands go away, but it's
+
+00:44:29.550 --> 00:44:30.410
+still mostly.
+
+00:44:30.410 --> 00:44:32.630
+There's like a little tiny blue area
+
+00:44:32.630 --> 00:44:34.490
+here, but it's a kind of jagged
+
+00:44:34.490 --> 00:44:35.490
+decision boundary.
+
+00:44:36.110 --> 00:44:39.870
+K = 5 Now there's only three regions.
+
+00:44:40.810 --> 00:44:43.510
+And K = 7, the boundaries get smoother.
+
+00:44:44.680 --> 00:44:47.200
+Also it's worth noting that if K = 1,
+
+00:44:47.200 --> 00:44:48.870
+you can never have any training error.
+
+00:44:48.870 --> 00:44:51.890
+So obviously like every training point
+
+00:44:51.890 --> 00:44:53.930
+will be closest to itself, so therefore
+
+00:44:53.930 --> 00:44:55.163
+it will make the correct prediction, it
+
+00:44:55.163 --> 00:44:56.350
+will predict its own value.
+
+00:44:57.170 --> 00:44:58.740
+Unless you have a bunch of points that
+
+00:44:58.740 --> 00:45:00.720
+are right on top of each other, but
+
+00:45:00.720 --> 00:45:02.510
+that's kind of a weird edge case.
+
+00:45:03.260 --> 00:45:06.840
+And but if K = 7, you can actually have
+
+00:45:06.840 --> 00:45:07.820
+misclassifications.
+
+00:45:07.820 --> 00:45:10.970
+So there's a green points that would be
+
+00:45:10.970 --> 00:45:12.536
+that are in the training data but would
+
+00:45:12.536 --> 00:45:14.200
+be classified as blue.
+
+00:45:19.540 --> 00:45:22.166
+So some comments on KNN.
+
+00:45:22.166 --> 00:45:26.130
+So it's really simple, which is a good
+
+00:45:26.130 --> 00:45:26.410
+thing.
+
+00:45:27.200 --> 00:45:29.440
+It's an excellent baseline and
+
+00:45:29.440 --> 00:45:30.660
+sometimes it's hard to beat.
+
+00:45:30.660 --> 00:45:33.050
+For example, we'll look at the digits
+
+00:45:33.050 --> 00:45:36.740
+task later the digit cannon with like
+
+00:45:36.740 --> 00:45:39.590
+some relatively simple like feature
+
+00:45:39.590 --> 00:45:40.540
+transformations.
+
+00:45:41.220 --> 00:45:43.330
+Can do as well as any other algorithm
+
+00:45:43.330 --> 00:45:44.500
+on digits.
+
+00:45:45.480 --> 00:45:47.220
+Even the very simple case that I give
+
+00:45:47.220 --> 00:45:50.080
+you gets within a couple percent error
+
+00:45:50.080 --> 00:45:52.040
+of the best error that's reported on
+
+00:45:52.040 --> 00:45:52.600
+that data set.
+
+00:45:55.640 --> 00:45:56.820
+Yeah, so it's simple.
+
+00:45:56.820 --> 00:45:57.540
+Hard to be in.
+
+00:45:57.540 --> 00:45:59.408
+Naturally scales with the data.
+
+00:45:59.408 --> 00:46:02.659
+So if you can apply CNN even if you
+
+00:46:02.660 --> 00:46:04.100
+only have one training example per
+
+00:46:04.100 --> 00:46:06.312
+class, and you can also apply if you
+
+00:46:06.312 --> 00:46:07.970
+have a million training examples per
+
+00:46:07.970 --> 00:46:08.370
+class.
+
+00:46:08.370 --> 00:46:10.050
+And it will tend to get better the more
+
+00:46:10.050 --> 00:46:11.169
+data you have.
+
+00:46:11.760 --> 00:46:13.380
+And if you only have one training data
+
+00:46:13.380 --> 00:46:15.160
+per class, A lot of other algorithms
+
+00:46:15.160 --> 00:46:16.680
+can't be used because there's not
+
+00:46:16.680 --> 00:46:18.980
+enough data to fit models to your one
+
+00:46:18.980 --> 00:46:22.040
+example, but K and can be used so for
+
+00:46:22.040 --> 00:46:22.970
+things like.
+
+00:46:23.720 --> 00:46:26.090
+Person like identity verification or
+
+00:46:26.090 --> 00:46:26.330
+something?
+
+00:46:26.330 --> 00:46:27.850
+You might only have one example of a
+
+00:46:27.850 --> 00:46:29.420
+face and you need to match based on
+
+00:46:29.420 --> 00:46:30.560
+that example.
+
+00:46:30.560 --> 00:46:31.880
+Then you're almost certainly going to
+
+00:46:31.880 --> 00:46:34.510
+end up using nearest neighbor as part
+
+00:46:34.510 --> 00:46:35.300
+of your algorithm.
+
+00:46:37.250 --> 00:46:40.040
+Higher K gives you smoother functions,
+
+00:46:40.040 --> 00:46:42.330
+so if you increase K you get a smoother
+
+00:46:42.330 --> 00:46:43.180
+prediction function.
+
+00:46:44.630 --> 00:46:47.500
+Now 1 disadvantage of K&N is that it
+
+00:46:47.500 --> 00:46:48.440
+can be slow.
+
+00:46:48.440 --> 00:46:50.910
+So in homework one, if you apply your
+
+00:46:50.910 --> 00:46:52.965
+full test set to the full training set,
+
+00:46:52.965 --> 00:46:56.390
+it will take 10s of minutes to
+
+00:46:56.390 --> 00:46:57.220
+evaluate.
+
+00:46:58.100 --> 00:47:00.080
+Maybe 30 minutes or 60 minutes.
+
+00:47:01.660 --> 00:47:03.210
+But there's tricks to speed it up.
+
+00:47:03.210 --> 00:47:05.300
+So like a simple thing that makes a
+
+00:47:05.300 --> 00:47:07.360
+little bit of impact is that when
+
+00:47:07.360 --> 00:47:11.950
+you're minimizing the L2 distance of XI
+
+00:47:11.950 --> 00:47:14.780
+and XT, you can actually like expand it
+
+00:47:14.780 --> 00:47:16.490
+and then notice that some terms don't
+
+00:47:16.490 --> 00:47:17.380
+have any impact.
+
+00:47:17.380 --> 00:47:17.880
+So.
+
+00:47:18.670 --> 00:47:19.645
+XT is the.
+
+00:47:19.645 --> 00:47:21.745
+I want to find the minimum training
+
+00:47:21.745 --> 00:47:24.910
+image indexed by I that minimizes the
+
+00:47:24.910 --> 00:47:27.930
+distance from all my Xis to XT which is
+
+00:47:27.930 --> 00:47:28.890
+a test image.
+
+00:47:28.890 --> 00:47:32.905
+It doesn't depend on this X t ^2 or the
+
+00:47:32.905 --> 00:47:35.910
+XT transpose XT and so I don't need to
+
+00:47:35.910 --> 00:47:36.530
+compute that.
+
+00:47:37.170 --> 00:47:39.170
+Also, this only needs to be computed
+
+00:47:39.170 --> 00:47:40.460
+once per training image.
+
+00:47:41.410 --> 00:47:43.405
+Not for every single XT that I'm
+
+00:47:43.405 --> 00:47:45.905
+testing, not for every test image that
+
+00:47:45.905 --> 00:47:47.509
+test example that I'm testing.
+
+00:47:48.220 --> 00:47:51.460
+And so it this is the only thing that
+
+00:47:51.460 --> 00:47:52.860
+you have to compute for every pair of
+
+00:47:52.860 --> 00:47:54.060
+training and test examples.
+
+00:47:56.600 --> 00:47:59.517
+In a GPU you can actually do the.
+
+00:47:59.517 --> 00:48:01.770
+You could do the MNIST nearest neighbor
+
+00:48:01.770 --> 00:48:03.595
+in sub second.
+
+00:48:03.595 --> 00:48:06.260
+It's extremely fast, it's just not fast
+
+00:48:06.260 --> 00:48:06.830
+on a CPU.
+
+00:48:08.020 --> 00:48:09.475
+There's also approximate nearest
+
+00:48:09.475 --> 00:48:11.560
+neighbor methods like flan, or even
+
+00:48:11.560 --> 00:48:13.930
+exact nearest neighbor methods that are
+
+00:48:13.930 --> 00:48:15.970
+much more efficient than the simple
+
+00:48:15.970 --> 00:48:17.310
+method that you would want to use for
+
+00:48:17.310 --> 00:48:17.750
+the assignment.
+
+00:48:20.720 --> 00:48:22.010
+Another thing that's nice is that
+
+00:48:22.010 --> 00:48:24.020
+there's no training time, so there's
+
+00:48:24.020 --> 00:48:25.243
+not really any training.
+
+00:48:25.243 --> 00:48:27.800
+The training data is your model, so you
+
+00:48:27.800 --> 00:48:29.115
+don't have to do anything to train it.
+
+00:48:29.115 --> 00:48:30.760
+You just get your data, you input the
+
+00:48:30.760 --> 00:48:30.950
+data.
+
+00:48:32.220 --> 00:48:33.680
+And last year to learn a distance
+
+00:48:33.680 --> 00:48:34.940
+function or learned features or
+
+00:48:34.940 --> 00:48:35.570
+something like that.
+
+00:48:37.730 --> 00:48:41.170
+Another thing is that with infinite
+
+00:48:41.170 --> 00:48:43.910
+examples, one nearest neighbor has
+
+00:48:43.910 --> 00:48:48.030
+provable is provably has error that is
+
+00:48:48.030 --> 00:48:50.140
+at most twice the Bayes optimal error.
+
+00:48:52.250 --> 00:48:55.640
+But that's kind of a useless, somewhat
+
+00:48:55.640 --> 00:48:59.573
+useless claim because you never have
+
+00:48:59.573 --> 00:49:02.116
+infinite examples, and if you have and
+
+00:49:02.116 --> 00:49:05.550
+so I'll explain why that thing works.
+
+00:49:05.550 --> 00:49:07.880
+I'm going to have to write on chalk so
+
+00:49:07.880 --> 00:49:09.220
+this might not carry over to the
+
+00:49:09.220 --> 00:49:12.101
+recording, but basically the idea is
+
+00:49:12.101 --> 00:49:15.949
+that if you have if you have infinite
+
+00:49:15.949 --> 00:49:17.509
+examples, then what it means is that
+
+00:49:17.510 --> 00:49:19.630
+for any possible feature value where
+
+00:49:19.630 --> 00:49:21.280
+there's non 0 probability.
+
+00:49:21.380 --> 00:49:23.040
+You've got infinite examples on that
+
+00:49:23.040 --> 00:49:24.310
+one feature value as well.
+
+00:49:25.210 --> 00:49:28.150
+And so when you assign a new test,
+
+00:49:28.150 --> 00:49:30.430
+point to that to a label.
+
+00:49:31.130 --> 00:49:34.870
+You're randomly choosing one of those
+
+00:49:34.870 --> 00:49:37.010
+infinite samples that has the exact
+
+00:49:37.010 --> 00:49:38.770
+same features as your test point.
+
+00:49:39.470 --> 00:49:42.140
+So if we look at a binary, this is for
+
+00:49:42.140 --> 00:49:43.740
+binary classification.
+
+00:49:43.740 --> 00:49:47.570
+So let's say that we have like.
+
+00:49:48.850 --> 00:49:52.940
+Given some, given some features X, this
+
+00:49:52.940 --> 00:49:54.580
+is just like the X of the test that I
+
+00:49:54.580 --> 00:49:55.210
+sampled.
+
+00:49:55.850 --> 00:49:59.360
+Let's say probability of y = 1 equals
+
+00:49:59.360 --> 00:50:00.050
+epsilon.
+
+00:50:00.720 --> 00:50:07.199
+And so probability of y = 0 given X = 1
+
+00:50:07.200 --> 00:50:08.330
+minus epsilon.
+
+00:50:09.650 --> 00:50:12.380
+Then when I sample a test value and
+
+00:50:12.380 --> 00:50:14.000
+let's say epsilon is really small.
+
+00:50:16.060 --> 00:50:18.710
+When I sample a test value, one thing
+
+00:50:18.710 --> 00:50:21.123
+that could happen is that I could
+
+00:50:21.123 --> 00:50:23.335
+sample one of these epsilon probability
+
+00:50:23.335 --> 00:50:27.360
+test values or test samples, and so the
+
+00:50:27.360 --> 00:50:28.469
+true label is 1.
+
+00:50:29.460 --> 00:50:33.010
+And then my error will be epsilon times
+
+00:50:33.010 --> 00:50:34.320
+1 minus epsilon.
+
+00:50:35.560 --> 00:50:38.520
+Or more probably, if Epsilon is small,
+
+00:50:38.520 --> 00:50:40.160
+I could sample one of the test samples
+
+00:50:40.160 --> 00:50:41.299
+where y = 0.
+
+00:50:42.420 --> 00:50:45.550
+And then my probability of sampling
+
+00:50:45.550 --> 00:50:47.634
+that is 1 minus epsilon and the
+
+00:50:47.634 --> 00:50:49.180
+probability of an error given that I
+
+00:50:49.180 --> 00:50:50.940
+sampled it is epsilon.
+
+00:50:50.940 --> 00:50:52.985
+So that's the probability that then I
+
+00:50:52.985 --> 00:50:54.149
+sample a training sample.
+
+00:50:54.149 --> 00:50:56.080
+I randomly choose a training sample of
+
+00:50:56.080 --> 00:50:58.020
+all the exact match matching training
+
+00:50:58.020 --> 00:51:00.390
+samples that has that class.
+
+00:51:01.330 --> 00:51:02.760
+And so the total error.
+
+00:51:03.790 --> 00:51:09.105
+Is Epsilon is 2 epsilon minus two
+
+00:51:09.105 --> 00:51:10.480
+epsilon squared?
+
+00:51:12.440 --> 00:51:15.130
+As Epsilon gets really small, this guy
+
+00:51:15.130 --> 00:51:16.350
+goes away, right?
+
+00:51:16.350 --> 00:51:18.540
+This will go to zero faster than this.
+
+00:51:19.490 --> 00:51:22.950
+And so my error is 2 epsilon.
+
+00:51:23.610 --> 00:51:26.000
+But the best thing I could have done
+
+00:51:26.000 --> 00:51:27.680
+was just chosen.
+
+00:51:27.680 --> 00:51:30.420
+In this case, the optimal decision
+
+00:51:30.420 --> 00:51:33.220
+would have been to choose Class 0 every
+
+00:51:33.220 --> 00:51:35.137
+time in this scenario, because this is
+
+00:51:35.137 --> 00:51:37.370
+the more probable one, and the error
+
+00:51:37.370 --> 00:51:38.970
+for this would just be epsilon.
+
+00:51:38.970 --> 00:51:41.014
+So my nearest neighbor error is 2
+
+00:51:41.014 --> 00:51:41.385
+epsilon.
+
+00:51:41.385 --> 00:51:43.240
+The optimal error is epsilon.
+
+00:51:44.950 --> 00:51:46.950
+So the reason that I show the
+
+00:51:46.950 --> 00:51:49.540
+derivation of that theorem is just
+
+00:51:49.540 --> 00:51:50.180
+that.
+
+00:51:50.300 --> 00:51:50.890
+
+
+00:51:52.000 --> 00:51:54.090
+It's like kind of ridiculously
+
+00:51:54.090 --> 00:51:54.606
+implausible.
+
+00:51:54.606 --> 00:51:56.910
+So the theorem only holds if you
+
+00:51:56.910 --> 00:51:58.626
+actually have infinite training samples
+
+00:51:58.626 --> 00:52:00.479
+for every single possible value of the
+
+00:52:00.480 --> 00:52:01.050
+features.
+
+00:52:01.050 --> 00:52:04.327
+So while while theoretically with
+
+00:52:04.327 --> 00:52:06.490
+infinite training samples one NN
+
+00:52:06.490 --> 00:52:08.120
+has error, that's at most twice the
+
+00:52:08.120 --> 00:52:10.950
+Bayes optimal error rate, in practice
+
+00:52:10.950 --> 00:52:12.355
+like that tells you absolutely nothing
+
+00:52:12.355 --> 00:52:12.870
+at all.
+
+00:52:12.870 --> 00:52:14.650
+So I just want to mention that because
+
+00:52:14.650 --> 00:52:16.690
+it's an often, it's an often quoted
+
+00:52:16.690 --> 00:52:17.690
+thing about nearest neighbor.
+
+00:52:17.690 --> 00:52:18.880
+It doesn't mean that it's any good,
+
+00:52:18.880 --> 00:52:21.980
+although it is good, just not for that.
+
+00:52:23.180 --> 00:52:24.420
+So then.
+
+00:52:24.500 --> 00:52:24.950
+
+
+00:52:25.830 --> 00:52:27.710
+So that was nearest neighbor.
+
+00:52:27.710 --> 00:52:29.570
+Now I want to talk a little bit about
+
+00:52:29.570 --> 00:52:31.930
+error, how we measure it and what
+
+00:52:31.930 --> 00:52:32.560
+causes it.
+
+00:52:33.690 --> 00:52:34.300
+So.
+
+00:52:34.950 --> 00:52:36.660
+When we measure and analyze
+
+00:52:36.660 --> 00:52:38.080
+classification error.
+
+00:52:39.760 --> 00:52:43.060
+The most common sounds a little
+
+00:52:43.060 --> 00:52:45.760
+redundant, but the most common way to
+
+00:52:45.760 --> 00:52:48.320
+measure the error of a classifier is
+
+00:52:48.320 --> 00:52:50.510
+with the classification error, which is
+
+00:52:50.510 --> 00:52:51.930
+the percent of examples that are
+
+00:52:51.930 --> 00:52:52.440
+incorrect.
+
+00:52:53.400 --> 00:52:55.470
+So mathematically it's just the sum
+
+00:52:55.470 --> 00:52:56.140
+over.
+
+00:52:57.850 --> 00:53:00.229
+I'm assuming that this like not equal
+
+00:53:00.230 --> 00:53:02.829
+sign just returns A1 or A01 if they're
+
+00:53:02.829 --> 00:53:04.609
+not equal, 0 if they're equal.
+
+00:53:05.120 --> 00:53:08.716
+And so it's just a count of the number
+
+00:53:08.716 --> 00:53:10.120
+of cases where the prediction is
+
+00:53:10.120 --> 00:53:12.390
+different than the true value divided
+
+00:53:12.390 --> 00:53:13.610
+by the number of cases that are
+
+00:53:13.610 --> 00:53:14.140
+evaluated.
+
+00:53:15.550 --> 00:53:17.570
+And then if you want to provide more
+
+00:53:17.570 --> 00:53:19.220
+insight into the kinds of errors that
+
+00:53:19.220 --> 00:53:21.030
+you get, you would use a confusion
+
+00:53:21.030 --> 00:53:21.590
+matrix.
+
+00:53:22.400 --> 00:53:24.950
+So a confusion matrix is a count of for
+
+00:53:24.950 --> 00:53:26.379
+each how many.
+
+00:53:26.380 --> 00:53:27.533
+There's two ways of doing it.
+
+00:53:27.533 --> 00:53:29.370
+One is just count wise.
+
+00:53:29.370 --> 00:53:32.850
+How many examples had a true prediction
+
+00:53:32.850 --> 00:53:35.580
+or a true value of 1 label and a
+
+00:53:35.580 --> 00:53:37.200
+predicted value of another label.
+
+00:53:37.860 --> 00:53:40.242
+So here these are the true labels.
+
+00:53:40.242 --> 00:53:43.210
+These are the predicted labels, and
+
+00:53:43.210 --> 00:53:48.520
+sometimes you normalize it by the
+
+00:53:48.520 --> 00:53:50.620
+fraction of true labels, typically.
+
+00:53:50.620 --> 00:53:53.352
+So this means that out of all of the
+
+00:53:53.352 --> 00:53:55.460
+true labels that were set, OSA,
+
+00:53:55.460 --> 00:53:58.230
+whatever that means of 100% of them,
+
+00:53:58.230 --> 00:53:59.760
+were assigned to set OSA.
+
+00:54:01.330 --> 00:54:04.890
+Out of all the test samples where the
+
+00:54:04.890 --> 00:54:07.762
+true label was versicolor, 62% were
+
+00:54:07.762 --> 00:54:10.740
+assigned a versicolor and 38% were
+
+00:54:10.740 --> 00:54:12.210
+assigned to VIRGINICA.
+
+00:54:13.150 --> 00:54:15.950
+And out of all the test samples where
+
+00:54:15.950 --> 00:54:18.320
+the true label is virginica, 100% were
+
+00:54:18.320 --> 00:54:19.650
+assigned to virginica.
+
+00:54:19.650 --> 00:54:21.610
+So this tells you like a little bit
+
+00:54:21.610 --> 00:54:22.950
+more than the classification error,
+
+00:54:22.950 --> 00:54:24.420
+because now you can see there's only
+
+00:54:24.420 --> 00:54:26.590
+mistakes made on this versa color and
+
+00:54:26.590 --> 00:54:28.250
+it only gets confused with virginica.
+
+00:54:30.900 --> 00:54:32.760
+So I'll give you an example here.
+
+00:54:34.790 --> 00:54:38.620
+So there's no document projector thing,
+
+00:54:38.620 --> 00:54:39.480
+unfortunately.
+
+00:54:40.140 --> 00:54:44.077
+Which I will try to fix, but I will
+
+00:54:44.077 --> 00:54:45.870
+this is simple enough that I can just
+
+00:54:45.870 --> 00:54:48.175
+draw on this slide or type on this
+
+00:54:48.175 --> 00:54:48.410
+slide.
+
+00:54:50.880 --> 00:54:51.120
+Yeah.
+
+00:54:54.590 --> 00:54:55.370
+
+
+00:54:58.460 --> 00:54:59.040
+There.
+
+00:55:05.270 --> 00:55:07.190
+OK, I don't want to figure that out.
+
+00:55:07.190 --> 00:55:08.530
+So.
+
+00:55:14.470 --> 00:55:14.940
+I.
+
+00:55:21.420 --> 00:55:23.060
+That sounds good.
+
+00:55:23.060 --> 00:55:23.500
+There it goes.
+
+00:55:25.990 --> 00:55:29.845
+OK, so I will just verbally do it.
+
+00:55:29.845 --> 00:55:31.770
+So let's say so these are the true
+
+00:55:31.770 --> 00:55:32.055
+labels.
+
+00:55:32.055 --> 00:55:34.430
+These are the predicted labels.
+
+00:55:34.430 --> 00:55:36.020
+What is the classification error?
+
+00:55:58.730 --> 00:56:00.082
+Yeah, 3 / 7.
+
+00:56:00.082 --> 00:56:04.860
+So there's 77 rows right that are other
+
+00:56:04.860 --> 00:56:08.463
+than the label row, and there are three
+
+00:56:08.463 --> 00:56:10.023
+three times that.
+
+00:56:10.023 --> 00:56:12.300
+One of the values is no and one of the
+
+00:56:12.300 --> 00:56:13.090
+values is yes.
+
+00:56:13.090 --> 00:56:16.580
+So the classification error is 3 / 7.
+
+00:56:17.810 --> 00:56:21.170
+And let's do the confusion matrix.
+
+00:56:28.020 --> 00:56:30.960
+Right, so the so the true label.
+
+00:56:30.960 --> 00:56:33.060
+So how many times do I have a true
+
+00:56:33.060 --> 00:56:35.070
+label that's known and a predicted
+
+00:56:35.070 --> 00:56:35.960
+label that's no.
+
+00:56:37.520 --> 00:56:38.080
+Two.
+
+00:56:38.080 --> 00:56:39.570
+OK, how many times do I have a true
+
+00:56:39.570 --> 00:56:41.265
+label that's known and predicted label?
+
+00:56:41.265 --> 00:56:41.850
+That's yes.
+
+00:56:45.390 --> 00:56:48.026
+OK, how many times do I have a true
+
+00:56:48.026 --> 00:56:49.535
+label that's yes and predicted label
+
+00:56:49.535 --> 00:56:50.060
+that's no?
+
+00:56:51.800 --> 00:56:54.190
+One, and I guess I have two of the
+
+00:56:54.190 --> 00:56:54.540
+others.
+
+00:56:55.650 --> 00:56:56.329
+Is that right?
+
+00:56:56.330 --> 00:56:58.300
+I have two times that there's a true
+
+00:56:58.300 --> 00:57:00.420
+label yes and a predicted label of no.
+
+00:57:00.420 --> 00:57:01.260
+Is that right?
+
+00:57:03.730 --> 00:57:05.049
+Or no, yes and yes.
+
+00:57:05.050 --> 00:57:06.050
+I'm on yes and yes.
+
+00:57:06.050 --> 00:57:06.920
+Two, yes.
+
+00:57:07.890 --> 00:57:08.740
+OK, cool.
+
+00:57:08.740 --> 00:57:09.380
+All right, good.
+
+00:57:09.380 --> 00:57:09.903
+Thumbs up.
+
+00:57:09.903 --> 00:57:11.750
+All right, so this sums up to 7.
+
+00:57:11.750 --> 00:57:13.510
+So this is a confusion matrix.
+
+00:57:13.510 --> 00:57:14.920
+That's just in terms of the total
+
+00:57:14.920 --> 00:57:15.380
+counts.
+
+00:57:16.340 --> 00:57:18.510
+And then if I want to convert this to.
+
+00:57:19.290 --> 00:57:23.000
+A normalized matrix, which is basically
+
+00:57:23.000 --> 00:57:25.330
+the probability that I predict a
+
+00:57:25.330 --> 00:57:27.530
+particular value given the true label.
+
+00:57:27.530 --> 00:57:29.540
+So this will be the probability that I
+
+00:57:29.540 --> 00:57:32.025
+predicted no given that the true label
+
+00:57:32.025 --> 00:57:32.720
+is no.
+
+00:57:33.360 --> 00:57:35.280
+Then I just divide by the total count
+
+00:57:35.280 --> 00:57:37.230
+or I divide by the.
+
+00:57:37.880 --> 00:57:40.250
+By the number of examples in each row.
+
+00:57:40.250 --> 00:57:42.580
+So this one would be what?
+
+00:57:42.580 --> 00:57:44.295
+What's the probability that I predict
+
+00:57:44.295 --> 00:57:46.260
+no given that the true answer is no?
+
+00:57:48.530 --> 00:57:49.200
+F right?
+
+00:57:49.200 --> 00:57:50.760
+I just divide this by 4.
+
+00:57:51.790 --> 00:57:53.680
+And likewise divide this by 4.
+
+00:57:53.680 --> 00:57:55.360
+And what is the probability that I
+
+00:57:55.360 --> 00:57:56.800
+predict no given that the true answer
+
+00:57:56.800 --> 00:57:57.340
+is yes?
+
+00:57:59.660 --> 00:58:02.440
+Right 1 / 3 and this will be 2 / 3.
+
+00:58:03.400 --> 00:58:05.210
+So that's how you compute the confusion
+
+00:58:05.210 --> 00:58:07.260
+matrix and the classification error.
+
+00:58:12.880 --> 00:58:15.560
+All right, so for regression error.
+
+00:58:15.650 --> 00:58:16.380
+
+
+00:58:17.890 --> 00:58:20.920
+You will usually use one of these.
+
+00:58:20.920 --> 00:58:23.316
+Root mean squared error is probably one
+
+00:58:23.316 --> 00:58:26.320
+of the most common, so that's just
+
+00:58:26.320 --> 00:58:27.280
+written there.
+
+00:58:27.280 --> 00:58:30.790
+You take this sum of squared values,
+
+00:58:30.790 --> 00:58:33.780
+and then you divide it by the total
+
+00:58:33.780 --> 00:58:34.989
+number of values.
+
+00:58:34.990 --> 00:58:37.580
+N is the range of I.
+
+00:58:38.250 --> 00:58:40.050
+And then you take the square root.
+
+00:58:40.050 --> 00:58:42.630
+So sometimes the mistake you can make
+
+00:58:42.630 --> 00:58:44.000
+on this is to do the order of
+
+00:58:44.000 --> 00:58:44.950
+operations wrong.
+
+00:58:45.570 --> 00:58:47.855
+Just remember it's in the name root
+
+00:58:47.855 --> 00:58:48.846
+mean squared.
+
+00:58:48.846 --> 00:58:53.260
+So you take the and then so it's like
+
+00:58:53.260 --> 00:58:55.594
+right now as an equation it's the root
+
+00:58:55.594 --> 00:58:58.346
+then the mean divided by north and then
+
+00:58:58.346 --> 00:59:00.946
+you have this summation squared so you
+
+00:59:00.946 --> 00:59:01.428
+take.
+
+00:59:01.428 --> 00:59:02.210
+So yeah.
+
+00:59:05.010 --> 00:59:05.500
+All right.
+
+00:59:05.500 --> 00:59:08.490
+So that's so root squared is kind of
+
+00:59:08.490 --> 00:59:09.960
+sensitive to your outliers.
+
+00:59:09.960 --> 00:59:13.850
+If you had if you had like some things
+
+00:59:13.850 --> 00:59:15.510
+that are mislabeled or just really
+
+00:59:15.510 --> 00:59:17.510
+weird examples they could end up
+
+00:59:17.510 --> 00:59:19.260
+dominating your RMSE error.
+
+00:59:19.260 --> 00:59:21.560
+So if like one of these guys, if I'm
+
+00:59:21.560 --> 00:59:23.490
+doing some regression or something and
+
+00:59:23.490 --> 00:59:26.500
+one of them is like way, way off,
+
+00:59:26.500 --> 00:59:29.122
+that's going to be the that the root
+
+00:59:29.122 --> 00:59:31.580
+mean squared error of that one example
+
+00:59:31.580 --> 00:59:33.060
+is going to be most of the.
+
+00:59:33.130 --> 00:59:34.010
+Mean squared error.
+
+00:59:35.430 --> 00:59:36.930
+So you can also sometimes do mean
+
+00:59:36.930 --> 00:59:39.000
+absolute error that will be less
+
+00:59:39.000 --> 00:59:40.940
+sensitive to outliers, things that have
+
+00:59:40.940 --> 00:59:42.000
+extraordinary error.
+
+00:59:43.150 --> 00:59:45.700
+And then both of these are sensitive to
+
+00:59:45.700 --> 00:59:46.480
+your units.
+
+00:59:46.480 --> 00:59:48.590
+So if you're measuring the root mean
+
+00:59:48.590 --> 00:59:51.090
+squared error and feet versus meters,
+
+00:59:51.090 --> 00:59:52.740
+you'll obviously get different values.
+
+00:59:53.900 --> 00:59:56.120
+And so a lot of times sometimes people
+
+00:59:56.120 --> 01:00:01.250
+use R2, which is the amount of
+
+01:00:01.250 --> 01:00:02.520
+explained variance.
+
+01:00:02.520 --> 01:00:07.329
+So you're normalizing so the R2 is 1
+
+01:00:07.330 --> 01:00:09.740
+minus this thing here, this ratio.
+
+01:00:10.470 --> 01:00:13.583
+And the numerator of this ratio is the
+
+01:00:13.583 --> 01:00:16.890
+sum of squared difference between your
+
+01:00:16.890 --> 01:00:18.460
+prediction and the true value.
+
+01:00:19.470 --> 01:00:21.535
+So if you divide that by N, it's the
+
+01:00:21.535 --> 01:00:21.800
+variance.
+
+01:00:21.800 --> 01:00:23.930
+It's the conditional variance of the.
+
+01:00:24.860 --> 01:00:27.936
+True prediction given your model's
+
+01:00:27.936 --> 01:00:28.819
+prediction.
+
+01:00:30.130 --> 01:00:32.746
+And then you divide it by the variance
+
+01:00:32.746 --> 01:00:35.854
+or the OR you could have a one over
+
+01:00:35.854 --> 01:00:37.402
+north here and one over north here and
+
+01:00:37.402 --> 01:00:39.230
+then this would be predicted the
+
+01:00:39.230 --> 01:00:40.805
+conditional variance and this is the
+
+01:00:40.805 --> 01:00:42.060
+variance of the true labels.
+
+01:00:43.280 --> 01:00:46.710
+So 1 minus that ratio is the amount of
+
+01:00:46.710 --> 01:00:48.160
+the variance that's explained and it
+
+01:00:48.160 --> 01:00:49.340
+doesn't have any units.
+
+01:00:49.340 --> 01:00:52.359
+If you measure it in feet or meters,
+
+01:00:52.360 --> 01:00:53.770
+you're going to get exactly the same
+
+01:00:53.770 --> 01:00:55.440
+value because the feet or the meters
+
+01:00:55.440 --> 01:00:57.519
+will cancel out and that ratio.
+
+01:01:00.130 --> 01:01:01.520
+That we might talk, well, we'll talk
+
+01:01:01.520 --> 01:01:03.120
+about that more perhaps when we talk
+
+01:01:03.120 --> 01:01:04.070
+about linear regression.
+
+01:01:05.230 --> 01:01:06.360
+But just worth knowing.
+
+01:01:07.750 --> 01:01:08.780
+At least at a high level.
+
+01:01:10.070 --> 01:01:12.100
+All right, so then there's a question
+
+01:01:12.100 --> 01:01:15.620
+of why if I fit a model as I can
+
+01:01:15.620 --> 01:01:18.120
+possibly fit it, then why do I still
+
+01:01:18.120 --> 01:01:20.230
+have error when I evaluate on my test
+
+01:01:20.230 --> 01:01:20.830
+samples?
+
+01:01:20.830 --> 01:01:23.060
+You'll see in your in your homework
+
+01:01:23.060 --> 01:01:24.670
+problem, you're not going to have any
+
+01:01:24.670 --> 01:01:26.180
+methods that achieve 0 error in
+
+01:01:26.180 --> 01:01:26.650
+testing.
+
+01:01:29.320 --> 01:01:31.050
+So there's several possible reasons.
+
+01:01:31.050 --> 01:01:33.280
+So one is that there could be an error
+
+01:01:33.280 --> 01:01:34.770
+that's intrinsic to the problem.
+
+01:01:34.770 --> 01:01:37.150
+It's not possible to have 0 error.
+
+01:01:37.150 --> 01:01:39.020
+So if you're trying to predict, for
+
+01:01:39.020 --> 01:01:41.660
+example, what the weather is tomorrow,
+
+01:01:41.660 --> 01:01:42.989
+then given your features, you're not
+
+01:01:42.990 --> 01:01:44.130
+going to have a perfect prediction.
+
+01:01:44.130 --> 01:01:45.666
+Nobody knows exactly what the weather
+
+01:01:45.666 --> 01:01:46.139
+is tomorrow.
+
+01:01:47.350 --> 01:01:49.350
+If you're trying to classify a
+
+01:01:49.350 --> 01:01:51.420
+handwritten character again, it might.
+
+01:01:51.420 --> 01:01:53.520
+You might not be able to get 0 error
+
+01:01:53.520 --> 01:01:55.630
+because somebody might write an A
+
+01:01:55.630 --> 01:01:57.370
+exactly the same way that somebody
+
+01:01:57.370 --> 01:02:00.260
+wrote a no another time or whatever.
+
+01:02:00.260 --> 01:02:02.190
+Sometimes it's just not possible to
+
+01:02:02.190 --> 01:02:04.630
+know exact, to be completely confident
+
+01:02:04.630 --> 01:02:07.783
+about what the true character of a
+
+01:02:07.783 --> 01:02:08.730
+handwritten character is.
+
+01:02:10.160 --> 01:02:11.810
+So there's a notion called the Bayes
+
+01:02:11.810 --> 01:02:14.410
+optimal error, and that's the error if
+
+01:02:14.410 --> 01:02:16.945
+the true function, the probability of
+
+01:02:16.945 --> 01:02:18.770
+the label given the data is known.
+
+01:02:18.770 --> 01:02:20.320
+So you can't do any better than that.
+
+01:02:23.510 --> 01:02:25.955
+Another source of error is called is
+
+01:02:25.955 --> 01:02:28.470
+model bias, which means that the model
+
+01:02:28.470 --> 01:02:29.970
+doesn't allow you to fit whatever you
+
+01:02:29.970 --> 01:02:30.200
+want.
+
+01:02:30.850 --> 01:02:33.600
+There's some things that some training
+
+01:02:33.600 --> 01:02:35.500
+data can't be fit necessarily.
+
+01:02:36.330 --> 01:02:39.290
+And so you can't achieve.
+
+01:02:39.290 --> 01:02:40.890
+Even if you had an infinite training
+
+01:02:40.890 --> 01:02:42.530
+set, you won't be able to achieve the
+
+01:02:42.530 --> 01:02:43.510
+Bayes optimal error.
+
+01:02:44.320 --> 01:02:47.030
+So one nearest neighbor, for example,
+
+01:02:47.030 --> 01:02:48.010
+has no bias.
+
+01:02:48.010 --> 01:02:50.550
+With one nearest neighbor you can fit
+
+01:02:50.550 --> 01:02:52.280
+the training set perfectly and if your
+
+01:02:52.280 --> 01:02:53.420
+test set comes from the same
+
+01:02:53.420 --> 01:02:54.160
+distribution.
+
+01:02:54.780 --> 01:02:56.519
+Then you're going to you're going to
+
+01:02:56.520 --> 01:02:57.860
+get twice the Bayes optimal error, but.
+
+01:02:59.130 --> 01:03:00.360
+You'll get close.
+
+01:03:01.040 --> 01:03:04.695
+So the One North has very minimal bias,
+
+01:03:04.695 --> 01:03:06.280
+I guess I should say.
+
+01:03:06.280 --> 01:03:08.060
+But if you're doing a linear fit, that
+
+01:03:08.060 --> 01:03:10.060
+has really high bias, because all you
+
+01:03:10.060 --> 01:03:10.850
+can do is fit a line.
+
+01:03:10.850 --> 01:03:12.147
+If the data is on a line, you'll still
+
+01:03:12.147 --> 01:03:13.390
+fit a line, it won't be a very good
+
+01:03:13.390 --> 01:03:13.540
+fit.
+
+01:03:15.390 --> 01:03:18.155
+Model variance means that if you were
+
+01:03:18.155 --> 01:03:20.290
+to sample different sets of data,
+
+01:03:20.290 --> 01:03:22.190
+you're going to come up with different
+
+01:03:22.190 --> 01:03:24.480
+predictions on your test data, or
+
+01:03:24.480 --> 01:03:26.870
+different parameters for your model.
+
+01:03:27.490 --> 01:03:31.100
+So the variance the.
+
+01:03:32.070 --> 01:03:34.070
+Bias and variance both have to do with
+
+01:03:34.070 --> 01:03:35.810
+the simplicity of your model.
+
+01:03:35.810 --> 01:03:37.780
+If you have a really complex model that
+
+01:03:37.780 --> 01:03:39.340
+can fit everything, anything.
+
+01:03:39.980 --> 01:03:42.600
+Then it's going to have low, then it's
+
+01:03:42.600 --> 01:03:44.892
+going to have low bias but high
+
+01:03:44.892 --> 01:03:45.220
+variance.
+
+01:03:45.220 --> 01:03:47.178
+If you have a really simple model, it's
+
+01:03:47.178 --> 01:03:50.216
+going to have high bias but low
+
+01:03:50.216 --> 01:03:50.650
+variance.
+
+01:03:52.150 --> 01:03:53.400
+The variance means that you have
+
+01:03:53.400 --> 01:03:55.200
+trouble fitting your model given a
+
+01:03:55.200 --> 01:03:56.510
+limited amount of training data.
+
+01:03:57.880 --> 01:03:59.030
+You can also have things like
+
+01:03:59.030 --> 01:04:00.850
+distribution shift that some things are
+
+01:04:00.850 --> 01:04:03.150
+more common and some samples are more
+
+01:04:03.150 --> 01:04:04.220
+common in the test set than the
+
+01:04:04.220 --> 01:04:06.450
+training set if they're not IID, which
+
+01:04:06.450 --> 01:04:07.610
+I discussed before.
+
+01:04:08.710 --> 01:04:10.350
+Or you could have in the worst case of
+
+01:04:10.350 --> 01:04:12.360
+function shift, which means that the.
+
+01:04:13.490 --> 01:04:16.375
+That the answer and the test data, the
+
+01:04:16.375 --> 01:04:17.691
+probability of a particular answer
+
+01:04:17.691 --> 01:04:20.023
+given the data given the features is
+
+01:04:20.023 --> 01:04:21.560
+different in testing than training.
+
+01:04:21.560 --> 01:04:24.305
+So one example is if you're trying if
+
+01:04:24.305 --> 01:04:26.065
+you're doing like language prediction
+
+01:04:26.065 --> 01:04:28.070
+and somebody says what is your favorite
+
+01:04:28.070 --> 01:04:31.250
+TV show and you trained based on data
+
+01:04:31.250 --> 01:04:36.197
+from 2010 to 2020, then probably the
+
+01:04:36.197 --> 01:04:38.192
+answer in that time range, the
+
+01:04:38.192 --> 01:04:40.047
+probability of different answers then
+
+01:04:40.047 --> 01:04:41.560
+is different than it is today.
+
+01:04:41.560 --> 01:04:42.980
+So you actually have.
+
+01:04:43.030 --> 01:04:44.470
+Changed your.
+
+01:04:44.470 --> 01:04:48.510
+If you're test set is from 2022, then
+
+01:04:48.510 --> 01:04:50.980
+the probability of Y the answer to that
+
+01:04:50.980 --> 01:04:53.910
+question is different in the test set
+
+01:04:53.910 --> 01:04:55.550
+than it is in a training set that came
+
+01:04:55.550 --> 01:04:57.130
+from 2000 to 2020.
+
+01:05:00.450 --> 01:05:03.714
+Then there's other things that are that
+
+01:05:03.714 --> 01:05:06.760
+are that are also can be issues if
+
+01:05:06.760 --> 01:05:08.210
+you're imperfectly optimized on the
+
+01:05:08.210 --> 01:05:08.880
+training set.
+
+01:05:09.660 --> 01:05:12.550
+Or if you are not able to optimize.
+
+01:05:13.420 --> 01:05:16.050
+For the same, if you're a training loss
+
+01:05:16.050 --> 01:05:17.480
+is different than your final
+
+01:05:17.480 --> 01:05:18.190
+evaluation.
+
+01:05:18.980 --> 01:05:20.450
+That's actually happens all the time
+
+01:05:20.450 --> 01:05:22.310
+because it's really hard to optimize
+
+01:05:22.310 --> 01:05:23.040
+for training error.
+
+01:05:26.620 --> 01:05:27.040
+So.
+
+01:05:28.040 --> 01:05:28.830
+Here's a question.
+
+01:05:28.830 --> 01:05:31.540
+So what happens if so?
+
+01:05:31.540 --> 01:05:34.222
+Suppose that you train a model and then
+
+01:05:34.222 --> 01:05:35.879
+you increase the number of training
+
+01:05:35.879 --> 01:05:38.200
+samples, and then you train it again.
+
+01:05:38.200 --> 01:05:40.170
+As you increase the number of training
+
+01:05:40.170 --> 01:05:41.880
+samples, do you expect the test error
+
+01:05:41.880 --> 01:05:43.850
+to go up or down or stay the same?
+
+01:05:48.170 --> 01:05:49.710
+So you'd expect it.
+
+01:05:49.710 --> 01:05:51.260
+Some people are saying down as you get
+
+01:05:51.260 --> 01:05:54.052
+more training data you should fit a
+
+01:05:54.052 --> 01:05:54.305
+better.
+
+01:05:54.305 --> 01:05:55.710
+You should have like a better
+
+01:05:55.710 --> 01:05:57.540
+understanding of your true parameters.
+
+01:05:57.540 --> 01:05:59.110
+So the test error should go down.
+
+01:05:59.870 --> 01:06:01.510
+So it might look something like this.
+
+01:06:03.130 --> 01:06:07.910
+If I get more training data and then I
+
+01:06:07.910 --> 01:06:09.170
+measure the training error.
+
+01:06:10.070 --> 01:06:12.510
+Do you expect the training error to go
+
+01:06:12.510 --> 01:06:14.080
+up or down or stay the same?
+
+01:06:16.740 --> 01:06:17.890
+There are how many people think it
+
+01:06:17.890 --> 01:06:18.560
+would go up?
+
+01:06:21.510 --> 01:06:23.280
+How many people think the training area
+
+01:06:23.280 --> 01:06:25.080
+would go down as they get more training
+
+01:06:25.080 --> 01:06:25.400
+data?
+
+01:06:27.750 --> 01:06:29.760
+OK, so there's a lot of uncertainty.
+
+01:06:29.760 --> 01:06:32.593
+So what I would expect is that the
+
+01:06:32.593 --> 01:06:35.410
+training error will go up because as
+
+01:06:35.410 --> 01:06:37.170
+you get more training data, it becomes
+
+01:06:37.170 --> 01:06:38.670
+harder to fit that data.
+
+01:06:38.670 --> 01:06:40.720
+Given the same model, it becomes harder
+
+01:06:40.720 --> 01:06:42.660
+and harder to fit an increasing size
+
+01:06:42.660 --> 01:06:43.250
+training set.
+
+01:06:44.120 --> 01:06:46.920
+And if you get infinite examples and
+
+01:06:46.920 --> 01:06:49.230
+you don't have any things like a
+
+01:06:49.230 --> 01:06:51.000
+function shift, then these two will
+
+01:06:51.000 --> 01:06:51.340
+meet.
+
+01:06:51.340 --> 01:06:54.122
+If you get infinite examples, then you
+
+01:06:54.122 --> 01:06:54.520
+will.
+
+01:06:54.520 --> 01:06:56.030
+You're training and tests are basically
+
+01:06:56.030 --> 01:06:56.520
+the same.
+
+01:06:57.140 --> 01:06:58.690
+And then you will have the same error,
+
+01:06:58.690 --> 01:07:00.030
+so they start to converge.
+
+01:07:02.070 --> 01:07:03.490
+And this is important concept
+
+01:07:03.490 --> 01:07:04.350
+generalization error.
+
+01:07:04.350 --> 01:07:06.530
+Generalization error is the difference
+
+01:07:06.530 --> 01:07:08.240
+between your test error and your
+
+01:07:08.240 --> 01:07:08.810
+training error.
+
+01:07:08.810 --> 01:07:10.805
+So your test error is your training
+
+01:07:10.805 --> 01:07:12.479
+error plus your generalization error.
+
+01:07:12.479 --> 01:07:15.250
+Generalization error is due to the
+
+01:07:15.250 --> 01:07:19.370
+ability of your or the failure of your
+
+01:07:19.370 --> 01:07:21.520
+model to make predictions on the data
+
+01:07:21.520 --> 01:07:22.500
+hasn't seen yet.
+
+01:07:22.500 --> 01:07:24.670
+So you could have something that has
+
+01:07:24.670 --> 01:07:26.480
+absolutely perfect training error but
+
+01:07:26.480 --> 01:07:28.370
+has enormous generalization error and
+
+01:07:28.370 --> 01:07:29.140
+that's no good.
+
+01:07:29.140 --> 01:07:30.780
+Or you could have something that has a
+
+01:07:30.780 --> 01:07:32.170
+lot of trouble fitting the training.
+
+01:07:32.230 --> 01:07:33.750
+Data, but its generalization error is
+
+01:07:33.750 --> 01:07:34.320
+very small.
+
+01:07:39.000 --> 01:07:39.460
+So.
+
+01:07:41.680 --> 01:07:43.470
+If you train so suppose you have
+
+01:07:43.470 --> 01:07:45.820
+infinite training examples, then
+
+01:07:45.820 --> 01:07:48.508
+eventually you're training error will
+
+01:07:48.508 --> 01:07:51.175
+reach some plateau, and your test error
+
+01:07:51.175 --> 01:07:53.239
+will also reach some plateau.
+
+01:07:54.150 --> 01:07:56.773
+This these will reach the same point if
+
+01:07:56.773 --> 01:07:58.640
+you don't have any function shift.
+
+01:07:58.640 --> 01:08:01.795
+So if you have some difference, if you
+
+01:08:01.795 --> 01:08:03.820
+have some gap to where they're
+
+01:08:03.820 --> 01:08:06.130
+converging, it either means that you
+
+01:08:06.130 --> 01:08:07.640
+have that you're not able to fully
+
+01:08:07.640 --> 01:08:10.056
+optimize your function, or that the
+
+01:08:10.056 --> 01:08:11.890
+that you have a function shift that the
+
+01:08:11.890 --> 01:08:13.160
+probability of the true label is
+
+01:08:13.160 --> 01:08:14.760
+changing between training and test.
+
+01:08:16.520 --> 01:08:19.117
+Now, this gap between the test area
+
+01:08:19.117 --> 01:08:20.750
+that you would get from infinite
+
+01:08:20.750 --> 01:08:22.733
+training examples and the actual test
+
+01:08:22.733 --> 01:08:24.310
+area that you're getting given finite
+
+01:08:24.310 --> 01:08:28.020
+training examples is due to the model
+
+01:08:28.020 --> 01:08:28.670
+variants.
+
+01:08:28.670 --> 01:08:30.615
+It's due to the model complexity and
+
+01:08:30.615 --> 01:08:32.500
+the inability to perfectly solve for
+
+01:08:32.500 --> 01:08:34.200
+the best parameters given your limited
+
+01:08:34.200 --> 01:08:34.770
+training data.
+
+01:08:35.900 --> 01:08:38.800
+And it can also be exacerbated by
+
+01:08:38.800 --> 01:08:40.840
+distribution shift if you like, your
+
+01:08:40.840 --> 01:08:42.710
+training data is more likely to sample
+
+01:08:42.710 --> 01:08:44.410
+some areas of the feature space than
+
+01:08:44.410 --> 01:08:45.110
+your test data.
+
+01:08:46.970 --> 01:08:49.990
+And this gap the training error.
+
+01:08:50.830 --> 01:08:52.876
+Is due to the limited power of your
+
+01:08:52.876 --> 01:08:55.360
+model to fit whatever whatever you give
+
+01:08:55.360 --> 01:08:55.590
+it.
+
+01:08:55.590 --> 01:08:58.200
+So it's due to the model bias, and it's
+
+01:08:58.200 --> 01:09:00.120
+also due to the unavoidable intrinsic
+
+01:09:00.120 --> 01:09:02.580
+error that even if you have infinite
+
+01:09:02.580 --> 01:09:04.180
+examples, there's some error that's
+
+01:09:04.180 --> 01:09:04.950
+unavoidable.
+
+01:09:05.780 --> 01:09:07.420
+Either because it's intrinsic to the
+
+01:09:07.420 --> 01:09:09.320
+problem or because your model has
+
+01:09:09.320 --> 01:09:10.250
+limited capacity.
+
+01:09:16.100 --> 01:09:16.590
+All right.
+
+01:09:16.590 --> 01:09:18.230
+So I'm bringing up a point that I
+
+01:09:18.230 --> 01:09:19.590
+raised earlier.
+
+01:09:20.930 --> 01:09:24.070
+And I want to see if you can still
+
+01:09:24.070 --> 01:09:25.350
+explain the answer.
+
+01:09:25.350 --> 01:09:27.510
+So why is it important to have a
+
+01:09:27.510 --> 01:09:28.570
+validation set?
+
+01:09:30.680 --> 01:09:32.180
+If I've got a bunch of models that I
+
+01:09:32.180 --> 01:09:35.400
+want to evaluate, why don't I just take
+
+01:09:35.400 --> 01:09:37.060
+do a train set and test set?
+
+01:09:37.710 --> 01:09:39.110
+Train them all in the training set,
+
+01:09:39.110 --> 01:09:40.760
+evaluate them all in the test set and
+
+01:09:40.760 --> 01:09:42.650
+then report the best performance.
+
+01:09:42.650 --> 01:09:43.970
+What's the issue with that?
+
+01:09:43.970 --> 01:09:46.120
+Why is that not a good procedure?
+
+01:09:47.970 --> 01:09:49.590
+I guess back with the orange shirt,
+
+01:09:49.590 --> 01:09:50.370
+easier in first.
+
+01:09:52.350 --> 01:09:54.756
+So your risk overfitting the model, so
+
+01:09:54.756 --> 01:09:56.190
+that the problem is that.
+
+01:09:56.980 --> 01:09:59.915
+You're the problem is that your test
+
+01:09:59.915 --> 01:10:02.840
+error measure will be biased, which
+
+01:10:02.840 --> 01:10:05.170
+means that it won't be the expected
+
+01:10:05.170 --> 01:10:07.620
+value is not the true value.
+
+01:10:07.620 --> 01:10:08.980
+In other words, you're going to tend to
+
+01:10:08.980 --> 01:10:11.400
+underestimate the error if you do this
+
+01:10:11.400 --> 01:10:13.800
+procedure because you're choosing the
+
+01:10:13.800 --> 01:10:15.529
+best model based on the test
+
+01:10:15.530 --> 01:10:16.430
+performance.
+
+01:10:16.430 --> 01:10:18.370
+But this test sample is just one random
+
+01:10:18.370 --> 01:10:19.880
+sample from the general test
+
+01:10:19.880 --> 01:10:21.250
+distribution, so if you're to take
+
+01:10:21.250 --> 01:10:22.530
+another sample, it might have a
+
+01:10:22.530 --> 01:10:23.200
+different answer.
+
+01:10:24.770 --> 01:10:28.290
+And there's been cases where one time
+
+01:10:28.290 --> 01:10:30.840
+somebody had some agency had some big
+
+01:10:30.840 --> 01:10:34.819
+challenge they had, they had, they
+
+01:10:34.820 --> 01:10:35.840
+thought they were doing the right
+
+01:10:35.840 --> 01:10:36.045
+thing.
+
+01:10:36.045 --> 01:10:37.898
+They had a test set, they had a train
+
+01:10:37.898 --> 01:10:38.104
+set.
+
+01:10:38.104 --> 01:10:40.827
+They said you can only evaluate on the
+
+01:10:40.827 --> 01:10:43.176
+train set and only test on the test
+
+01:10:43.176 --> 01:10:43.469
+set.
+
+01:10:43.470 --> 01:10:45.135
+But they provided both the train set
+
+01:10:45.135 --> 01:10:46.960
+and the test set to the researchers.
+
+01:10:47.600 --> 01:10:50.780
+And one group like iterated through a
+
+01:10:50.780 --> 01:10:53.400
+million different models and found a
+
+01:10:53.400 --> 01:10:55.451
+model that got that you could train on
+
+01:10:55.451 --> 01:10:57.080
+the train set and achieved perfect
+
+01:10:57.080 --> 01:10:58.400
+error on the test set.
+
+01:10:58.400 --> 01:11:00.182
+But then when they applied a held out
+
+01:11:00.182 --> 01:11:02.459
+test set, it did like really really
+
+01:11:02.460 --> 01:11:04.180
+badly, like almost chance performance.
+
+01:11:05.170 --> 01:11:08.930
+So the so training on your, even doing
+
+01:11:08.930 --> 01:11:10.319
+model selection on your.
+
+01:11:11.920 --> 01:11:13.850
+On your test set, it's called like meta
+
+01:11:13.850 --> 01:11:16.405
+overfitting that you're kind of still
+
+01:11:16.405 --> 01:11:17.920
+like an overfit to that test set.
+
+01:11:21.020 --> 01:11:21.330
+Right.
+
+01:11:21.330 --> 01:11:24.730
+So I have just a little more time.
+
+01:11:26.140 --> 01:11:28.790
+And I'm going to show you two things.
+
+01:11:28.790 --> 01:11:30.660
+So one is homework #1.
+
+01:11:31.810 --> 01:11:33.840
+So, homework one you have.
+
+01:11:35.670 --> 01:11:37.000
+2 problems.
+
+01:11:37.000 --> 01:11:38.580
+One is digit classification.
+
+01:11:38.580 --> 01:11:40.140
+You have to try to assign each of these
+
+01:11:40.140 --> 01:11:42.960
+digits into a particular category.
+
+01:11:43.900 --> 01:11:47.060
+And so the digit numbers are zero to
+
+01:11:47.060 --> 01:11:47.440
+10.
+
+01:11:48.430 --> 01:11:52.110
+And these are small images 28 by 28.
+
+01:11:52.110 --> 01:11:53.910
+The code is there to just reshape it
+
+01:11:53.910 --> 01:11:56.150
+into a 784 dimensional vector.
+
+01:11:57.270 --> 01:11:59.500
+And I've split it into multiple
+
+01:11:59.500 --> 01:12:02.650
+different training and test sets, so I
+
+01:12:02.650 --> 01:12:03.940
+provide starter code.
+
+01:12:05.220 --> 01:12:07.720
+But the starter code is really just to
+
+01:12:07.720 --> 01:12:09.025
+get the data there for you.
+
+01:12:09.025 --> 01:12:11.550
+I don't do the actual like K&N or
+
+01:12:11.550 --> 01:12:13.100
+anything like that yourself.
+
+01:12:13.100 --> 01:12:14.422
+So this is starter code.
+
+01:12:14.422 --> 01:12:15.660
+You can look at it to get an
+
+01:12:15.660 --> 01:12:17.120
+understanding of the syntax if you're
+
+01:12:17.120 --> 01:12:19.140
+not too familiar with Python, but it's
+
+01:12:19.140 --> 01:12:20.735
+just creating train, Val, test splits
+
+01:12:20.735 --> 01:12:22.460
+and I also create train splits at
+
+01:12:22.460 --> 01:12:23.310
+different sizes.
+
+01:12:24.090 --> 01:12:25.210
+So you can see that here.
+
+01:12:26.210 --> 01:12:27.980
+And darn it.
+
+01:12:29.460 --> 01:12:30.040
+OK, good.
+
+01:12:33.290 --> 01:12:34.290
+Sorry about that.
+
+01:12:36.090 --> 01:12:38.060
+Alright, so here's the starter code.
+
+01:12:39.120 --> 01:12:42.110
+So you fill in like the K&N function,
+
+01:12:42.110 --> 01:12:43.740
+you can change the function definition
+
+01:12:43.740 --> 01:12:45.540
+if you want, and then you'll also do
+
+01:12:45.540 --> 01:12:47.232
+Naive Bayes and logistic regression,
+
+01:12:47.232 --> 01:12:49.000
+and then you can have some code for
+
+01:12:49.000 --> 01:12:51.550
+experiments, and then there's a
+
+01:12:51.550 --> 01:12:52.850
+temperature regression problem.
+
+01:12:54.950 --> 01:12:57.770
+So there's a couple things that I want
+
+01:12:57.770 --> 01:12:59.640
+to say about all this.
+
+01:12:59.640 --> 01:13:02.930
+So one is that there's two challenges.
+
+01:13:02.930 --> 01:13:05.830
+One is digit classification.
+
+01:13:06.810 --> 01:13:08.400
+And one is temperature regression.
+
+01:13:08.400 --> 01:13:10.210
+For temperature regression, you get the
+
+01:13:10.210 --> 01:13:11.750
+previous temperatures of a bunch of
+
+01:13:11.750 --> 01:13:11.960
+U.S.
+
+01:13:11.960 --> 01:13:13.397
+cities, and you have to predict the
+
+01:13:13.397 --> 01:13:14.400
+temperature for the next day in
+
+01:13:14.400 --> 01:13:14.930
+Cleveland.
+
+01:13:16.170 --> 01:13:17.881
+And you're going to use.
+
+01:13:17.881 --> 01:13:18.907
+You're going to.
+
+01:13:18.907 --> 01:13:20.960
+For both of these you'll use Canon
+
+01:13:20.960 --> 01:13:22.720
+Naive Bayes, and for one you'll use
+
+01:13:22.720 --> 01:13:24.190
+logistic regression, the other linear
+
+01:13:24.190 --> 01:13:24.690
+regression.
+
+01:13:25.510 --> 01:13:26.900
+At the end of today you should be able
+
+01:13:26.900 --> 01:13:28.440
+to do the key and part of these.
+
+01:13:29.520 --> 01:13:30.940
+And then for.
+
+01:13:32.620 --> 01:13:34.880
+For the digits, you'll look at the
+
+01:13:34.880 --> 01:13:37.830
+error versus training size and also do
+
+01:13:37.830 --> 01:13:39.300
+some parameter selection.
+
+01:13:40.350 --> 01:13:43.790
+Using a validation set and then for
+
+01:13:43.790 --> 01:13:46.280
+temperature, you'll identify the most
+
+01:13:46.280 --> 01:13:47.270
+important features.
+
+01:13:47.270 --> 01:13:49.450
+I'll explain how you do that next
+
+01:13:49.450 --> 01:13:51.070
+Thursday, so that's not something you
+
+01:13:51.070 --> 01:13:52.270
+can implement based on the lecture
+
+01:13:52.270 --> 01:13:52.670
+today yet.
+
+01:13:53.370 --> 01:13:55.070
+And then there's also a stretch goals
+
+01:13:55.070 --> 01:13:56.890
+if you want to earn additional points.
+
+01:13:57.490 --> 01:13:59.230
+So these are just trying to improve the
+
+01:13:59.230 --> 01:14:00.540
+classification or regression
+
+01:14:00.540 --> 01:14:03.430
+performance, or to design a data set.
+
+01:14:03.430 --> 01:14:05.160
+We're naive's outperforms the other
+
+01:14:05.160 --> 01:14:05.390
+two.
+
+01:14:07.080 --> 01:14:09.400
+When you do these homeworks you have
+
+01:14:09.400 --> 01:14:11.145
+this is linked from the website, so
+
+01:14:11.145 --> 01:14:12.280
+this gives you like the main
+
+01:14:12.280 --> 01:14:12.840
+assignment.
+
+01:14:14.200 --> 01:14:16.920
+There's a starter code the data.
+
+01:14:17.620 --> 01:14:19.290
+You can look at the tips and tricks.
+
+01:14:19.290 --> 01:14:25.780
+So this has different examples of
+
+01:14:25.780 --> 01:14:28.510
+Python usage in this case that might be
+
+01:14:28.510 --> 01:14:30.740
+handy, and also talks about Google
+
+01:14:30.740 --> 01:14:32.820
+Colab which you can use to do the
+
+01:14:32.820 --> 01:14:33.230
+assignment.
+
+01:14:33.230 --> 01:14:34.900
+And then there's some more general tips
+
+01:14:34.900 --> 01:14:35.710
+on the assignment.
+
+01:14:38.340 --> 01:14:42.380
+And then for when you report things,
+
+01:14:42.380 --> 01:14:44.990
+you'll report you'll do like a PDF or
+
+01:14:44.990 --> 01:14:46.810
+HTML of your Jupiter notebook.
+
+01:14:47.470 --> 01:14:50.540
+But you will also mainly just fill out
+
+01:14:50.540 --> 01:14:53.700
+these numbers which are the like kind
+
+01:14:53.700 --> 01:14:56.120
+of the answers to the experiments, and
+
+01:14:56.120 --> 01:14:57.655
+this is the main thing that we'll look
+
+01:14:57.655 --> 01:14:58.660
+at to grade.
+
+01:14:58.660 --> 01:15:00.340
+And then they'll only they may only
+
+01:15:00.340 --> 01:15:01.955
+look at the code if they're not sure if
+
+01:15:01.955 --> 01:15:03.490
+you did it right given your answers
+
+01:15:03.490 --> 01:15:03.710
+here.
+
+01:15:04.620 --> 01:15:05.970
+So you need to fill this out.
+
+01:15:07.150 --> 01:15:09.060
+And you say, how many points do you
+
+01:15:09.060 --> 01:15:10.115
+think you should get for that?
+
+01:15:10.115 --> 01:15:12.190
+And so then the TAS will say, the
+
+01:15:12.190 --> 01:15:14.148
+graders will say the difference between
+
+01:15:14.148 --> 01:15:15.790
+the points that you get and what you
+
+01:15:15.790 --> 01:15:16.460
+thought you should get.
+
+01:15:20.560 --> 01:15:22.590
+So I think that's all I want to say
+
+01:15:22.590 --> 01:15:23.740
+about homework one.
+
+01:15:26.900 --> 01:15:27.590
+Let me see.
+
+01:15:27.590 --> 01:15:28.155
+All right.
+
+01:15:28.155 --> 01:15:29.480
+So we're out of time.
+
+01:15:29.480 --> 01:15:31.130
+So I'm going to talk about this at the
+
+01:15:31.130 --> 01:15:33.470
+start of the next class and I'll do a
+
+01:15:33.470 --> 01:15:35.390
+recap of KNN.
+
+01:15:37.160 --> 01:15:40.330
+And so next week I'll talk about Naive
+
+01:15:40.330 --> 01:15:43.010
+Bayes and linear logistic regression.
+
+01:15:44.260 --> 01:15:44.810
+Thanks.
+