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+WEBVTT Kind: captions; Language: en-US
+
+NOTE
+Created on 2024-02-07T20:53:13.8059397Z by ClassTranscribe
+
+00:01:57.930 --> 00:01:59.190
+It seems like there's like.
+
+00:02:01.950 --> 00:02:02.550
+Yes, it's OK.
+
+00:02:03.590 --> 00:02:04.800
+Alright, good morning everybody.
+
+00:02:08.160 --> 00:02:10.626
+So I thought it I was trying to figure
+
+00:02:10.626 --> 00:02:12.030
+out why this seems like there's a lot
+
+00:02:12.030 --> 00:02:13.520
+of light on the screen, but I can't
+
+00:02:13.520 --> 00:02:14.192
+figure it out.
+
+00:02:14.192 --> 00:02:16.300
+I thought it was interesting that this
+
+00:02:16.300 --> 00:02:17.490
+for this picture.
+
+00:02:17.580 --> 00:02:18.110
+And.
+
+00:02:19.140 --> 00:02:20.760
+So I'm generating all of these with
+
+00:02:20.760 --> 00:02:21.510
+Dolly.
+
+00:02:21.510 --> 00:02:22.880
+This one was a dirt Rd.
+
+00:02:22.880 --> 00:02:24.500
+splits around a large gnarly tree
+
+00:02:24.500 --> 00:02:25.640
+fractal art.
+
+00:02:25.640 --> 00:02:27.830
+But I thought it was really funny how
+
+00:02:27.830 --> 00:02:30.780
+it without my bidding it put like some
+
+00:02:30.780 --> 00:02:32.530
+kind of superhero or something behind
+
+00:02:32.530 --> 00:02:34.756
+the tree there's like some looks like
+
+00:02:34.756 --> 00:02:36.360
+there's like some superhero that's like
+
+00:02:36.360 --> 00:02:37.230
+flying in and.
+
+00:02:38.130 --> 00:02:39.420
+I don't know where that came from.
+
+00:02:41.170 --> 00:02:42.430
+Can you guys see the screen OK?
+
+00:02:43.750 --> 00:02:44.830
+Seems a little faded.
+
+00:03:05.390 --> 00:03:05.650
+But.
+
+00:03:12.610 --> 00:03:13.580
+OK I.
+
+00:03:16.440 --> 00:03:18.730
+Yeah, I put the lights are on all off.
+
+00:03:21.400 --> 00:03:22.580
+But those are still on.
+
+00:03:25.090 --> 00:03:27.020
+Alright, let me just take one second.
+
+00:03:48.110 --> 00:03:48.600
+All right.
+
+00:03:48.600 --> 00:03:50.860
+Anyway, I'll move with it.
+
+00:03:51.500 --> 00:03:53.410
+Alright, so.
+
+00:03:53.540 --> 00:03:55.570
+And so for some Logistics, I wanted to
+
+00:03:55.570 --> 00:03:57.160
+I never got to introduce some of the
+
+00:03:57.160 --> 00:03:58.740
+TAS because the couple couldn't be here
+
+00:03:58.740 --> 00:04:00.110
+in the first day and I kept forgetting.
+
+00:04:01.130 --> 00:04:03.890
+So, Josh, are you here?
+
+00:04:04.950 --> 00:04:08.900
+OK, cool if you want to just actually.
+
+00:04:10.130 --> 00:04:11.160
+I can give my mic.
+
+00:04:11.160 --> 00:04:12.780
+If you want to just introduce yourself
+
+00:04:12.780 --> 00:04:14.540
+a little bit, you can say like what
+
+00:04:14.540 --> 00:04:14.940
+kind of.
+
+00:04:19.890 --> 00:04:20.450
+Yeah.
+
+00:04:20.450 --> 00:04:20.870
+Hi, everyone.
+
+00:04:20.870 --> 00:04:21.290
+I'm Josh.
+
+00:04:21.290 --> 00:04:23.110
+I've been applying machine learning to
+
+00:04:23.110 --> 00:04:25.980
+autonomous cars and airplanes.
+
+00:04:27.150 --> 00:04:27.480
+Cool.
+
+00:04:27.480 --> 00:04:27.900
+Thank you.
+
+00:04:28.830 --> 00:04:31.020
+And cassette, cassette.
+
+00:04:37.760 --> 00:04:38.320
+Yeah.
+
+00:04:41.120 --> 00:04:46.150
+OK hey everyone, I'm a TA for CS441 and
+
+00:04:46.150 --> 00:04:49.230
+I have experience with NLP majorly.
+
+00:04:49.230 --> 00:04:49.720
+Thank you.
+
+00:04:50.960 --> 00:04:51.190
+Great.
+
+00:04:51.190 --> 00:04:52.080
+Thank you.
+
+00:04:52.080 --> 00:04:54.230
+And I don't think Peter's here, but
+
+00:04:54.230 --> 00:04:55.820
+Peter, are you here, OK.
+
+00:04:56.520 --> 00:04:58.240
+Usually has a conflict on Tuesday, so
+
+00:04:58.240 --> 00:05:00.780
+also we have Pedro is a.
+
+00:05:01.510 --> 00:05:04.170
+A pro stock course Assistant.
+
+00:05:04.170 --> 00:05:07.020
+So it's not like a regular TA, but
+
+00:05:07.020 --> 00:05:07.650
+he's.
+
+00:05:08.730 --> 00:05:10.510
+Doing a postdoc with Nancy Amato.
+
+00:05:11.170 --> 00:05:12.880
+And here is helping out with the online
+
+00:05:12.880 --> 00:05:15.190
+course for a couple semesters.
+
+00:05:15.830 --> 00:05:17.060
+And so he's helping out with this
+
+00:05:17.060 --> 00:05:19.140
+course and he's.
+
+00:05:20.920 --> 00:05:23.700
+One of the things he's doing is holding
+
+00:05:23.700 --> 00:05:25.640
+office hours, and so especially if you
+
+00:05:25.640 --> 00:05:27.710
+have, if you want help with your
+
+00:05:27.710 --> 00:05:31.940
+projects or homeworks, they're like
+
+00:05:31.940 --> 00:05:34.000
+higher level advice, then he can be a
+
+00:05:34.000 --> 00:05:35.676
+really good resource for that.
+
+00:05:35.676 --> 00:05:37.400
+So I know a lot of people want to meet
+
+00:05:37.400 --> 00:05:39.250
+with me about their side projects,
+
+00:05:39.250 --> 00:05:40.720
+which is also fine, you're welcome to
+
+00:05:40.720 --> 00:05:42.100
+do that.
+
+00:05:42.100 --> 00:05:44.090
+But he's also a good person for that.
+
+00:05:46.480 --> 00:05:49.550
+Alright, so just as a reminder for
+
+00:05:49.550 --> 00:05:51.210
+anybody who wasn't here, the first
+
+00:05:51.210 --> 00:05:53.630
+lecture, all the notes and everything
+
+00:05:53.630 --> 00:05:55.635
+are on this web page.
+
+00:05:55.635 --> 00:05:57.890
+So make sure that you go there and sign
+
+00:05:57.890 --> 00:06:00.290
+up for CampusWire where announcements
+
+00:06:00.290 --> 00:06:01.600
+will be made.
+
+00:06:01.600 --> 00:06:06.120
+Also, I sent a survey by e-mail and I
+
+00:06:06.120 --> 00:06:07.760
+got a little bit of responses last
+
+00:06:07.760 --> 00:06:08.240
+night.
+
+00:06:08.240 --> 00:06:10.390
+Do you take some time to respond to it
+
+00:06:10.390 --> 00:06:11.300
+please?
+
+00:06:11.300 --> 00:06:12.290
+There's two parts.
+
+00:06:12.290 --> 00:06:14.340
+One is just asking for feedback about
+
+00:06:14.340 --> 00:06:15.300
+like piece of the course.
+
+00:06:15.380 --> 00:06:16.340
+And stuff like that.
+
+00:06:16.420 --> 00:06:16.900
+And.
+
+00:06:17.720 --> 00:06:20.640
+One part is asking about your interests
+
+00:06:20.640 --> 00:06:23.060
+for some of the possible.
+
+00:06:24.070 --> 00:06:26.332
+Challenges that I'll pick for final
+
+00:06:26.332 --> 00:06:29.810
+project and so basically for the final
+
+00:06:29.810 --> 00:06:32.149
+project there will be 3 challenges that
+
+00:06:32.150 --> 00:06:33.600
+are like pre selected.
+
+00:06:34.230 --> 00:06:35.720
+But if you don't want to do those, you
+
+00:06:35.720 --> 00:06:38.370
+can also just do some benchmark that's
+
+00:06:38.370 --> 00:06:40.070
+online or you can even do a custom
+
+00:06:40.070 --> 00:06:40.860
+task.
+
+00:06:40.860 --> 00:06:43.960
+And I'll post the specifications for
+
+00:06:43.960 --> 00:06:46.640
+final project soon as homework 2.
+
+00:06:47.960 --> 00:06:50.140
+Also, just based on the feedback I've
+
+00:06:50.140 --> 00:06:52.810
+seen so far, I think nobody thinks it's
+
+00:06:52.810 --> 00:06:54.570
+way too easy or too slow.
+
+00:06:54.570 --> 00:06:57.150
+Some people think it's much too fast
+
+00:06:57.150 --> 00:06:57.930
+and too hard.
+
+00:06:57.930 --> 00:06:59.710
+So I'm going to take some time on
+
+00:06:59.710 --> 00:07:03.450
+Thursday to Reconsolidate and present.
+
+00:07:03.450 --> 00:07:07.280
+Kind of go over what we've done so far,
+
+00:07:07.280 --> 00:07:09.750
+talk in more depth or maybe not more
+
+00:07:09.750 --> 00:07:11.439
+depth, but at least go over the
+
+00:07:11.440 --> 00:07:12.150
+concepts.
+
+00:07:13.270 --> 00:07:16.080
+And the algorithms and a little bit of
+
+00:07:16.080 --> 00:07:18.380
+code now that you've had a first pass
+
+00:07:18.380 --> 00:07:18.640
+edit.
+
+00:07:20.460 --> 00:07:22.830
+So I'll tap the brakes a little bit to
+
+00:07:22.830 --> 00:07:24.500
+do that because I think it's really
+
+00:07:24.500 --> 00:07:27.215
+important that these that everyone is
+
+00:07:27.215 --> 00:07:28.790
+really solid on these fundamentals.
+
+00:07:28.790 --> 00:07:31.260
+And I know that there's a pretty big
+
+00:07:31.260 --> 00:07:33.090
+range of backgrounds of people taking
+
+00:07:33.090 --> 00:07:35.060
+the course, many people from other
+
+00:07:35.060 --> 00:07:35.710
+departments.
+
+00:07:37.290 --> 00:07:39.900
+As well as other different kinds of.
+
+00:07:41.230 --> 00:07:43.280
+Of like academic foundations.
+
+00:07:44.270 --> 00:07:44.610
+Alright.
+
+00:07:45.910 --> 00:07:47.890
+So just to recap what we talked about
+
+00:07:47.890 --> 00:07:49.640
+in the last few lectures, very briefly,
+
+00:07:49.640 --> 00:07:51.040
+we talked about Nearest neighbor.
+
+00:07:51.780 --> 00:07:53.210
+And the superpower is the nearest
+
+00:07:53.210 --> 00:07:55.170
+neighbor are that it can instantly
+
+00:07:55.170 --> 00:07:56.230
+learn new classes.
+
+00:07:56.230 --> 00:07:58.020
+You can just add a new example to your
+
+00:07:58.020 --> 00:07:58.790
+training set.
+
+00:07:58.790 --> 00:08:00.780
+And since there's no model that has to
+
+00:08:00.780 --> 00:08:04.110
+be like tuned, you can just learn super
+
+00:08:04.110 --> 00:08:04.720
+quickly.
+
+00:08:04.720 --> 00:08:07.450
+And it's also a pretty good predictor
+
+00:08:07.450 --> 00:08:08.980
+from either one or many examples.
+
+00:08:08.980 --> 00:08:10.430
+So it's a really good.
+
+00:08:10.530 --> 00:08:13.690
+It's a really good algorithm to have in
+
+00:08:13.690 --> 00:08:15.330
+your tool belt as a baseline and
+
+00:08:15.330 --> 00:08:16.760
+sometimes as a best performer.
+
+00:08:18.500 --> 00:08:20.160
+We also talked about Naive bees.
+
+00:08:21.050 --> 00:08:24.140
+Night Bayes is not a great performer as
+
+00:08:24.140 --> 00:08:26.984
+like a full algorithm, but it's often
+
+00:08:26.984 --> 00:08:27.426
+a.
+
+00:08:27.426 --> 00:08:30.075
+It's an important concept because it's
+
+00:08:30.075 --> 00:08:31.760
+often part of an assumption that you
+
+00:08:31.760 --> 00:08:32.920
+make when you're trying to model
+
+00:08:32.920 --> 00:08:35.560
+probabilities that you'll assume that
+
+00:08:35.560 --> 00:08:37.630
+the different features are independent
+
+00:08:37.630 --> 00:08:39.010
+given the thing that you're trying to
+
+00:08:39.010 --> 00:08:39.330
+predict.
+
+00:08:41.780 --> 00:08:44.290
+It does have its pros, so the pros are
+
+00:08:44.290 --> 00:08:46.560
+that it's really fast to estimate even
+
+00:08:46.560 --> 00:08:48.113
+if you've got a lot of data.
+
+00:08:48.113 --> 00:08:49.909
+And if you don't have a lot of data and
+
+00:08:49.910 --> 00:08:51.130
+you're trying to get a probabilistic
+
+00:08:51.130 --> 00:08:53.300
+classifier, then it might be your best
+
+00:08:53.300 --> 00:08:53.750
+choice.
+
+00:08:53.750 --> 00:08:56.700
+Because of its strong assumptions, you
+
+00:08:56.700 --> 00:08:59.880
+can get decent estimates on those
+
+00:08:59.880 --> 00:09:02.160
+single variable functions from even
+
+00:09:02.160 --> 00:09:02.800
+limited data.
+
+00:09:05.460 --> 00:09:07.964
+We talked about logistic regression.
+
+00:09:07.964 --> 00:09:10.830
+Logistic regression is another super
+
+00:09:10.830 --> 00:09:12.230
+widely used classifier.
+
+00:09:13.580 --> 00:09:16.400
+I think the AML book says that SVM is
+
+00:09:16.400 --> 00:09:18.776
+should be or like go to as a first as
+
+00:09:18.776 --> 00:09:20.660
+like a first thing you try, but in my
+
+00:09:20.660 --> 00:09:22.130
+opinion Logistic Regression is.
+
+00:09:23.810 --> 00:09:25.085
+It's very effective.
+
+00:09:25.085 --> 00:09:26.810
+It's a very effective predictor if you
+
+00:09:26.810 --> 00:09:28.720
+have high dimensional features and it
+
+00:09:28.720 --> 00:09:30.250
+also provides good confidence
+
+00:09:30.250 --> 00:09:31.460
+estimates, meaning that.
+
+00:09:32.150 --> 00:09:35.320
+You get not only most likely class, but
+
+00:09:35.320 --> 00:09:37.470
+the probability that prediction is
+
+00:09:37.470 --> 00:09:40.800
+correct and those probabilities fairly
+
+00:09:40.800 --> 00:09:41.400
+trustworthy.
+
+00:09:43.320 --> 00:09:44.970
+We also talked about Linear Regression,
+
+00:09:44.970 --> 00:09:46.560
+where you're fitting a line to a set of
+
+00:09:46.560 --> 00:09:47.050
+points.
+
+00:09:47.670 --> 00:09:50.610
+And you can extrapolate to predict like
+
+00:09:50.610 --> 00:09:52.620
+new values that are outside of your
+
+00:09:52.620 --> 00:09:53.790
+Training range.
+
+00:09:54.530 --> 00:09:55.840
+And so.
+
+00:09:56.730 --> 00:09:58.450
+Linear regression is also useful for
+
+00:09:58.450 --> 00:10:00.270
+explaining relationships you're very
+
+00:10:00.270 --> 00:10:02.100
+commonly see, like trend lines.
+
+00:10:02.100 --> 00:10:03.390
+That's just Linear Regression.
+
+00:10:04.130 --> 00:10:05.850
+And you can predict continuous values
+
+00:10:05.850 --> 00:10:07.600
+from many variables in linear
+
+00:10:07.600 --> 00:10:10.130
+regression is also like probably the
+
+00:10:10.130 --> 00:10:12.760
+most common tool for.
+
+00:10:12.830 --> 00:10:15.590
+For things like, I don't know, like
+
+00:10:15.590 --> 00:10:17.790
+economics or analyzing.
+
+00:10:18.770 --> 00:10:23.100
+Yeah, time series analyzing like fMRI
+
+00:10:23.100 --> 00:10:25.930
+data or all kinds of scientific and
+
+00:10:25.930 --> 00:10:27.180
+economic analysis.
+
+00:10:30.420 --> 00:10:33.810
+So almost all algorithms involve these
+
+00:10:33.810 --> 00:10:35.760
+Nearest neighbor, logistic regression
+
+00:10:35.760 --> 00:10:36.850
+or linear regression.
+
+00:10:37.540 --> 00:10:41.040
+And the reason that there's thousand
+
+00:10:41.040 --> 00:10:43.330
+papers published in the last 10 years
+
+00:10:43.330 --> 00:10:45.060
+or so, probably a lot more than that
+
+00:10:45.060 --> 00:10:47.030
+actually, is that.
+
+00:10:47.850 --> 00:10:50.120
+Is really the feature learning, so it's
+
+00:10:50.120 --> 00:10:52.090
+getting the right representation so
+
+00:10:52.090 --> 00:10:54.490
+that when you feed that representation
+
+00:10:54.490 --> 00:10:56.610
+into these like Linear models or
+
+00:10:56.610 --> 00:10:59.080
+Nearest neighbor, you get good results.
+
+00:11:00.080 --> 00:11:00.660
+And so.
+
+00:11:01.510 --> 00:11:03.020
+Pretty much the rest of what we're
+
+00:11:03.020 --> 00:11:05.160
+going to learn in the supervised
+
+00:11:05.160 --> 00:11:07.520
+learning section of the course is how
+
+00:11:07.520 --> 00:11:08.460
+to learn features.
+
+00:11:11.930 --> 00:11:14.150
+So I did want to just briefly go over
+
+00:11:14.150 --> 00:11:15.640
+the homework and remind you that it's
+
+00:11:15.640 --> 00:11:18.180
+due on February 6th on Monday.
+
+00:11:19.060 --> 00:11:21.400
+And I'll be going over some related
+
+00:11:21.400 --> 00:11:22.830
+things again in more detail on
+
+00:11:22.830 --> 00:11:23.350
+Thursday.
+
+00:11:24.300 --> 00:11:27.200
+But there's two parts to the main
+
+00:11:27.200 --> 00:11:27.590
+homework.
+
+00:11:27.590 --> 00:11:29.770
+There's Digit Classification where
+
+00:11:29.770 --> 00:11:31.186
+you're trying to predict a label zero
+
+00:11:31.186 --> 00:11:33.530
+to 9 based on a 28 by 28 image.
+
+00:11:34.410 --> 00:11:36.409
+These images get reshaped into like a
+
+00:11:36.410 --> 00:11:38.840
+single vector, so you have a feature
+
+00:11:38.840 --> 00:11:41.020
+vector that corresponds to the pixel
+
+00:11:41.020 --> 00:11:42.280
+intensities of the image.
+
+00:11:44.350 --> 00:11:46.510
+And then you have to do K and Naive
+
+00:11:46.510 --> 00:11:49.200
+Bayes, linear logistic regression.
+
+00:11:50.060 --> 00:11:52.510
+And plot the Error versus.
+
+00:11:52.670 --> 00:11:55.420
+A plot Error versus Training size to
+
+00:11:55.420 --> 00:11:57.310
+get a sense for like how performance
+
+00:11:57.310 --> 00:11:58.745
+changes as you vary the number of
+
+00:11:58.745 --> 00:11:59.530
+training examples.
+
+00:12:00.380 --> 00:12:02.820
+And then to select the best parameter
+
+00:12:02.820 --> 00:12:06.490
+using validation set which is a really
+
+00:12:06.490 --> 00:12:07.240
+hyper parameter.
+
+00:12:07.240 --> 00:12:09.020
+Tuning is like something that you do
+
+00:12:09.020 --> 00:12:10.100
+all the time in machine learning.
+
+00:12:13.150 --> 00:12:14.839
+The second problem is Temperature
+
+00:12:14.840 --> 00:12:15.700
+Regression.
+
+00:12:15.700 --> 00:12:18.182
+So I got this Temperature.
+
+00:12:18.182 --> 00:12:20.178
+This data set of like the temperature
+
+00:12:20.178 --> 00:12:22.890
+is a big cities in the US and then
+
+00:12:22.890 --> 00:12:24.111
+made-up a problem from it.
+
+00:12:24.111 --> 00:12:26.550
+So the problem is to try to predict the
+
+00:12:26.550 --> 00:12:28.220
+next day's temperature in Cleveland
+
+00:12:28.220 --> 00:12:30.000
+which stays zero given all the previous
+
+00:12:30.000 --> 00:12:30.550
+temperatures.
+
+00:12:31.490 --> 00:12:34.350
+And these features have meanings.
+
+00:12:34.350 --> 00:12:37.417
+Every feature is some previous is, like
+
+00:12:37.417 --> 00:12:39.530
+the temperature of 1 in the big cities
+
+00:12:39.530 --> 00:12:40.990
+from one in the past five days.
+
+00:12:42.570 --> 00:12:44.753
+But you can kind of.
+
+00:12:44.753 --> 00:12:46.110
+You don't really need to know those
+
+00:12:46.110 --> 00:12:48.110
+meanings in order to solve the problem
+
+00:12:48.110 --> 00:12:48.480
+again.
+
+00:12:48.480 --> 00:12:50.780
+You essentially just have a feature
+
+00:12:50.780 --> 00:12:53.730
+vector of a bunch of continuous values
+
+00:12:53.730 --> 00:12:55.570
+in this case, and you're trying to
+
+00:12:55.570 --> 00:12:57.290
+predict a new continuous value, which
+
+00:12:57.290 --> 00:13:00.460
+is Cleveland Cleveland's temperature in
+
+00:13:00.460 --> 00:13:01.240
+the next day.
+
+00:13:02.010 --> 00:13:04.545
+And again you can use KNN and a Bayes
+
+00:13:04.545 --> 00:13:06.000
+and now Linear Regression.
+
+00:13:07.020 --> 00:13:08.935
+KNN implementation will be essentially
+
+00:13:08.935 --> 00:13:11.440
+the same for these A2 line change of
+
+00:13:11.440 --> 00:13:13.820
+code because now instead of predicting
+
+00:13:13.820 --> 00:13:16.230
+a categorical variable, you're
+
+00:13:16.230 --> 00:13:18.440
+predicting a continuous variable.
+
+00:13:18.440 --> 00:13:20.580
+So if K is greater than one, you
+
+00:13:20.580 --> 00:13:23.770
+average the predictions for Regression
+
+00:13:23.770 --> 00:13:26.280
+where for the Classification you choose
+
+00:13:26.280 --> 00:13:27.430
+the most common prediction.
+
+00:13:28.580 --> 00:13:29.840
+That's the only change.
+
+00:13:29.840 --> 00:13:31.590
+Naive Bayes does change quite a bit
+
+00:13:31.590 --> 00:13:32.710
+because you're using a different
+
+00:13:32.710 --> 00:13:33.590
+probabilistic model.
+
+00:13:34.360 --> 00:13:36.710
+And remember that there's one lecture
+
+00:13:36.710 --> 00:13:38.670
+slide that has the derivation for how
+
+00:13:38.670 --> 00:13:40.545
+you do the inference for nibbies under
+
+00:13:40.545 --> 00:13:41.050
+the setting.
+
+00:13:42.330 --> 00:13:44.760
+And then for linear and logistic
+
+00:13:44.760 --> 00:13:46.820
+regression you're able to use the
+
+00:13:46.820 --> 00:13:48.350
+modules in sklearn.
+
+00:13:49.890 --> 00:13:51.680
+And then the final part is to identify
+
+00:13:51.680 --> 00:13:53.550
+the most important features using L1
+
+00:13:53.550 --> 00:13:54.320
+Linear Regression.
+
+00:13:55.030 --> 00:13:57.160
+So the reason that we use.
+
+00:13:58.020 --> 00:13:59.810
+And when we do like.
+
+00:14:01.000 --> 00:14:03.170
+Linear and logistic regression, we're
+
+00:14:03.170 --> 00:14:03.580
+trying.
+
+00:14:03.580 --> 00:14:05.228
+We're mainly trying to fit the data.
+
+00:14:05.228 --> 00:14:06.600
+We're trying to come up with a model
+
+00:14:06.600 --> 00:14:08.340
+that fits the data or fits our
+
+00:14:08.340 --> 00:14:09.920
+predictions given the features.
+
+00:14:10.630 --> 00:14:13.720
+But also we often express some
+
+00:14:13.720 --> 00:14:14.490
+preference.
+
+00:14:15.190 --> 00:14:19.892
+Over the model, in particular that the
+
+00:14:19.892 --> 00:14:21.669
+weights don't get too large, and the
+
+00:14:21.670 --> 00:14:25.170
+reason for that is to avoid like
+
+00:14:25.170 --> 00:14:27.070
+overfitting or over relying on
+
+00:14:27.070 --> 00:14:30.410
+particular features, as well as to
+
+00:14:30.410 --> 00:14:34.795
+improve the generalization to new data
+
+00:14:34.795 --> 00:14:36.209
+and generalization.
+
+00:14:36.210 --> 00:14:37.810
+Research shows that if you can fit
+
+00:14:37.810 --> 00:14:39.220
+something with smaller weights, then
+
+00:14:39.220 --> 00:14:42.013
+you're more likely to generalize to new
+
+00:14:42.013 --> 00:14:42.209
+data.
+
+00:14:44.640 --> 00:14:46.550
+And here we're going to use it for
+
+00:14:46.550 --> 00:14:47.520
+feature selection, yeah?
+
+00:14:58.910 --> 00:15:02.370
+The so the parameters are.
+
+00:15:02.370 --> 00:15:04.510
+You're talking about 1/3.
+
+00:15:04.510 --> 00:15:07.825
+OK, so for Naive Bayes the parameter is
+
+00:15:07.825 --> 00:15:10.430
+the prior, so that's like the alpha of
+
+00:15:10.430 --> 00:15:11.010
+like your.
+
+00:15:11.670 --> 00:15:14.903
+In the, it's the initial count, so you
+
+00:15:14.903 --> 00:15:15.882
+have a Naive Bayes.
+
+00:15:15.882 --> 00:15:17.360
+You have a prior that's essentially
+
+00:15:17.360 --> 00:15:19.200
+that you pretend like you've seen all
+
+00:15:19.200 --> 00:15:20.230
+combinations of.
+
+00:15:20.950 --> 00:15:23.930
+Of things that you're counting, you
+
+00:15:23.930 --> 00:15:26.210
+pretend that you see alpha times, and
+
+00:15:26.210 --> 00:15:28.510
+so that kind of gives you a bias
+
+00:15:28.510 --> 00:15:30.200
+towards estimating that everything's
+
+00:15:30.200 --> 00:15:33.170
+equally likely, and that alpha is a
+
+00:15:33.170 --> 00:15:34.190
+parameter that you can use.
+
+00:15:34.810 --> 00:15:36.270
+You can learn using validation.
+
+00:15:37.010 --> 00:15:39.920
+For Logistic Regression, it's the
+
+00:15:39.920 --> 00:15:42.650
+Lambda which is your weight on the
+
+00:15:42.650 --> 00:15:43.760
+regularization term.
+
+00:15:45.650 --> 00:15:48.180
+And for K&N, it's your K, which is the
+
+00:15:48.180 --> 00:15:49.320
+number of nearest neighbors you
+
+00:15:49.320 --> 00:15:49.710
+consider.
+
+00:15:57.960 --> 00:15:58.220
+Yeah.
+
+00:16:00.180 --> 00:16:03.284
+So the K&N is.
+
+00:16:03.284 --> 00:16:05.686
+It's almost the same whether you're
+
+00:16:05.686 --> 00:16:08.260
+doing Regression or Classification.
+
+00:16:08.260 --> 00:16:09.980
+When you find the K nearest neighbors,
+
+00:16:09.980 --> 00:16:11.790
+it's the exact same code.
+
+00:16:11.790 --> 00:16:14.016
+The difference is that if you're doing
+
+00:16:14.016 --> 00:16:15.270
+Regression, you're trying to predict
+
+00:16:15.270 --> 00:16:16.200
+continuous values.
+
+00:16:16.200 --> 00:16:19.340
+So if K is greater than one, then you
+
+00:16:19.340 --> 00:16:21.532
+want to average those continuous values
+
+00:16:21.532 --> 00:16:23.150
+to get your final prediction.
+
+00:16:23.850 --> 00:16:26.060
+And if you're doing Classification, you
+
+00:16:26.060 --> 00:16:28.490
+find the most common label instead of
+
+00:16:28.490 --> 00:16:29.803
+averaging because you don't want to
+
+00:16:29.803 --> 00:16:31.470
+say, well it could be a four, it could
+
+00:16:31.470 --> 00:16:31.980
+be a 9.
+
+00:16:31.980 --> 00:16:33.110
+So I'm going to like split the
+
+00:16:33.110 --> 00:16:34.270
+difference and say it's a 6.
+
+00:16:42.030 --> 00:16:45.420
+That are averaging just that you so
+
+00:16:45.420 --> 00:16:47.600
+like if K&N returns like the
+
+00:16:47.600 --> 00:16:54.870
+temperatures of 1012 and 13 then you
+
+00:16:54.870 --> 00:16:57.190
+would say that the average temperature
+
+00:16:57.190 --> 00:16:59.530
+is like 11.3 or whatever that works out
+
+00:16:59.530 --> 00:16:59.730
+to.
+
+00:17:04.600 --> 00:17:06.440
+Yeah, at the end, if K is greater than
+
+00:17:06.440 --> 00:17:09.333
+one, then you take the arithmetic mean
+
+00:17:09.333 --> 00:17:11.210
+of the average of the.
+
+00:17:11.940 --> 00:17:14.560
+Predictions of your K nearest
+
+00:17:14.560 --> 00:17:14.970
+neighbors.
+
+00:17:16.590 --> 00:17:16.790
+Yeah.
+
+00:17:18.610 --> 00:17:20.560
+And so you could also get a variance
+
+00:17:20.560 --> 00:17:22.370
+from that, which you don't need to do
+
+00:17:22.370 --> 00:17:24.500
+for the homework, but so as a result
+
+00:17:24.500 --> 00:17:26.550
+you can have some like confidence bound
+
+00:17:26.550 --> 00:17:27.840
+on your estimate as well.
+
+00:17:30.050 --> 00:17:31.780
+Alright then you have stretch goals,
+
+00:17:31.780 --> 00:17:32.170
+so.
+
+00:17:32.850 --> 00:17:34.100
+Stretch goals are.
+
+00:17:35.130 --> 00:17:37.000
+Mainly intended for people taking the
+
+00:17:37.000 --> 00:17:39.020
+four credit version, but you can anyone
+
+00:17:39.020 --> 00:17:39.510
+can try them.
+
+00:17:40.240 --> 00:17:42.570
+So there's just improving the MNIST
+
+00:17:42.570 --> 00:17:44.370
+classification, like some ideas.
+
+00:17:44.370 --> 00:17:47.360
+Or you could try to crop around the
+
+00:17:47.360 --> 00:17:49.000
+Digit, or you could make sure that
+
+00:17:49.000 --> 00:17:51.840
+they're all centered, or do some
+
+00:17:51.840 --> 00:17:53.410
+whitening or other kinds of feature
+
+00:17:53.410 --> 00:17:54.340
+transformations.
+
+00:17:55.430 --> 00:17:56.770
+Improving Temperature Regression.
+
+00:17:56.770 --> 00:18:00.070
+To be honest, I'm not sure exactly how
+
+00:18:00.070 --> 00:18:01.829
+much this can be improved or how to
+
+00:18:01.830 --> 00:18:02.280
+improve it.
+
+00:18:03.030 --> 00:18:04.720
+Again, there's.
+
+00:18:04.720 --> 00:18:07.370
+What I would do is try like subtracting
+
+00:18:07.370 --> 00:18:08.110
+off the mean.
+
+00:18:08.110 --> 00:18:09.220
+For example, you can.
+
+00:18:10.380 --> 00:18:12.370
+You can normalize your features before
+
+00:18:12.370 --> 00:18:15.540
+you do the fitting by subtracting off
+
+00:18:15.540 --> 00:18:16.750
+means and dividing by steering
+
+00:18:16.750 --> 00:18:17.410
+deviations.
+
+00:18:17.410 --> 00:18:18.140
+That's one idea.
+
+00:18:19.060 --> 00:18:22.320
+But we'll look at it after submissions
+
+00:18:22.320 --> 00:18:24.095
+if it turns out that.
+
+00:18:24.095 --> 00:18:27.020
+So the targets I Choose are because I
+
+00:18:27.020 --> 00:18:29.273
+was able to do like some simple things
+
+00:18:29.273 --> 00:18:32.383
+to bring down the Error by a few tenths
+
+00:18:32.383 --> 00:18:33.510
+of a percent.
+
+00:18:33.510 --> 00:18:35.000
+So I kind of figured that if you do
+
+00:18:35.000 --> 00:18:36.346
+more things, you'll be able to bring it
+
+00:18:36.346 --> 00:18:38.420
+down further, but it's hard to tell so.
+
+00:18:39.240 --> 00:18:40.960
+If you do this and you put a lot of
+
+00:18:40.960 --> 00:18:42.600
+effort into it, describe your effort
+
+00:18:42.600 --> 00:18:45.594
+and we'll assign points even if you
+
+00:18:45.594 --> 00:18:47.680
+even if it turns out that there's not
+
+00:18:47.680 --> 00:18:48.640
+like a big improvement.
+
+00:18:48.640 --> 00:18:50.676
+So don't stress out if you can't get
+
+00:18:50.676 --> 00:18:51.609
+like 119.
+
+00:18:52.450 --> 00:18:54.200
+RMS a year or something like that.
+
+00:18:55.130 --> 00:18:55.335
+Right.
+
+00:18:55.335 --> 00:18:57.306
+The last one is to generate a train
+
+00:18:57.306 --> 00:18:58.806
+set, train Test, Classification set.
+
+00:18:58.806 --> 00:19:00.380
+So this actually means don't like
+
+00:19:00.380 --> 00:19:02.020
+generate it out of MNIST to create
+
+00:19:02.020 --> 00:19:02.804
+synthetic data.
+
+00:19:02.804 --> 00:19:05.020
+So you can Naive Bayes make certain
+
+00:19:05.020 --> 00:19:05.405
+assumptions.
+
+00:19:05.405 --> 00:19:07.180
+So if you generate your data according
+
+00:19:07.180 --> 00:19:09.390
+to those Assumptions, you should be
+
+00:19:09.390 --> 00:19:11.900
+able to create a problem that we're
+
+00:19:11.900 --> 00:19:13.520
+Naive bees can outperform the other
+
+00:19:13.520 --> 00:19:13.980
+methods.
+
+00:19:18.970 --> 00:19:22.130
+So for these homeworks, make sure that
+
+00:19:22.130 --> 00:19:24.020
+you of course read the assignment.
+
+00:19:24.020 --> 00:19:25.040
+Read the tips.
+
+00:19:25.530 --> 00:19:26.210
+
+
+00:19:27.060 --> 00:19:29.190
+And then you should be adding code to
+
+00:19:29.190 --> 00:19:30.045
+the starter code.
+
+00:19:30.045 --> 00:19:31.610
+The starter code doesn't really solve
+
+00:19:31.610 --> 00:19:33.030
+the problems for you, but it loads the
+
+00:19:33.030 --> 00:19:34.570
+data and gives you some examples.
+
+00:19:34.570 --> 00:19:38.160
+So for example, for example, there's a.
+
+00:19:38.810 --> 00:19:41.340
+In the Regression, I think it includes
+
+00:19:41.340 --> 00:19:43.710
+like a baseline where it computes RMSE
+
+00:19:43.710 --> 00:19:46.450
+and median absolute error, so that
+
+00:19:46.450 --> 00:19:48.760
+function can essentially be reused
+
+00:19:48.760 --> 00:19:50.060
+later to compute the errors.
+
+00:19:51.120 --> 00:19:53.073
+And that baseline gives you some idea
+
+00:19:53.073 --> 00:19:55.390
+of like what kind of performance you
+
+00:19:55.390 --> 00:19:55.870
+might get.
+
+00:19:55.870 --> 00:19:57.320
+Like you should beat that baseline
+
+00:19:57.320 --> 00:19:58.620
+because that's just based on a single
+
+00:19:58.620 --> 00:19:58.940
+feature.
+
+00:20:00.300 --> 00:20:02.980
+And then you complete the report and
+
+00:20:02.980 --> 00:20:04.940
+make sure to include expected points.
+
+00:20:04.940 --> 00:20:07.040
+So when the grader is graded they will
+
+00:20:07.040 --> 00:20:09.140
+essentially just say if they disagree
+
+00:20:09.140 --> 00:20:09.846
+with you.
+
+00:20:09.846 --> 00:20:12.470
+So you if you claim like 10 points but
+
+00:20:12.470 --> 00:20:14.345
+something was wrong then they might say
+
+00:20:14.345 --> 00:20:16.310
+you lose like 3 points for this reason
+
+00:20:16.310 --> 00:20:20.340
+and so that streamlines their grading.
+
+00:20:21.930 --> 00:20:23.580
+The assignment, the report Submit your
+
+00:20:23.580 --> 00:20:26.070
+notebook and either if you just have
+
+00:20:26.070 --> 00:20:28.800
+one file, submitting the IPYNB is fine
+
+00:20:28.800 --> 00:20:29.890
+or otherwise you can zip it.
+
+00:20:30.860 --> 00:20:32.220
+And that's it.
+
+00:20:33.960 --> 00:20:34.620
+Yeah, question.
+
+00:20:41.730 --> 00:20:47.160
+So you need in three Credit was at 450,
+
+00:20:47.160 --> 00:20:47.640
+is that right?
+
+00:20:48.650 --> 00:20:50.810
+So think I think in the three credit
+
+00:20:50.810 --> 00:20:52.300
+you need 450 points.
+
+00:20:53.660 --> 00:20:55.430
+Each assignment without doing any
+
+00:20:55.430 --> 00:20:56.230
+stretch goals.
+
+00:20:56.230 --> 00:20:58.620
+Each assignment is worth 100 points and
+
+00:20:58.620 --> 00:21:01.240
+the final project is worth 50 points.
+
+00:21:01.240 --> 00:21:02.673
+I mean sorry, the final projects worth
+
+00:21:02.673 --> 00:21:03.460
+100 points also.
+
+00:21:04.150 --> 00:21:06.310
+So if you're in the three Credit
+
+00:21:06.310 --> 00:21:08.210
+version and you don't do any stretch
+
+00:21:08.210 --> 00:21:10.960
+goals, and you do all the assignments
+
+00:21:10.960 --> 00:21:12.500
+and you do the final project, you will
+
+00:21:12.500 --> 00:21:13.570
+have more points than you need.
+
+00:21:14.190 --> 00:21:17.740
+So the so you can kind of pick
+
+00:21:17.740 --> 00:21:19.270
+something that you don't want to do and
+
+00:21:19.270 --> 00:21:20.910
+skip it if you're in the three credit
+
+00:21:20.910 --> 00:21:24.100
+course and or like if you just are
+
+00:21:24.100 --> 00:21:26.330
+already a machine learning guru, you
+
+00:21:26.330 --> 00:21:29.290
+can do like 3 assignments with all the
+
+00:21:29.290 --> 00:21:31.630
+extra parts and then take a vacation.
+
+00:21:32.920 --> 00:21:34.720
+If you're in the four credit version,
+
+00:21:34.720 --> 00:21:37.490
+then you will have to do some of the.
+
+00:21:37.670 --> 00:21:39.520
+Some of the stretch goals in order to
+
+00:21:39.520 --> 00:21:41.470
+get your full points, which are 550.
+
+00:21:49.580 --> 00:21:52.715
+Alright, so now I'm going to move on to
+
+00:21:52.715 --> 00:21:54.180
+the main topic.
+
+00:21:54.180 --> 00:21:57.340
+So we've seen so far, we've seen 2 main
+
+00:21:57.340 --> 00:21:59.116
+choices for how to use the features.
+
+00:21:59.116 --> 00:22:01.025
+We could do Nearest neighbor when we
+
+00:22:01.025 --> 00:22:03.200
+use all the features jointly in order
+
+00:22:03.200 --> 00:22:05.280
+to find similar examples, and then we
+
+00:22:05.280 --> 00:22:06.970
+predict the most similar label.
+
+00:22:07.910 --> 00:22:10.160
+Or we can use a linear model where
+
+00:22:10.160 --> 00:22:11.980
+essentially you're making a prediction
+
+00:22:11.980 --> 00:22:14.530
+out of a of all the feature values.
+
+00:22:16.070 --> 00:22:18.490
+But there's some other things that are
+
+00:22:18.490 --> 00:22:20.270
+kind of intuitive, so.
+
+00:22:21.220 --> 00:22:24.010
+For example, if you consider this where
+
+00:22:24.010 --> 00:22:26.260
+you're trying to split the red X's from
+
+00:22:26.260 --> 00:22:27.710
+the Green O's.
+
+00:22:28.370 --> 00:22:30.820
+What's like another way that you might
+
+00:22:30.820 --> 00:22:33.180
+try to define what that Decision
+
+00:22:33.180 --> 00:22:35.130
+boundary is if you wanted to, say, tell
+
+00:22:35.130 --> 00:22:35.730
+somebody else?
+
+00:22:35.730 --> 00:22:37.110
+Like how do you identify whether
+
+00:22:37.110 --> 00:22:38.770
+something is a no?
+
+00:22:52.240 --> 00:22:55.600
+Yeah, I mean you so your jaw some kind
+
+00:22:55.600 --> 00:22:56.200
+of boundary.
+
+00:22:57.150 --> 00:22:57.690
+And.
+
+00:22:58.620 --> 00:23:00.315
+And one way that you might think about
+
+00:23:00.315 --> 00:23:03.440
+that is creating a kind of like simple
+
+00:23:03.440 --> 00:23:04.220
+rule like this.
+
+00:23:04.220 --> 00:23:05.890
+Like you might say that if.
+
+00:23:06.600 --> 00:23:09.040
+You basically draw a boundary, but if
+
+00:23:09.040 --> 00:23:11.252
+you want to specify you might say if X2
+
+00:23:11.252 --> 00:23:15.820
+is less than .6 and X2 is greater than
+
+00:23:15.820 --> 00:23:16.500
+two.
+
+00:23:17.460 --> 00:23:21.480
+And tX2, oops, that's just say X1 and
+
+00:23:21.480 --> 00:23:22.082
+the last one.
+
+00:23:22.082 --> 00:23:24.630
+And if X1 is less than seven then it's
+
+00:23:24.630 --> 00:23:26.672
+an O and otherwise it's an X.
+
+00:23:26.672 --> 00:23:28.110
+So basically you could create like a
+
+00:23:28.110 --> 00:23:29.502
+set of rules like that, right?
+
+00:23:29.502 --> 00:23:32.161
+So say if it meets these criteria then
+
+00:23:32.161 --> 00:23:34.819
+it's one class and if it meets these
+
+00:23:34.820 --> 00:23:37.070
+other criteria it's another class.
+
+00:23:40.160 --> 00:23:42.930
+And So what we're going to learn today
+
+00:23:42.930 --> 00:23:45.280
+is how we can try to learn these rules
+
+00:23:45.280 --> 00:23:48.220
+automatically, even if we have a lot of
+
+00:23:48.220 --> 00:23:50.520
+features in more complicated kinds of
+
+00:23:50.520 --> 00:23:51.250
+predictions.
+
+00:23:52.920 --> 00:23:55.108
+So this is basically the idea of
+
+00:23:55.108 --> 00:23:55.744
+Decision trees.
+
+00:23:55.744 --> 00:23:58.490
+So we all use Decision trees in our own
+
+00:23:58.490 --> 00:24:00.264
+life, even if we don't think about it
+
+00:24:00.264 --> 00:24:00.812
+that way.
+
+00:24:00.812 --> 00:24:02.710
+Like you often say, if this happens,
+
+00:24:02.710 --> 00:24:04.121
+I'll do that, and if it doesn't, then
+
+00:24:04.121 --> 00:24:05.029
+I'll do this other thing.
+
+00:24:05.030 --> 00:24:06.685
+That's like a Decision tree, right?
+
+00:24:06.685 --> 00:24:10.400
+You had some kind of criteria, and
+
+00:24:10.400 --> 00:24:12.306
+depending on the outcome of that
+
+00:24:12.306 --> 00:24:13.886
+criteria, you do one thing.
+
+00:24:13.886 --> 00:24:16.680
+And if it's the other way, if you get
+
+00:24:16.680 --> 00:24:17.900
+the other outcome, then you would be
+
+00:24:17.900 --> 00:24:18.920
+doing the other thing.
+
+00:24:18.920 --> 00:24:20.310
+And maybe you have a whole chain of
+
+00:24:20.310 --> 00:24:22.090
+them if I.
+
+00:24:22.250 --> 00:24:23.700
+If I have time today, I'm going to go
+
+00:24:23.700 --> 00:24:25.990
+to the grocery store, but if the car is
+
+00:24:25.990 --> 00:24:27.330
+not there then I'm going to do this
+
+00:24:27.330 --> 00:24:28.480
+instead and so on.
+
+00:24:29.850 --> 00:24:32.370
+All right, so in Decision trees, the
+
+00:24:32.370 --> 00:24:34.500
+Training is essentially to iteratively
+
+00:24:34.500 --> 00:24:37.340
+Choose the attribute and split in a
+
+00:24:37.340 --> 00:24:40.080
+split value that will best separate
+
+00:24:40.080 --> 00:24:41.530
+your classes from each other.
+
+00:24:42.920 --> 00:24:44.610
+Or if you're doing continuous values
+
+00:24:44.610 --> 00:24:47.010
+that kind of group things into similar
+
+00:24:47.010 --> 00:24:48.240
+prediction values.
+
+00:24:49.480 --> 00:24:52.440
+So for example you might say if these
+
+00:24:52.440 --> 00:24:56.600
+red circles are oranges and these
+
+00:24:56.600 --> 00:24:59.264
+triangles are lemons, where there
+
+00:24:59.264 --> 00:25:01.090
+oranges and lemons are plotted
+
+00:25:01.090 --> 00:25:02.250
+according to their width and their
+
+00:25:02.250 --> 00:25:02.750
+height.
+
+00:25:02.750 --> 00:25:07.726
+You might decide well if it's less than
+
+00:25:07.726 --> 00:25:10.170
+6.5 centimeters then.
+
+00:25:10.170 --> 00:25:12.690
+Or I'll use greater since it's there if
+
+00:25:12.690 --> 00:25:14.190
+it's greater than 6.5 centimeters.
+
+00:25:15.450 --> 00:25:17.267
+Then I'm going to split it into this
+
+00:25:17.267 --> 00:25:19.410
+section where it's like mostly oranges
+
+00:25:19.410 --> 00:25:22.110
+and if it's less than 6.5 centimeters
+
+00:25:22.110 --> 00:25:24.395
+width, then I'll split it into this
+
+00:25:24.395 --> 00:25:26.220
+section where it's mostly lemons.
+
+00:25:27.250 --> 00:25:30.560
+Neither of these a perfect split still.
+
+00:25:30.560 --> 00:25:32.910
+So then I go further and say if it was
+
+00:25:32.910 --> 00:25:35.309
+on this side of the split, if it's
+
+00:25:35.310 --> 00:25:37.915
+greater than 95 centimeter height then
+
+00:25:37.915 --> 00:25:40.350
+it's a lemon, and if it's less than
+
+00:25:40.350 --> 00:25:42.130
+that then it's a.
+
+00:25:42.820 --> 00:25:43.760
+Then it's an orange.
+
+00:25:44.900 --> 00:25:46.660
+And now that's like a pretty confident
+
+00:25:46.660 --> 00:25:47.170
+prediction.
+
+00:25:47.930 --> 00:25:49.610
+And then if I'm on this side then I can
+
+00:25:49.610 --> 00:25:51.560
+split it by height and say if it's less
+
+00:25:51.560 --> 00:25:51.990
+than.
+
+00:25:53.690 --> 00:25:55.530
+If it's greater than 6 centimeters then
+
+00:25:55.530 --> 00:25:57.714
+it's a lemon, and if it's less than 6
+
+00:25:57.714 --> 00:25:59.450
+centimeters then it's an orange.
+
+00:25:59.450 --> 00:26:01.130
+So you can like iteratively Choose a
+
+00:26:01.130 --> 00:26:03.180
+test and then keep splitting the data.
+
+00:26:03.780 --> 00:26:06.510
+And every time you choose a test, test
+
+00:26:06.510 --> 00:26:09.510
+another test that splits the data
+
+00:26:09.510 --> 00:26:10.910
+further according to what you're trying
+
+00:26:10.910 --> 00:26:11.320
+to predict.
+
+00:26:12.270 --> 00:26:14.890
+Essentially, this method Combines a
+
+00:26:14.890 --> 00:26:16.760
+feature selection and modeling with
+
+00:26:16.760 --> 00:26:17.410
+prediction.
+
+00:26:18.670 --> 00:26:20.420
+So at the end of this, you transform
+
+00:26:20.420 --> 00:26:22.940
+what we're two continuous values into
+
+00:26:22.940 --> 00:26:24.770
+these four discrete values.
+
+00:26:25.450 --> 00:26:27.360
+Of different chunks, different
+
+00:26:27.360 --> 00:26:30.130
+partitions of the feature space and for
+
+00:26:30.130 --> 00:26:31.350
+each of those.
+
+00:26:32.420 --> 00:26:34.850
+Each of those parts of the partition.
+
+00:26:35.810 --> 00:26:38.360
+You make a prediction.
+
+00:26:39.240 --> 00:26:41.620
+A partitioning is just when you take a
+
+00:26:41.620 --> 00:26:44.390
+continuous space and divide it up into
+
+00:26:44.390 --> 00:26:46.850
+different cells that cover the entire
+
+00:26:46.850 --> 00:26:47.400
+space.
+
+00:26:47.400 --> 00:26:49.859
+That's a partition where the cells
+
+00:26:49.860 --> 00:26:51.040
+don't overlap with each other.
+
+00:26:54.340 --> 00:26:56.460
+And then if you want to classify, once
+
+00:26:56.460 --> 00:26:57.940
+you've trained your tree, you get some
+
+00:26:57.940 --> 00:26:59.450
+new test sample and you want to know is
+
+00:26:59.450 --> 00:27:01.450
+that a lemon or an orange kind of looks
+
+00:27:01.450 --> 00:27:01.920
+in between.
+
+00:27:02.610 --> 00:27:05.295
+So you is it greater than 6.5
+
+00:27:05.295 --> 00:27:05.740
+centimeters?
+
+00:27:05.740 --> 00:27:06.185
+No.
+
+00:27:06.185 --> 00:27:08.355
+Is a tight greater than 6 centimeters?
+
+00:27:08.355 --> 00:27:08.690
+No.
+
+00:27:08.690 --> 00:27:10.110
+And so therefore it's an orange
+
+00:27:10.110 --> 00:27:10.970
+according to your rule.
+
+00:27:13.260 --> 00:27:15.053
+And you could take this tree and could
+
+00:27:15.053 --> 00:27:17.456
+you could rewrite it as a set of rules,
+
+00:27:17.456 --> 00:27:20.560
+like one rule is greater than 6.5,
+
+00:27:20.560 --> 00:27:23.478
+height greater than 9.5, another rule
+
+00:27:23.478 --> 00:27:26.020
+is greater than 65, height less than
+
+00:27:26.020 --> 00:27:27.330
+9.5, and so on.
+
+00:27:27.330 --> 00:27:28.640
+There's like 4 different rules
+
+00:27:28.640 --> 00:27:31.180
+represented by this tree, and each rule
+
+00:27:31.180 --> 00:27:33.950
+corresponds to some section of the
+
+00:27:33.950 --> 00:27:36.440
+feature space, and each rule yields
+
+00:27:36.440 --> 00:27:37.140
+some prediction.
+
+00:27:40.950 --> 00:27:44.020
+So here's another example with some
+
+00:27:44.020 --> 00:27:45.580
+discrete inputs.
+
+00:27:45.580 --> 00:27:48.030
+So here the prediction problem is to
+
+00:27:48.030 --> 00:27:49.955
+tell whether or not somebody's going to
+
+00:27:49.955 --> 00:27:50.350
+wait.
+
+00:27:50.350 --> 00:27:52.440
+If they go to a restaurant and they're
+
+00:27:52.440 --> 00:27:54.173
+told they have to wait, so do they wait
+
+00:27:54.173 --> 00:27:55.160
+or do they leave?
+
+00:27:56.290 --> 00:27:58.170
+And the features are things like
+
+00:27:58.170 --> 00:28:00.160
+whether there's an alternative nearby,
+
+00:28:00.160 --> 00:28:02.240
+whether there's a bar they can wait at,
+
+00:28:02.240 --> 00:28:03.900
+whether it's Friday or Saturday,
+
+00:28:03.900 --> 00:28:05.289
+whether they're Hungry, whether the
+
+00:28:05.290 --> 00:28:07.106
+restaurants full, what the price is,
+
+00:28:07.106 --> 00:28:08.740
+whether it's raining, whether they had
+
+00:28:08.740 --> 00:28:10.560
+a Reservation, what type of restaurant
+
+00:28:10.560 --> 00:28:12.900
+is, and they would wait time.
+
+00:28:12.900 --> 00:28:14.747
+And these are all categorical, so the
+
+00:28:14.747 --> 00:28:16.100
+wait time is split into different
+
+00:28:16.100 --> 00:28:16.540
+chunks.
+
+00:28:20.660 --> 00:28:22.670
+And so you could.
+
+00:28:24.110 --> 00:28:27.810
+You could train a tree from these
+
+00:28:27.810 --> 00:28:29.820
+categorical variables, and of course I
+
+00:28:29.820 --> 00:28:31.590
+will tell you more about like how you
+
+00:28:31.590 --> 00:28:32.390
+would learn this tree.
+
+00:28:33.960 --> 00:28:35.670
+But you might have a tree like this
+
+00:28:35.670 --> 00:28:36.500
+where you say.
+
+00:28:37.730 --> 00:28:39.770
+First, are there are there people in
+
+00:28:39.770 --> 00:28:40.370
+the restaurant?
+
+00:28:40.370 --> 00:28:41.800
+Patrons means like it's a restaurant
+
+00:28:41.800 --> 00:28:42.684
+full or not.
+
+00:28:42.684 --> 00:28:46.310
+If it's not full, then you leave right
+
+00:28:46.310 --> 00:28:47.790
+away because they're just being rude.
+
+00:28:47.790 --> 00:28:49.330
+If they tell, you have to wait I guess.
+
+00:28:49.930 --> 00:28:52.140
+If it's partly full then you'll wait,
+
+00:28:52.140 --> 00:28:54.080
+and if it's full then you then you have
+
+00:28:54.080 --> 00:28:55.680
+like consider further things.
+
+00:28:55.680 --> 00:28:58.360
+If it's a WaitEstimate, really short,
+
+00:28:58.360 --> 00:28:58.990
+then you wait.
+
+00:28:58.990 --> 00:28:59.660
+Is it really long?
+
+00:28:59.660 --> 00:29:00.170
+Then you don't.
+
+00:29:00.960 --> 00:29:03.290
+Otherwise, are you hungry?
+
+00:29:03.290 --> 00:29:04.693
+If you're not, then you'll wait.
+
+00:29:04.693 --> 00:29:06.600
+If you are, then you keep thinking.
+
+00:29:06.600 --> 00:29:08.320
+So you have like, all this series of
+
+00:29:08.320 --> 00:29:08.820
+choices.
+
+00:29:10.350 --> 00:29:12.790
+That these trees and practice like if
+
+00:29:12.790 --> 00:29:14.230
+you were to use a Decision tree on
+
+00:29:14.230 --> 00:29:14.680
+MNIST.
+
+00:29:15.810 --> 00:29:17.600
+Where the features are pretty weak
+
+00:29:17.600 --> 00:29:19.510
+individually, they're just like pixel
+
+00:29:19.510 --> 00:29:20.140
+values.
+
+00:29:20.140 --> 00:29:21.610
+You can imagine that this tree could
+
+00:29:21.610 --> 00:29:23.160
+get really complicated and long.
+
+00:29:27.970 --> 00:29:28.390
+Right.
+
+00:29:28.390 --> 00:29:31.840
+So just to mostly be state.
+
+00:29:32.450 --> 00:29:34.080
+And then Decision tree.
+
+00:29:34.080 --> 00:29:36.410
+The internal nodes are Test Attributes,
+
+00:29:36.410 --> 00:29:38.150
+so it's some kind of like feature.
+
+00:29:38.150 --> 00:29:40.050
+Attribute and feature are synonymous,
+
+00:29:40.050 --> 00:29:41.110
+they're the same thing.
+
+00:29:41.830 --> 00:29:45.880
+Some kind of feature attribute and.
+
+00:29:45.960 --> 00:29:47.420
+And if it's a continuous attribute then
+
+00:29:47.420 --> 00:29:48.420
+you have to have some kind of
+
+00:29:48.420 --> 00:29:53.420
+threshold, so width greater than 6.5 or
+
+00:29:53.420 --> 00:29:54.650
+is it raining or not?
+
+00:29:54.650 --> 00:29:56.050
+Those are two examples of.
+
+00:29:56.740 --> 00:29:57.440
+Of tests.
+
+00:29:58.370 --> 00:29:59.984
+Then depending on the outcome of that
+
+00:29:59.984 --> 00:30:02.310
+test, you split in different ways, and
+
+00:30:02.310 --> 00:30:03.860
+when you're Training, you split all
+
+00:30:03.860 --> 00:30:05.935
+your data according to that test, and
+
+00:30:05.935 --> 00:30:07.960
+then you're going to solve again within
+
+00:30:07.960 --> 00:30:09.390
+each of those nodes separately.
+
+00:30:10.480 --> 00:30:11.570
+For the next Test.
+
+00:30:12.260 --> 00:30:14.110
+Until you get to a leaf node, and at
+
+00:30:14.110 --> 00:30:16.125
+the leaf node you provide an output or
+
+00:30:16.125 --> 00:30:18.532
+a prediction, which could be, which in
+
+00:30:18.532 --> 00:30:20.480
+this case is a class, in this
+
+00:30:20.480 --> 00:30:21.780
+particular example whether it's a
+
+00:30:21.780 --> 00:30:22.540
+Linear orange.
+
+00:30:25.060 --> 00:30:25.260
+Yep.
+
+00:30:29.360 --> 00:30:31.850
+So the question is how does it Decision
+
+00:30:31.850 --> 00:30:34.700
+tree account for anomalies as in late
+
+00:30:34.700 --> 00:30:36.480
+mislabeled data or really weird
+
+00:30:36.480 --> 00:30:37.260
+examples or?
+
+00:30:50.100 --> 00:30:52.370
+So the so the question is like how does
+
+00:30:52.370 --> 00:30:54.400
+it Decision tree deal with weird or
+
+00:30:54.400 --> 00:30:55.860
+unlikely examples?
+
+00:30:55.860 --> 00:30:58.020
+And that's a good question because one
+
+00:30:58.020 --> 00:31:00.200
+of the things about a Decision tree is
+
+00:31:00.200 --> 00:31:01.510
+that if you train it.
+
+00:31:02.350 --> 00:31:04.460
+If you train it, if you train the full
+
+00:31:04.460 --> 00:31:06.560
+tree, then you can always.
+
+00:31:06.560 --> 00:31:09.970
+As long as the feature vectors for each
+
+00:31:09.970 --> 00:31:11.560
+sample are unique, you can always get
+
+00:31:11.560 --> 00:31:13.470
+perfect Classification Error.
+
+00:31:13.470 --> 00:31:14.900
+A tree has no bias.
+
+00:31:14.900 --> 00:31:16.580
+You can always like fit your training
+
+00:31:16.580 --> 00:31:18.980
+data perfectly because you just keep on
+
+00:31:18.980 --> 00:31:20.530
+chopping it into smaller and smaller
+
+00:31:20.530 --> 00:31:22.070
+bits until finally the answer.
+
+00:31:22.800 --> 00:31:24.960
+So as a result, that can be dangerous
+
+00:31:24.960 --> 00:31:26.767
+because if you do have some unusual
+
+00:31:26.767 --> 00:31:29.100
+examples, you can end up creating rules
+
+00:31:29.100 --> 00:31:31.410
+based on those examples that don't
+
+00:31:31.410 --> 00:31:32.920
+generalize well tuning data.
+
+00:31:33.640 --> 00:31:36.191
+And so some things that you can do are
+
+00:31:36.191 --> 00:31:38.119
+you can stop Training, stop Training
+
+00:31:38.120 --> 00:31:38.590
+early.
+
+00:31:38.590 --> 00:31:40.440
+So you can say I'm not going to split
+
+00:31:40.440 --> 00:31:42.530
+once I only have 5 examples of my leaf
+
+00:31:42.530 --> 00:31:43.990
+node, I'm going to quit splitting and
+
+00:31:43.990 --> 00:31:45.460
+I'll just output my best guess.
+
+00:31:46.520 --> 00:31:47.070
+
+
+00:31:47.990 --> 00:31:49.240
+There's also like.
+
+00:31:52.250 --> 00:31:53.770
+Probably on Tuesday.
+
+00:31:53.770 --> 00:31:54.810
+Actually, I'm going to talk about
+
+00:31:54.810 --> 00:31:56.790
+ensembles, which is ways of combining
+
+00:31:56.790 --> 00:31:58.770
+money trees, which is another way of
+
+00:31:58.770 --> 00:31:59.840
+getting rid of this problem.
+
+00:32:01.360 --> 00:32:01.750
+Question.
+
+00:32:09.850 --> 00:32:11.190
+That's a good question too.
+
+00:32:11.190 --> 00:32:12.890
+So the question is whether Decision
+
+00:32:12.890 --> 00:32:14.500
+trees are always binary.
+
+00:32:14.500 --> 00:32:17.880
+So like in this example, it's not
+
+00:32:17.880 --> 00:32:21.640
+binary, they're splitting like the
+
+00:32:21.640 --> 00:32:23.250
+Patrons is splitting based on three
+
+00:32:23.250 --> 00:32:23.780
+values.
+
+00:32:24.510 --> 00:32:28.260
+But typically they are binary.
+
+00:32:28.260 --> 00:32:29.030
+So if you're.
+
+00:32:29.810 --> 00:32:32.277
+If you're using continuous values, it
+
+00:32:32.277 --> 00:32:32.535
+will.
+
+00:32:32.535 --> 00:32:34.410
+It will almost always be binary,
+
+00:32:34.410 --> 00:32:35.440
+because you could.
+
+00:32:35.440 --> 00:32:37.330
+Even if you wanted to split continuous
+
+00:32:37.330 --> 00:32:40.260
+variables into many different chunks,
+
+00:32:40.260 --> 00:32:42.350
+you can do that through a sequence of
+
+00:32:42.350 --> 00:32:43.380
+binary decisions.
+
+00:32:44.780 --> 00:32:47.620
+In SK learn as well, their Decision
+
+00:32:47.620 --> 00:32:50.160
+trees cannot deal with like multi
+
+00:32:50.160 --> 00:32:53.040
+valued attributes and so you need to
+
+00:32:53.040 --> 00:32:55.000
+convert them into binary attributes in
+
+00:32:55.000 --> 00:32:56.470
+order to use sklearn.
+
+00:32:57.350 --> 00:32:59.470
+And I think often that's done as a
+
+00:32:59.470 --> 00:33:01.590
+design Decision, because otherwise like
+
+00:33:01.590 --> 00:33:03.050
+some features will be like
+
+00:33:03.050 --> 00:33:04.780
+intrinsically more powerful than other
+
+00:33:04.780 --> 00:33:06.690
+features if they create like more
+
+00:33:06.690 --> 00:33:07.340
+splits.
+
+00:33:07.340 --> 00:33:09.160
+So it can cause like a bias in your
+
+00:33:09.160 --> 00:33:09.990
+feature selection.
+
+00:33:10.740 --> 00:33:12.990
+So they don't have to be binary, but
+
+00:33:12.990 --> 00:33:15.160
+it's a common common setting.
+
+00:33:21.880 --> 00:33:24.480
+Alright, so the Training 4 Decision
+
+00:33:24.480 --> 00:33:26.760
+tree again without yet getting into the
+
+00:33:26.760 --> 00:33:27.000
+math.
+
+00:33:27.710 --> 00:33:30.935
+Is Recursively for each node in the
+
+00:33:30.935 --> 00:33:32.590
+tree, if the labels and the node are
+
+00:33:32.590 --> 00:33:33.120
+mixed.
+
+00:33:33.120 --> 00:33:35.256
+So to start with, we're at the of the
+
+00:33:35.256 --> 00:33:38.030
+tree and we have all this data, and so
+
+00:33:38.030 --> 00:33:39.676
+essentially there's just right now some
+
+00:33:39.676 --> 00:33:41.025
+probability that's a no, some
+
+00:33:41.025 --> 00:33:41.950
+probability that's an 784x1.
+
+00:33:41.950 --> 00:33:43.900
+Those probabilities are close to 5050.
+
+00:33:45.530 --> 00:33:47.410
+Then I'm going to choose some attribute
+
+00:33:47.410 --> 00:33:50.020
+and split the values based on the data
+
+00:33:50.020 --> 00:33:51.200
+that reaches that node.
+
+00:33:52.310 --> 00:33:54.310
+So here I Choose this attribute the
+
+00:33:54.310 --> 00:33:55.430
+tree I'm creating up there.
+
+00:33:56.110 --> 00:33:58.060
+X2 is less than .6.
+
+00:34:00.630 --> 00:34:05.310
+If it's less than .6 then I go down one
+
+00:34:05.310 --> 00:34:07.067
+branch and if it's greater than I go
+
+00:34:07.067 --> 00:34:08.210
+down the other branch.
+
+00:34:08.210 --> 00:34:10.870
+So now then I can now start making
+
+00:34:10.870 --> 00:34:13.440
+decisions separately about this region
+
+00:34:13.440 --> 00:34:14.260
+in this region.
+
+00:34:15.910 --> 00:34:19.200
+So then I Choose another node and I say
+
+00:34:19.200 --> 00:34:21.660
+if X1 is less than 7.
+
+00:34:22.630 --> 00:34:24.360
+So I create this split and this only
+
+00:34:24.360 --> 00:34:25.490
+pertains to the data.
+
+00:34:25.490 --> 00:34:27.570
+Now that came down the first node so
+
+00:34:27.570 --> 00:34:28.989
+it's this side of the data.
+
+00:34:29.710 --> 00:34:31.292
+So if it's over here, then it's a no,
+
+00:34:31.292 --> 00:34:33.220
+if it's over here, then it's an X and
+
+00:34:33.220 --> 00:34:34.620
+Now I don't need to create anymore
+
+00:34:34.620 --> 00:34:36.690
+Decision nodes for this whole region of
+
+00:34:36.690 --> 00:34:38.870
+space because I have perfect
+
+00:34:38.870 --> 00:34:39.630
+Classification.
+
+00:34:40.760 --> 00:34:43.010
+Then I go to my top side.
+
+00:34:43.730 --> 00:34:45.390
+And I can make another split.
+
+00:34:45.390 --> 00:34:47.760
+So here there's actually more than one
+
+00:34:47.760 --> 00:34:48.015
+choice.
+
+00:34:48.015 --> 00:34:49.960
+I think that's like kind of equally
+
+00:34:49.960 --> 00:34:51.460
+good, but.
+
+00:34:51.570 --> 00:34:56.230
+Again, say if X2 is less than .8, then
+
+00:34:56.230 --> 00:34:57.960
+it goes down here where I'm still
+
+00:34:57.960 --> 00:34:58.250
+unsure.
+
+00:34:58.250 --> 00:35:00.080
+If it's greater than eight, then it's
+
+00:35:00.080 --> 00:35:00.980
+definitely a red X.
+
+00:35:03.260 --> 00:35:05.120
+And then I can keep doing that until I
+
+00:35:05.120 --> 00:35:07.190
+finally have a perfect Classification
+
+00:35:07.190 --> 00:35:08.030
+in the training data.
+
+00:35:08.810 --> 00:35:10.000
+So that's the full tree.
+
+00:35:11.070 --> 00:35:13.830
+And if you could stop early, you could
+
+00:35:13.830 --> 00:35:15.739
+say I'm not going to go past like 3
+
+00:35:15.740 --> 00:35:18.310
+levels, or that I'm going to stop
+
+00:35:18.310 --> 00:35:20.910
+splitting once my leaf node doesn't
+
+00:35:20.910 --> 00:35:23.210
+have more than five examples.
+
+00:35:39.470 --> 00:35:41.560
+Well, the question was does the first
+
+00:35:41.560 --> 00:35:42.320
+split matter?
+
+00:35:42.320 --> 00:35:43.929
+So I guess there's two parts to that.
+
+00:35:43.930 --> 00:35:45.880
+One is that I will tell you how we do
+
+00:35:45.880 --> 00:35:46.980
+this computationally.
+
+00:35:46.980 --> 00:35:48.780
+So you try to greedily find like the
+
+00:35:48.780 --> 00:35:49.900
+best split every time.
+
+00:35:50.990 --> 00:35:53.530
+And the other thing is that finding the
+
+00:35:53.530 --> 00:35:57.290
+minimum size tree is like a
+
+00:35:57.290 --> 00:35:59.540
+computationally hard problem.
+
+00:36:00.540 --> 00:36:01.766
+So it's infeasible.
+
+00:36:01.766 --> 00:36:04.530
+So you end up with a greedy solution
+
+00:36:04.530 --> 00:36:06.020
+where for every node you're choosing
+
+00:36:06.020 --> 00:36:08.200
+the best split for that node.
+
+00:36:08.200 --> 00:36:10.045
+But that doesn't necessarily give you
+
+00:36:10.045 --> 00:36:11.680
+the shortest tree overall, because you
+
+00:36:11.680 --> 00:36:13.020
+don't know like what kinds of splits
+
+00:36:13.020 --> 00:36:14.250
+will be available to you later.
+
+00:36:16.710 --> 00:36:19.050
+So it does matter, but you have like
+
+00:36:19.050 --> 00:36:20.630
+there's an algorithm for doing it in a
+
+00:36:20.630 --> 00:36:21.550
+decent way, yeah.
+
+00:36:55.320 --> 00:36:55.860
+
+
+00:36:57.660 --> 00:36:59.080
+There have well.
+
+00:37:01.160 --> 00:37:02.650
+How will you know that it will work for
+
+00:37:02.650 --> 00:37:03.320
+like new data?
+
+00:37:05.000 --> 00:37:09.209
+So basically if you want to know, you
+
+00:37:09.210 --> 00:37:10.740
+do always want to know, you always want
+
+00:37:10.740 --> 00:37:12.420
+to know, right, if you if the model
+
+00:37:12.420 --> 00:37:13.620
+that you learned is going to work for
+
+00:37:13.620 --> 00:37:14.540
+new data.
+
+00:37:14.540 --> 00:37:16.370
+And so that's why I typically you would
+
+00:37:16.370 --> 00:37:18.030
+carve off, if you have some Training
+
+00:37:18.030 --> 00:37:19.800
+set, you'd carve off a validation set.
+
+00:37:20.450 --> 00:37:22.380
+And you would train it say with like
+
+00:37:22.380 --> 00:37:25.040
+70% of the Training examples and test
+
+00:37:25.040 --> 00:37:27.850
+it on the 30% of the held out Samples?
+
+00:37:28.530 --> 00:37:30.040
+And then there was held out Samples
+
+00:37:30.040 --> 00:37:32.170
+will give you an estimate of how well
+
+00:37:32.170 --> 00:37:33.260
+your method works.
+
+00:37:33.260 --> 00:37:35.250
+And so then like if you find for
+
+00:37:35.250 --> 00:37:37.626
+example that I trained a full tree and
+
+00:37:37.626 --> 00:37:39.850
+of course I got like 0% Training error,
+
+00:37:39.850 --> 00:37:41.850
+but my Test error is like 40%.
+
+00:37:42.590 --> 00:37:44.990
+Then you would probably say maybe I
+
+00:37:44.990 --> 00:37:46.803
+should try Training a shorter tree and
+
+00:37:46.803 --> 00:37:48.930
+then you can like retrain it with some
+
+00:37:48.930 --> 00:37:51.120
+constraints and then test it again on
+
+00:37:51.120 --> 00:37:52.755
+your validation set and Choose like
+
+00:37:52.755 --> 00:37:53.830
+your Parameters that way.
+
+00:37:54.860 --> 00:37:57.581
+There's also I'll talk about most
+
+00:37:57.581 --> 00:37:59.140
+likely, most likely this.
+
+00:37:59.140 --> 00:38:01.020
+I was planning to do it Thursday, but
+
+00:38:01.020 --> 00:38:02.187
+I'll probably do it next Tuesday.
+
+00:38:02.187 --> 00:38:04.580
+I'll talk about ensembles, including
+
+00:38:04.580 --> 00:38:06.622
+random forests, and those are like kind
+
+00:38:06.622 --> 00:38:09.150
+of like brain dead always work methods
+
+00:38:09.150 --> 00:38:11.080
+that combine a lot of trees and are
+
+00:38:11.080 --> 00:38:13.439
+really reliable whether you have a lot
+
+00:38:13.439 --> 00:38:16.087
+of data or well, you kind of need data.
+
+00:38:16.087 --> 00:38:17.665
+But whether you have a lot of features
+
+00:38:17.665 --> 00:38:19.850
+or a little features, they always work.
+
+00:38:20.480 --> 00:38:21.480
+They always work pretty well.
+
+00:38:23.820 --> 00:38:25.950
+Right, so in prediction then you just
+
+00:38:25.950 --> 00:38:27.560
+basically descend the tree, so you
+
+00:38:27.560 --> 00:38:29.920
+check the conditions is tX2 greater
+
+00:38:29.920 --> 00:38:32.370
+than .6 blah blah blah blah blah until
+
+00:38:32.370 --> 00:38:33.750
+you find yourself in a leaf node.
+
+00:38:34.380 --> 00:38:36.630
+So for example, if I have this data
+
+00:38:36.630 --> 00:38:38.500
+point and I'm trying to classify it, I
+
+00:38:38.500 --> 00:38:40.902
+would end up following these rules down
+
+00:38:40.902 --> 00:38:44.290
+to down to the leaf node of.
+
+00:38:45.960 --> 00:38:47.418
+Yeah, like right over here, right?
+
+00:38:47.418 --> 00:38:50.158
+X2 is less than .6 and X1 is less than
+
+00:38:50.158 --> 00:38:50.460
+.7.
+
+00:38:51.260 --> 00:38:52.740
+And so that's going to be no.
+
+00:38:53.860 --> 00:38:56.500
+And if I am over here then I end up
+
+00:38:56.500 --> 00:38:59.420
+following going down to here to here.
+
+00:39:00.480 --> 00:39:03.020
+To here to here and I end up in this
+
+00:39:03.020 --> 00:39:07.299
+leaf node and so it's an X and it
+
+00:39:07.300 --> 00:39:09.395
+doesn't matter like where it falls in
+
+00:39:09.395 --> 00:39:10.580
+this part of the space.
+
+00:39:10.580 --> 00:39:11.700
+Usually this isn't like.
+
+00:39:12.390 --> 00:39:13.770
+Even something you necessarily
+
+00:39:13.770 --> 00:39:15.520
+visualize, but.
+
+00:39:16.060 --> 00:39:18.025
+But it's worth noting that even parts
+
+00:39:18.025 --> 00:39:20.020
+of your feature space that are kind of
+
+00:39:20.020 --> 00:39:22.640
+far away from any Example can still get
+
+00:39:22.640 --> 00:39:24.360
+classified by this Decision tree.
+
+00:39:25.070 --> 00:39:27.670
+And it's not necessarily the Nearest
+
+00:39:27.670 --> 00:39:28.450
+neighbor Decision.
+
+00:39:28.450 --> 00:39:31.186
+Like this star here is actually closer
+
+00:39:31.186 --> 00:39:33.390
+to the 784x1 than it is to the O's, but
+
+00:39:33.390 --> 00:39:35.010
+it would still be a no because it's on
+
+00:39:35.010 --> 00:39:36.050
+that side of the boundary.
+
+00:39:40.650 --> 00:39:42.350
+So the key question is, how do you
+
+00:39:42.350 --> 00:39:45.810
+choose what attribute to split and
+
+00:39:45.810 --> 00:39:46.384
+where to split?
+
+00:39:46.384 --> 00:39:48.390
+So how do you decide what test you're
+
+00:39:48.390 --> 00:39:50.000
+going to use for a given node?
+
+00:39:50.920 --> 00:39:53.615
+And so let's take this example.
+
+00:39:53.615 --> 00:39:56.290
+So here I've got some table of features
+
+00:39:56.290 --> 00:39:57.180
+and predictions.
+
+00:39:58.020 --> 00:39:59.010
+And if.
+
+00:40:00.410 --> 00:40:02.280
+And if I were to split, these are
+
+00:40:02.280 --> 00:40:04.570
+binary features so they just have two
+
+00:40:04.570 --> 00:40:06.430
+values T2 false I guess.
+
+00:40:07.400 --> 00:40:07.940
+If.
+
+00:40:09.620 --> 00:40:12.440
+If I split based on X1 and I go in One
+
+00:40:12.440 --> 00:40:14.570
+Direction, then it's all true.
+
+00:40:15.200 --> 00:40:17.585
+The prediction is true and if I go in
+
+00:40:17.585 --> 00:40:19.920
+the other direction then 3/4 of the
+
+00:40:19.920 --> 00:40:21.080
+time the prediction is false.
+
+00:40:22.810 --> 00:40:26.343
+If I split based on X2, then 3/4 of the
+
+00:40:26.343 --> 00:40:27.948
+time the prediction is true.
+
+00:40:27.948 --> 00:40:31.096
+If it's true and 50% of the time the
+
+00:40:31.096 --> 00:40:32.819
+prediction is false, X2 is false.
+
+00:40:33.530 --> 00:40:36.300
+So which of these features is a better
+
+00:40:36.300 --> 00:40:37.400
+Test?
+
+00:40:39.550 --> 00:40:41.530
+So how many people think that the left
+
+00:40:41.530 --> 00:40:42.530
+is a better Test?
+
+00:40:43.790 --> 00:40:45.070
+How many people think they're right is
+
+00:40:45.070 --> 00:40:45.730
+a better Test.
+
+00:40:46.840 --> 00:40:48.380
+Right the left is a better Test
+
+00:40:48.380 --> 00:40:48.950
+because.
+
+00:40:50.620 --> 00:40:53.380
+Because my uncertainty is greatly
+
+00:40:53.380 --> 00:40:54.990
+reduced on the left side.
+
+00:40:54.990 --> 00:40:58.750
+So initially, initially I had like a
+
+00:40:58.750 --> 00:41:01.280
+5/8 chance of getting it right if I
+
+00:41:01.280 --> 00:41:02.280
+just guessed true.
+
+00:41:02.910 --> 00:41:06.706
+But if I know X1, then I've got a 100%
+
+00:41:06.706 --> 00:41:08.600
+chance of getting it right, at least in
+
+00:41:08.600 --> 00:41:09.494
+the training data.
+
+00:41:09.494 --> 00:41:13.338
+If I know that X1 is true, and I've got
+
+00:41:13.338 --> 00:41:15.132
+a 3/4 chance of getting it right if I
+
+00:41:15.132 --> 00:41:16.280
+know that X1 is false.
+
+00:41:16.280 --> 00:41:19.135
+So X1 tells me a lot about the
+
+00:41:19.135 --> 00:41:19.572
+prediction.
+
+00:41:19.572 --> 00:41:22.035
+It greatly reduces my uncertainty about
+
+00:41:22.035 --> 00:41:22.890
+the prediction.
+
+00:41:24.510 --> 00:41:26.412
+And to quantify this, we need to
+
+00:41:26.412 --> 00:41:28.560
+quantify uncertainty and then be able
+
+00:41:28.560 --> 00:41:32.350
+to measure how much a certain feature
+
+00:41:32.350 --> 00:41:33.950
+reduces our uncertainty in the
+
+00:41:33.950 --> 00:41:34.720
+prediction.
+
+00:41:34.720 --> 00:41:36.800
+And that's called the information gain.
+
+00:41:40.470 --> 00:41:44.540
+So to quantify the uncertainty, I'll
+
+00:41:44.540 --> 00:41:45.595
+use these two examples.
+
+00:41:45.595 --> 00:41:47.790
+So imagine that you're flipping a coin.
+
+00:41:47.790 --> 00:41:50.150
+These are like heads and tails, or
+
+00:41:50.150 --> 00:41:51.510
+present them as zeros and ones.
+
+00:41:52.180 --> 00:41:54.820
+And so one time I've got two different
+
+00:41:54.820 --> 00:41:56.186
+sequences, let's say two different
+
+00:41:56.186 --> 00:41:57.740
+coins and one in the coins.
+
+00:41:57.740 --> 00:42:00.120
+It's a biased coin, so I end up with
+
+00:42:00.120 --> 00:42:03.330
+zeros or heads like 16 out of 18 times.
+
+00:42:04.250 --> 00:42:06.520
+And the other for the other Coin I get
+
+00:42:06.520 --> 00:42:09.400
+closer to 5058 out of.
+
+00:42:10.050 --> 00:42:12.390
+18 times I get heads so.
+
+00:42:13.530 --> 00:42:17.520
+Which of these has higher uncertainty?
+
+00:42:18.540 --> 00:42:19.730
+The left or the right?
+
+00:42:21.330 --> 00:42:22.580
+Right, correct.
+
+00:42:22.580 --> 00:42:23.070
+They're right.
+
+00:42:23.070 --> 00:42:24.900
+Has a lot higher uncertainty.
+
+00:42:24.900 --> 00:42:27.370
+So if I with that Coin, I really don't
+
+00:42:27.370 --> 00:42:28.470
+know if it's going to be heads or
+
+00:42:28.470 --> 00:42:30.860
+tails, but on the left side, I'm pretty
+
+00:42:30.860 --> 00:42:31.820
+sure it's going to be heads.
+
+00:42:32.590 --> 00:42:33.360
+Or zeros.
+
+00:42:34.720 --> 00:42:36.770
+So we can measure that with this
+
+00:42:36.770 --> 00:42:38.645
+function called Entropy.
+
+00:42:38.645 --> 00:42:41.350
+So the entropy is a measure of
+
+00:42:41.350 --> 00:42:42.030
+uncertainty.
+
+00:42:42.960 --> 00:42:45.740
+And it's defined as the negative sum
+
+00:42:45.740 --> 00:42:48.070
+over all the values of some variable of
+
+00:42:48.070 --> 00:42:50.220
+the probability of that value.
+
+00:42:51.020 --> 00:42:53.490
+Times the log probability that value,
+
+00:42:53.490 --> 00:42:56.470
+and people usually sometimes use like
+
+00:42:56.470 --> 00:42:57.520
+log base 2.
+
+00:42:58.630 --> 00:43:00.700
+Just because that way the Entropy
+
+00:43:00.700 --> 00:43:02.550
+ranges from zero to 1 if you have
+
+00:43:02.550 --> 00:43:03.490
+binary variables.
+
+00:43:07.600 --> 00:43:10.820
+So for this case here, the Entropy
+
+00:43:10.820 --> 00:43:13.280
+would be -, 8 ninths, because eight out
+
+00:43:13.280 --> 00:43:14.600
+of nine times it's zero.
+
+00:43:15.270 --> 00:43:17.300
+Times log two of eight ninths.
+
+00:43:18.230 --> 00:43:21.210
+Minus one ninth times, log 2 of 1 ninth
+
+00:43:21.210 --> 00:43:22.790
+and that works out to about 1/2.
+
+00:43:24.370 --> 00:43:28.480
+And over here the Entropy is -, 4
+
+00:43:28.480 --> 00:43:30.270
+ninths because four out of nine times,
+
+00:43:30.270 --> 00:43:32.900
+or 8 out of 18 times, it's a 0.
+
+00:43:34.410 --> 00:43:37.104
+Times log 24 ninths, minus five ninths,
+
+00:43:37.104 --> 00:43:39.010
+times log two of five ninths, and
+
+00:43:39.010 --> 00:43:41.490
+that's about 99.
+
+00:43:43.430 --> 00:43:45.280
+The Entropy measure is how surprised
+
+00:43:45.280 --> 00:43:47.595
+are we by some new value of this
+
+00:43:47.595 --> 00:43:47.830
+Sequence?
+
+00:43:47.830 --> 00:43:50.123
+How surprised are we likely to be in,
+
+00:43:50.123 --> 00:43:52.460
+or how much information does it convey
+
+00:43:52.460 --> 00:43:54.895
+that we know that we're in this
+
+00:43:54.895 --> 00:43:56.974
+Sequence, or more generally, that we
+
+00:43:56.974 --> 00:43:57.940
+know some feature?
+
+00:44:01.100 --> 00:44:03.425
+So this is just showing the Entropy if
+
+00:44:03.425 --> 00:44:05.450
+the probability if you have a binary
+
+00:44:05.450 --> 00:44:06.340
+variable X.
+
+00:44:07.110 --> 00:44:09.720
+And the probability of X is 0, then
+
+00:44:09.720 --> 00:44:12.180
+your Entropy is 0 because you always
+
+00:44:12.180 --> 00:44:15.127
+know that if probability of X = 2 is
+
+00:44:15.127 --> 00:44:16.818
+zero, that means that probability of X
+
+00:44:16.818 --> 00:44:18.210
+equals false is 1.
+
+00:44:18.860 --> 00:44:20.530
+And so therefore you have complete
+
+00:44:20.530 --> 00:44:22.470
+confidence that the value will be
+
+00:44:22.470 --> 00:44:22.810
+false.
+
+00:44:24.070 --> 00:44:27.740
+If probability of X is true is 1, then
+
+00:44:27.740 --> 00:44:29.590
+you have complete confidence that the
+
+00:44:29.590 --> 00:44:30.650
+value will be true.
+
+00:44:31.440 --> 00:44:35.570
+But if it's .5, then you have no
+
+00:44:35.570 --> 00:44:37.120
+information about whether it's true or
+
+00:44:37.120 --> 00:44:39.520
+false, and so you have maximum entropy,
+
+00:44:39.520 --> 00:44:40.190
+which is 1.
+
+00:44:45.770 --> 00:44:47.280
+So here's another example.
+
+00:44:47.280 --> 00:44:49.340
+So suppose that we've got two
+
+00:44:49.340 --> 00:44:51.070
+variables, whether it's raining or not,
+
+00:44:51.070 --> 00:44:52.220
+and whether it's cloudy or not.
+
+00:44:52.820 --> 00:44:55.700
+And we've observed 100 days and marked
+
+00:44:55.700 --> 00:44:57.260
+down whether it's rainy or cloudy.
+
+00:44:58.870 --> 00:45:00.150
+Many and or Cloudy.
+
+00:45:00.930 --> 00:45:01.500
+
+
+00:45:02.600 --> 00:45:06.300
+So 24 days it was raining and cloudy.
+
+00:45:06.300 --> 00:45:08.210
+One day it was raining and not Cloudy.
+
+00:45:09.320 --> 00:45:11.244
+25 days it was not raining and cloudy
+
+00:45:11.244 --> 00:45:13.409
+and 50 days it was not raining and not
+
+00:45:13.409 --> 00:45:13.649
+Cloudy.
+
+00:45:15.620 --> 00:45:17.980
+The probabilities are just dividing by
+
+00:45:17.980 --> 00:45:18.766
+the total there.
+
+00:45:18.766 --> 00:45:20.850
+So the probability of Cloudy and not
+
+00:45:20.850 --> 00:45:22.630
+raining is 25 out of 100.
+
+00:45:24.040 --> 00:45:26.660
+And so I can also compute an Entropy of
+
+00:45:26.660 --> 00:45:27.855
+this whole joint distribution.
+
+00:45:27.855 --> 00:45:31.150
+So I can say that the entropy of X&Y
+
+00:45:31.150 --> 00:45:33.446
+together is the sum all the different
+
+00:45:33.446 --> 00:45:35.428
+values of X and the over all the
+
+00:45:35.428 --> 00:45:36.419
+different values of Y.
+
+00:45:37.060 --> 00:45:39.770
+Of probability of X&Y times log 2,
+
+00:45:39.770 --> 00:45:41.920
+probability of X&Y, and then that's all
+
+00:45:41.920 --> 00:45:42.880
+just like written out here.
+
+00:45:43.650 --> 00:45:45.115
+And then I get some Entropy value.
+
+00:45:45.115 --> 00:45:47.940
+And sometimes people call those units
+
+00:45:47.940 --> 00:45:51.490
+bits, so 156 bits because that's the
+
+00:45:51.490 --> 00:45:53.008
+amount of, that's the number of bits
+
+00:45:53.008 --> 00:45:54.680
+that I would need that I would expect
+
+00:45:54.680 --> 00:45:55.040
+to.
+
+00:45:55.790 --> 00:45:57.780
+Be able to like represent this.
+
+00:45:58.630 --> 00:45:59.700
+This information.
+
+00:46:00.430 --> 00:46:04.395
+If you if it were always not Cloudy and
+
+00:46:04.395 --> 00:46:04.990
+not raining.
+
+00:46:05.850 --> 00:46:08.020
+If it were 100% of the time not Cloudy
+
+00:46:08.020 --> 00:46:10.280
+and not raining, then you'd have 0 bits
+
+00:46:10.280 --> 00:46:11.830
+because you don't need any data to
+
+00:46:11.830 --> 00:46:12.810
+represent the.
+
+00:46:13.710 --> 00:46:15.770
+That uncertainty, it's just always
+
+00:46:15.770 --> 00:46:16.300
+true.
+
+00:46:16.300 --> 00:46:18.300
+I mean it's always like one value.
+
+00:46:18.300 --> 00:46:20.790
+So 15 bits means that you have pretty
+
+00:46:20.790 --> 00:46:21.490
+high uncertainty.
+
+00:46:25.250 --> 00:46:27.680
+There's also a concept called specific
+
+00:46:27.680 --> 00:46:28.510
+Entropy.
+
+00:46:28.510 --> 00:46:29.780
+So that is.
+
+00:46:29.780 --> 00:46:33.560
+That means that if one thing, then how
+
+00:46:33.560 --> 00:46:34.516
+much does that?
+
+00:46:34.516 --> 00:46:36.610
+How much uncertainty do you have left?
+
+00:46:37.460 --> 00:46:41.170
+So, for example, what is the entropy of
+
+00:46:41.170 --> 00:46:43.610
+cloudiness given that I know that it's
+
+00:46:43.610 --> 00:46:44.000
+raining?
+
+00:46:45.420 --> 00:46:48.940
+And the Conditional Entropy is very
+
+00:46:48.940 --> 00:46:51.280
+similar form, it's just negative sum
+
+00:46:51.280 --> 00:46:52.720
+over the values of the.
+
+00:46:53.710 --> 00:46:54.970
+The thing that you're measuring the
+
+00:46:54.970 --> 00:46:55.780
+Entropy over.
+
+00:46:56.800 --> 00:46:58.880
+The probability of that given the thing
+
+00:46:58.880 --> 00:46:59.500
+that.
+
+00:47:00.150 --> 00:47:03.610
+Times the log probability of Y given X,
+
+00:47:03.610 --> 00:47:04.760
+where Y is the thing you're measuring
+
+00:47:04.760 --> 00:47:06.400
+the uncertainty of, and X is a thing
+
+00:47:06.400 --> 00:47:06.850
+that you know.
+
+00:47:09.200 --> 00:47:12.660
+So if I know that it's Cloudy, then
+
+00:47:12.660 --> 00:47:15.690
+there's a 24 out of 25 chance that
+
+00:47:15.690 --> 00:47:16.150
+it's.
+
+00:47:17.340 --> 00:47:17.950
+Wait, no.
+
+00:47:17.950 --> 00:47:19.910
+If I know that it's raining, sorry.
+
+00:47:19.910 --> 00:47:21.599
+If I know that it's raining, then
+
+00:47:21.600 --> 00:47:23.931
+there's a 24 out of 25 chance that it's
+
+00:47:23.931 --> 00:47:24.430
+Cloudy, right?
+
+00:47:24.430 --> 00:47:26.190
+And then one out of 25 chance that it's
+
+00:47:26.190 --> 00:47:26.760
+not Cloudy.
+
+00:47:27.600 --> 00:47:30.340
+So I get 24 to 25 there and one out of
+
+00:47:30.340 --> 00:47:33.070
+25 there, and now my Entropy is greatly
+
+00:47:33.070 --> 00:47:33.660
+reduced.
+
+00:47:39.810 --> 00:47:41.280
+And then you can also measure.
+
+00:47:41.930 --> 00:47:44.250
+In expected Conditional Entropy.
+
+00:47:46.020 --> 00:47:50.570
+So that's just the probability of.
+
+00:47:50.570 --> 00:47:53.870
+That's just taking the specific
+
+00:47:53.870 --> 00:47:54.940
+Conditional Entropy.
+
+00:47:55.780 --> 00:47:58.660
+At times the probability of each of the
+
+00:47:58.660 --> 00:48:00.360
+values that I might know.
+
+00:48:01.260 --> 00:48:03.710
+Summed up over the different values,
+
+00:48:03.710 --> 00:48:04.180
+so.
+
+00:48:04.900 --> 00:48:06.130
+The.
+
+00:48:06.820 --> 00:48:09.920
+The expected Conditional value Entropy
+
+00:48:09.920 --> 00:48:11.950
+for knowing whether or not it's raining
+
+00:48:11.950 --> 00:48:15.179
+would be the Conditional Entropy.
+
+00:48:16.040 --> 00:48:19.010
+Of it raining if I know it's raining.
+
+00:48:19.920 --> 00:48:21.280
+Times the probability that it's
+
+00:48:21.280 --> 00:48:21.720
+raining.
+
+00:48:22.460 --> 00:48:24.460
+Plus the.
+
+00:48:25.190 --> 00:48:28.270
+Entropy of cloudiness given that it's
+
+00:48:28.270 --> 00:48:30.210
+not raining, times the probability
+
+00:48:30.210 --> 00:48:30.900
+that's not raining.
+
+00:48:33.530 --> 00:48:35.550
+And that's also equal to this thing.
+
+00:48:42.960 --> 00:48:43.400
+Right.
+
+00:48:43.400 --> 00:48:46.168
+So if I want to know what is the
+
+00:48:46.168 --> 00:48:47.790
+entropy of cloudiness, I guess I said
+
+00:48:47.790 --> 00:48:48.730
+it a little early.
+
+00:48:48.730 --> 00:48:50.890
+What is the entropy of cloudiness given
+
+00:48:50.890 --> 00:48:52.720
+whether that we know whether or not
+
+00:48:52.720 --> 00:48:53.340
+it's raining?
+
+00:48:54.310 --> 00:48:56.240
+Then that is.
+
+00:48:56.850 --> 00:48:59.540
+Going to be like 1/4, which is the
+
+00:48:59.540 --> 00:49:02.009
+probability that it's raining, is that
+
+00:49:02.010 --> 00:49:02.320
+right?
+
+00:49:02.320 --> 00:49:04.790
+25 out of 100 times it's raining.
+
+00:49:05.490 --> 00:49:08.225
+So 1/4 is the probability that it's
+
+00:49:08.225 --> 00:49:11.240
+raining times the Entropy of cloudiness
+
+00:49:11.240 --> 00:49:13.840
+given that it's raining plus three
+
+00:49:13.840 --> 00:49:15.710
+quarter times it's not raining times
+
+00:49:15.710 --> 00:49:17.570
+the entropy of the cloudiness given
+
+00:49:17.570 --> 00:49:18.810
+that it's not raining.
+
+00:49:20.470 --> 00:49:23.420
+So that's a measure of how much does
+
+00:49:23.420 --> 00:49:25.930
+knowing whether or not it's rainy, or
+
+00:49:25.930 --> 00:49:28.470
+how much uncertainty do I have left if
+
+00:49:28.470 --> 00:49:29.880
+I know whether or not it's raining.
+
+00:49:32.430 --> 00:49:34.030
+How much do I expect to have left?
+
+00:49:37.700 --> 00:49:39.800
+So some useful things to know is that
+
+00:49:39.800 --> 00:49:41.585
+the Entropy is always nonnegative.
+
+00:49:41.585 --> 00:49:43.580
+You can never have negative Entropy,
+
+00:49:43.580 --> 00:49:45.410
+but do make sure you remember.
+
+00:49:46.480 --> 00:49:47.310
+
+
+00:49:48.750 --> 00:49:50.380
+So do make sure you remember these
+
+00:49:50.380 --> 00:49:53.390
+negative signs in this like
+
+00:49:53.390 --> 00:49:54.910
+probability, otherwise if you end up
+
+00:49:54.910 --> 00:49:56.780
+with a negative Entropy that you left
+
+00:49:56.780 --> 00:49:57.490
+something out.
+
+00:49:59.760 --> 00:50:02.815
+You also have this chain rule, so the
+
+00:50:02.815 --> 00:50:06.320
+entropy X&Y is the entropy of X given Y
+
+00:50:06.320 --> 00:50:08.580
+plus the entropy of Y, which kind of
+
+00:50:08.580 --> 00:50:10.260
+makes sense because the Entropy of
+
+00:50:10.260 --> 00:50:11.280
+knowing two things.
+
+00:50:12.310 --> 00:50:14.540
+Of the values of two things, is the
+
+00:50:14.540 --> 00:50:15.914
+value of knowing one.
+
+00:50:15.914 --> 00:50:18.785
+Is the OR sorry, the Entropy or the
+
+00:50:18.785 --> 00:50:20.199
+uncertainty of knowing two things?
+
+00:50:20.199 --> 00:50:22.179
+Is the uncertainty of knowing one of
+
+00:50:22.180 --> 00:50:22.580
+them?
+
+00:50:23.280 --> 00:50:24.940
+Plus the uncertainty of knowing the
+
+00:50:24.940 --> 00:50:26.515
+other one, given that you already know
+
+00:50:26.515 --> 00:50:27.350
+One South.
+
+00:50:27.350 --> 00:50:30.169
+It's either Entropy of X given Y plus
+
+00:50:30.169 --> 00:50:32.323
+Entropy of Y, or Entropy of Y given X
+
+00:50:32.323 --> 00:50:33.250
+plus Entropy of 784x1.
+
+00:50:34.640 --> 00:50:38.739
+X&Y are independent, then Entropy of Y
+
+00:50:38.740 --> 00:50:40.659
+given X is equal the entropy of Y.
+
+00:50:42.870 --> 00:50:44.520
+Meaning that 784X1 doesn't reduce our
+
+00:50:44.520 --> 00:50:45.240
+uncertainty at all.
+
+00:50:46.530 --> 00:50:48.845
+And Entropy of anything with itself is
+
+00:50:48.845 --> 00:50:50.330
+0, because once you know it, then
+
+00:50:50.330 --> 00:50:51.480
+there's no uncertainty anymore.
+
+00:50:52.880 --> 00:50:53.390
+And then?
+
+00:50:54.110 --> 00:50:57.970
+If you do know something, Entropy of Y
+
+00:50:57.970 --> 00:50:59.780
+given X or at least has to be less than
+
+00:50:59.780 --> 00:51:01.430
+or equal the entropy of Y.
+
+00:51:01.430 --> 00:51:04.020
+So knowing something can never increase
+
+00:51:04.020 --> 00:51:04.690
+your uncertainty.
+
+00:51:07.660 --> 00:51:09.520
+So then finally we can get to this
+
+00:51:09.520 --> 00:51:11.132
+information gain.
+
+00:51:11.132 --> 00:51:14.730
+So information gain is the change in
+
+00:51:14.730 --> 00:51:17.530
+the Entropy due to learning something
+
+00:51:17.530 --> 00:51:17.810
+new.
+
+00:51:20.100 --> 00:51:23.310
+So I can say, for example, what is?
+
+00:51:23.310 --> 00:51:26.160
+How much does knowing whether or not
+
+00:51:26.160 --> 00:51:27.010
+it's rainy?
+
+00:51:27.960 --> 00:51:30.610
+Reduce my uncertainty of cloudiness.
+
+00:51:31.620 --> 00:51:34.542
+So that would be the Entropy of
+
+00:51:34.542 --> 00:51:37.242
+cloudiness minus the entropy of
+
+00:51:37.242 --> 00:51:39.120
+cloudiness given whether or not it's
+
+00:51:39.120 --> 00:51:39.450
+raining.
+
+00:51:41.710 --> 00:51:43.990
+So that's the Entropy of cloudiness
+
+00:51:43.990 --> 00:51:46.500
+minus the entropy of cloudiness given
+
+00:51:46.500 --> 00:51:47.640
+whether it's raining.
+
+00:51:47.640 --> 00:51:49.660
+And that's 25 bits.
+
+00:51:49.660 --> 00:51:50.993
+So that's like the value.
+
+00:51:50.993 --> 00:51:52.860
+It's essentially the value of knowing
+
+00:51:52.860 --> 00:51:54.100
+whether or not it's meaning.
+
+00:51:59.210 --> 00:52:01.140
+And then finally we can use this in our
+
+00:52:01.140 --> 00:52:02.140
+Decision tree.
+
+00:52:02.140 --> 00:52:03.660
+So if we recall.
+
+00:52:04.300 --> 00:52:07.310
+The Decision tree algorithm is that.
+
+00:52:08.410 --> 00:52:10.940
+If I'm trying to I go through like
+
+00:52:10.940 --> 00:52:12.700
+splitting my data.
+
+00:52:13.550 --> 00:52:15.050
+Choose some Test.
+
+00:52:15.050 --> 00:52:17.280
+According to the test, I split the data
+
+00:52:17.280 --> 00:52:18.970
+into different nodes and then I choose
+
+00:52:18.970 --> 00:52:20.440
+a new test for each of those nodes.
+
+00:52:21.440 --> 00:52:22.840
+So the key thing we're trying to figure
+
+00:52:22.840 --> 00:52:24.007
+out is how do we do that Test?
+
+00:52:24.007 --> 00:52:25.800
+How do we choose the features or
+
+00:52:25.800 --> 00:52:27.480
+attributes and the splitting value?
+
+00:52:28.370 --> 00:52:30.100
+To try to split things into different
+
+00:52:30.100 --> 00:52:32.030
+classes, or in other words, to try to
+
+00:52:32.030 --> 00:52:33.640
+reduce the uncertainty of our
+
+00:52:33.640 --> 00:52:34.150
+prediction.
+
+00:52:36.190 --> 00:52:39.790
+And the solution is to choose the
+
+00:52:39.790 --> 00:52:42.450
+attribute to choose the Test that
+
+00:52:42.450 --> 00:52:44.780
+maximizes the information gain.
+
+00:52:44.780 --> 00:52:46.770
+In other words, that reduces the
+
+00:52:46.770 --> 00:52:49.600
+entropy of the most for the current
+
+00:52:49.600 --> 00:52:50.370
+data in that node.
+
+00:52:52.000 --> 00:52:52.530
+So.
+
+00:52:53.260 --> 00:52:56.478
+What you would do is for each for each
+
+00:52:56.478 --> 00:52:58.700
+discrete attribute or discrete feature.
+
+00:52:59.630 --> 00:53:02.063
+You can compute the information gain of
+
+00:53:02.063 --> 00:53:04.140
+using that using that feature.
+
+00:53:04.140 --> 00:53:06.620
+So in the case of.
+
+00:53:07.360 --> 00:53:08.280
+Go back a bit.
+
+00:53:09.010 --> 00:53:11.670
+To this simple true false all right, so
+
+00:53:11.670 --> 00:53:12.650
+for example.
+
+00:53:13.650 --> 00:53:15.520
+Here I started out with a pretty high
+
+00:53:15.520 --> 00:53:17.550
+Entropy, close to one because 5/8 of
+
+00:53:17.550 --> 00:53:18.050
+the time.
+
+00:53:18.690 --> 00:53:20.850
+The value of Y is true and three it's
+
+00:53:20.850 --> 00:53:21.180
+false.
+
+00:53:22.030 --> 00:53:26.620
+And so I can say for X1, what's my
+
+00:53:26.620 --> 00:53:28.970
+Entropy after X1?
+
+00:53:28.970 --> 00:53:31.020
+It's a 5050 chance that it goes either
+
+00:53:31.020 --> 00:53:31.313
+way.
+
+00:53:31.313 --> 00:53:34.020
+So this will be 50 * 0 because the
+
+00:53:34.020 --> 00:53:36.541
+Entropy here is 0 and this will be 50
+
+00:53:36.541 --> 00:53:36.815
+times.
+
+00:53:36.815 --> 00:53:38.630
+I don't know, one or something,
+
+00:53:38.630 --> 00:53:40.659
+whatever that Entropy is, and so this
+
+00:53:40.659 --> 00:53:42.100
+Entropy will be really low.
+
+00:53:43.000 --> 00:53:45.700
+And this Entropy is just about as high
+
+00:53:45.700 --> 00:53:46.590
+as I started with.
+
+00:53:46.590 --> 00:53:48.330
+It's only a little bit lower maybe
+
+00:53:48.330 --> 00:53:50.510
+because if I go this way, I have
+
+00:53:50.510 --> 00:53:52.691
+Entropy of 1, there's a 50% chance of
+
+00:53:52.691 --> 00:53:55.188
+that, and if I go this way, then I have
+
+00:53:55.188 --> 00:53:56.721
+lower Entropy and there's a 50% chance
+
+00:53:56.721 --> 00:53:57.159
+of that.
+
+00:53:57.870 --> 00:54:00.010
+And so my information gain is my
+
+00:54:00.010 --> 00:54:01.600
+initial entropy of Y.
+
+00:54:02.980 --> 00:54:06.550
+Minus the entropy of each of these, and
+
+00:54:06.550 --> 00:54:08.005
+here the Entropy gain.
+
+00:54:08.005 --> 00:54:10.210
+The information gain of X1 is much
+
+00:54:10.210 --> 00:54:12.940
+lower than X2 and so I Choose X1.
+
+00:54:18.810 --> 00:54:20.420
+So if I have discrete values, I just
+
+00:54:20.420 --> 00:54:22.449
+compute the information gain for the
+
+00:54:22.450 --> 00:54:24.290
+current node for each of those discrete
+
+00:54:24.290 --> 00:54:25.725
+values, and then I choose the one with
+
+00:54:25.725 --> 00:54:26.860
+the highest information gain.
+
+00:54:27.780 --> 00:54:29.650
+If I have continuous values, it's
+
+00:54:29.650 --> 00:54:31.576
+slightly more complicated because then
+
+00:54:31.576 --> 00:54:34.395
+I have to also choose a threshold in
+
+00:54:34.395 --> 00:54:36.230
+the lemons and.
+
+00:54:36.920 --> 00:54:40.150
+And oranges we were choosing saying if
+
+00:54:40.150 --> 00:54:42.010
+the height is greater than six then we
+
+00:54:42.010 --> 00:54:42.620
+go one way.
+
+00:54:44.560 --> 00:54:46.640
+So we have to choose which feature and
+
+00:54:46.640 --> 00:54:47.420
+which threshold.
+
+00:54:48.430 --> 00:54:49.580
+So typically.
+
+00:54:51.060 --> 00:54:53.512
+Something this I don't know.
+
+00:54:53.512 --> 00:54:56.295
+Like who thought putting a projector in
+
+00:54:56.295 --> 00:54:57.930
+a jewel would be like a nice way to?
+
+00:54:58.590 --> 00:55:00.260
+Right and stuff, but anyway.
+
+00:55:04.700 --> 00:55:06.340
+But at least it's something, all right?
+
+00:55:06.340 --> 00:55:08.400
+So let's say that I have some feature.
+
+00:55:09.420 --> 00:55:11.910
+And I've got like some different
+
+00:55:11.910 --> 00:55:13.240
+classes and that feature.
+
+00:55:16.190 --> 00:55:18.560
+So what I would do is I would usually
+
+00:55:18.560 --> 00:55:19.950
+you would sort the values.
+
+00:55:20.890 --> 00:55:22.440
+And you're never going to want to split
+
+00:55:22.440 --> 00:55:24.010
+between two of the same class, so I
+
+00:55:24.010 --> 00:55:26.469
+would never split between the two X's,
+
+00:55:26.470 --> 00:55:29.250
+because that's always going to be worse
+
+00:55:29.250 --> 00:55:31.070
+than some split that's between
+
+00:55:31.070 --> 00:55:31.930
+different classes.
+
+00:55:32.630 --> 00:55:35.450
+So I can consider the thresholds that
+
+00:55:35.450 --> 00:55:35.810
+are.
+
+00:55:36.460 --> 00:55:37.730
+Between different classes.
+
+00:55:42.380 --> 00:55:44.000
+Really.
+
+00:55:44.000 --> 00:55:44.530
+No.
+
+00:55:46.130 --> 00:55:48.380
+Yeah, I can, but I'm not going to draw
+
+00:55:48.380 --> 00:55:50.220
+that long, so it's not worth it to me
+
+00:55:50.220 --> 00:55:50.860
+to move on here.
+
+00:55:50.860 --> 00:55:52.160
+Then I have to move my laptop and.
+
+00:55:53.030 --> 00:55:56.030
+So I'm fine.
+
+00:55:56.750 --> 00:55:59.310
+So I would choose these two thresholds.
+
+00:55:59.310 --> 00:56:01.680
+If it's this threshold, then it's
+
+00:56:01.680 --> 00:56:04.152
+basically two and zero.
+
+00:56:04.152 --> 00:56:07.470
+So it's a very low Entropy here.
+
+00:56:07.470 --> 00:56:10.420
+And the probability of that is 2 out of
+
+00:56:10.420 --> 00:56:11.505
+five, right?
+
+00:56:11.505 --> 00:56:16.820
+So it would be 0.4 * 0 is the.
+
+00:56:17.460 --> 00:56:18.580
+Entropy on this side.
+
+00:56:19.570 --> 00:56:20.820
+And if I go this way?
+
+00:56:21.670 --> 00:56:23.500
+Then it's going to be.
+
+00:56:24.440 --> 00:56:25.290
+Then I've got.
+
+00:56:26.660 --> 00:56:27.840
+Sorry, two out of seven.
+
+00:56:29.750 --> 00:56:31.320
+Out of seven times.
+
+00:56:32.470 --> 00:56:33.930
+Times Entropy of 0 this way.
+
+00:56:34.650 --> 00:56:37.630
+And if I go this way, then it's five
+
+00:56:37.630 --> 00:56:38.020
+out of.
+
+00:56:38.980 --> 00:56:39.760
+7.
+
+00:56:41.040 --> 00:56:41.770
+Times.
+
+00:56:44.510 --> 00:56:47.560
+Two out of five times log.
+
+00:56:52.980 --> 00:56:53.690
+Thank you.
+
+00:56:53.690 --> 00:56:55.330
+I always forget the minus sign.
+
+00:56:56.140 --> 00:56:58.270
+OK, so minus 5 to 7, which is a
+
+00:56:58.270 --> 00:56:59.880
+probability that I go in this direction
+
+00:56:59.880 --> 00:57:03.805
+times one out of five times log one out
+
+00:57:03.805 --> 00:57:04.700
+of five.
+
+00:57:05.550 --> 00:57:07.760
+Plus four out of five.
+
+00:57:09.170 --> 00:57:10.710
+Four to five times log.
+
+00:57:13.360 --> 00:57:14.100
+Right.
+
+00:57:14.100 --> 00:57:15.750
+So there's a one fifth chance that it's
+
+00:57:15.750 --> 00:57:16.270
+an X.
+
+00:57:17.350 --> 00:57:19.180
+I do 1/5 times log 1/5.
+
+00:57:19.820 --> 00:57:22.200
+Minus 4/5 chance that it's a no, so
+
+00:57:22.200 --> 00:57:23.790
+minus 4/5 times log four fifth.
+
+00:57:24.510 --> 00:57:26.210
+And this whole thing is the Entropy
+
+00:57:26.210 --> 00:57:27.140
+after that split.
+
+00:57:28.590 --> 00:57:30.650
+And then likewise I can evaluate this
+
+00:57:30.650 --> 00:57:32.850
+split as well and so.
+
+00:57:33.620 --> 00:57:35.650
+Out of these two splits, which one do
+
+00:57:35.650 --> 00:57:37.190
+you think will have the most
+
+00:57:37.190 --> 00:57:38.040
+information gain?
+
+00:57:41.220 --> 00:57:43.320
+Yeah, the left split, the first one has
+
+00:57:43.320 --> 00:57:45.050
+the most information gain because then
+
+00:57:45.050 --> 00:57:47.168
+I get a confident Decision about two
+
+00:57:47.168 --> 00:57:49.943
+X's and like 4 out of five chance of
+
+00:57:49.943 --> 00:57:51.739
+getting it right on the other side,
+
+00:57:51.740 --> 00:57:53.520
+where if I choose the right split, I
+
+00:57:53.520 --> 00:57:56.791
+only get a perfect confidence about 1X
+
+00:57:56.791 --> 00:57:59.529
+and A2 out of three chance of getting
+
+00:57:59.529 --> 00:58:00.529
+it right on the other side.
+
+00:58:15.920 --> 00:58:19.580
+OK, so if I continuous features I would
+
+00:58:19.580 --> 00:58:21.490
+just try all the different like
+
+00:58:21.490 --> 00:58:23.110
+candidate thresholds for all those
+
+00:58:23.110 --> 00:58:24.690
+features and then choose the best one.
+
+00:58:26.430 --> 00:58:28.360
+And.
+
+00:58:28.460 --> 00:58:29.720
+She's the best one, all right.
+
+00:58:29.720 --> 00:58:30.090
+That's it.
+
+00:58:30.090 --> 00:58:31.430
+And then I do that for all the nodes,
+
+00:58:31.430 --> 00:58:32.590
+then I do it Recursively.
+
+00:58:33.670 --> 00:58:35.660
+So if you have a lot of features and a
+
+00:58:35.660 --> 00:58:37.050
+lot of data, this can kind of take a
+
+00:58:37.050 --> 00:58:37.600
+long time.
+
+00:58:38.250 --> 00:58:40.610
+But I mean these operations are super
+
+00:58:40.610 --> 00:58:41.710
+fast so.
+
+00:58:42.980 --> 00:58:45.919
+In practice, when you run it so in
+
+00:58:45.920 --> 00:58:48.380
+homework two, I'll have you train tree
+
+00:58:48.380 --> 00:58:50.930
+train forests of Decision trees, where
+
+00:58:50.930 --> 00:58:54.165
+you train 100 of them for example, and
+
+00:58:54.165 --> 00:58:56.090
+it takes like a few seconds, so it's
+
+00:58:56.090 --> 00:58:57.204
+like pretty fast.
+
+00:58:57.204 --> 00:58:59.070
+These are these are actually not that
+
+00:58:59.070 --> 00:59:01.030
+computationally expensive, even though
+
+00:59:01.030 --> 00:59:02.610
+doing it manually would take forever.
+
+00:59:05.590 --> 00:59:06.980
+So.
+
+00:59:08.860 --> 00:59:10.970
+We're close to the we're close to the
+
+00:59:10.970 --> 00:59:11.690
+end of the lecture.
+
+00:59:12.320 --> 00:59:14.320
+But I will give you just a second to
+
+00:59:14.320 --> 00:59:15.230
+catch your breath.
+
+00:59:15.230 --> 00:59:17.030
+And while you're doing that, think
+
+00:59:17.030 --> 00:59:17.690
+about.
+
+00:59:19.060 --> 00:59:22.640
+If I were to try and in this case I'm
+
+00:59:22.640 --> 00:59:23.760
+showing like all the different
+
+00:59:23.760 --> 00:59:25.210
+examples, the numbers are different
+
+00:59:25.210 --> 00:59:27.530
+examples there and the color is whether
+
+00:59:27.530 --> 00:59:28.270
+they wait or not.
+
+00:59:28.850 --> 00:59:30.570
+And I'm trying to decide whether I'm
+
+00:59:30.570 --> 00:59:33.090
+going to make a decision based on the
+
+00:59:33.090 --> 00:59:35.096
+type of restaurant or based on whether
+
+00:59:35.096 --> 00:59:35.860
+the restaurant's full.
+
+00:59:36.490 --> 00:59:40.840
+So take a moment to stretch or zone
+
+00:59:40.840 --> 00:59:42.760
+out, and then I'll ask you what the
+
+00:59:42.760 --> 00:59:43.200
+answer is.
+
+01:00:05.270 --> 01:00:06.606
+Part of it, yeah.
+
+01:00:06.606 --> 01:00:08.755
+So this is all Training one tree.
+
+01:00:08.755 --> 01:00:10.840
+And for a random forest you just
+
+01:00:10.840 --> 01:00:14.246
+randomly sample features and randomly
+
+01:00:14.246 --> 01:00:16.760
+sample data, and then you train a tree
+
+01:00:16.760 --> 01:00:19.250
+and then you do that like N times and
+
+01:00:19.250 --> 01:00:20.600
+then you average the predictions.
+
+01:00:27.420 --> 01:00:27.810
+Yeah.
+
+01:00:30.860 --> 01:00:33.610
+And so essentially, since the previous
+
+01:00:33.610 --> 01:00:35.440
+Entropy is fixed when you're trying to
+
+01:00:35.440 --> 01:00:36.140
+make a decision.
+
+01:00:36.910 --> 01:00:38.739
+You're just essentially choosing the
+
+01:00:38.740 --> 01:00:41.810
+Decision, choosing the attribute that
+
+01:00:41.810 --> 01:00:45.320
+will minimize your expected Entropy
+
+01:00:45.320 --> 01:00:47.160
+after, like given that attribute.
+
+01:00:57.950 --> 01:01:00.790
+Alright, so how many people think that
+
+01:01:00.790 --> 01:01:02.610
+we should split?
+
+01:01:03.300 --> 01:01:04.710
+How many people think we should split
+
+01:01:04.710 --> 01:01:05.580
+based on type?
+
+01:01:08.180 --> 01:01:09.580
+How many people think we should split
+
+01:01:09.580 --> 01:01:10.520
+based on Patrons?
+
+01:01:12.730 --> 01:01:13.680
+Yeah, OK.
+
+01:01:14.430 --> 01:01:17.380
+So I would say the answer is Patrons
+
+01:01:17.380 --> 01:01:19.870
+and because splitting based on type.
+
+01:01:20.590 --> 01:01:22.310
+I end up no matter what type of
+
+01:01:22.310 --> 01:01:24.200
+restaurant is, I end up with an equal
+
+01:01:24.200 --> 01:01:26.120
+number of greens and Reds.
+
+01:01:26.120 --> 01:01:30.140
+So green green means I didn't like say
+
+01:01:30.140 --> 01:01:32.672
+it very clearly, but green means that
+
+01:01:32.672 --> 01:01:35.842
+you think that you go, that you wait,
+
+01:01:35.842 --> 01:01:37.540
+and red means that you don't wait.
+
+01:01:38.460 --> 01:01:40.820
+So type tells me nothing, right?
+
+01:01:40.820 --> 01:01:42.310
+It doesn't help me split anything at
+
+01:01:42.310 --> 01:01:42.455
+all.
+
+01:01:42.455 --> 01:01:44.898
+I knew initially I had complete Entropy
+
+01:01:44.898 --> 01:01:47.780
+Entropy of 1 and after knowing type I
+
+01:01:47.780 --> 01:01:48.880
+still have Entropy of 1.
+
+01:01:49.900 --> 01:01:52.140
+Where if I know Patrons, then a lot of
+
+01:01:52.140 --> 01:01:55.720
+the time I have my Decision, and only
+
+01:01:55.720 --> 01:01:57.230
+some fraction of the time I still have
+
+01:01:57.230 --> 01:01:57.590
+to.
+
+01:01:57.590 --> 01:01:59.040
+I need more information.
+
+01:02:00.990 --> 01:02:02.700
+So here's like all the math.
+
+01:02:04.250 --> 01:02:05.230
+To go through that but.
+
+01:02:08.910 --> 01:02:11.790
+All right, So what if I?
+
+01:02:12.780 --> 01:02:14.730
+So sometimes a lot of times trees are
+
+01:02:14.730 --> 01:02:16.930
+used for continuous values and then
+
+01:02:16.930 --> 01:02:18.320
+it's called a Regression tree.
+
+01:02:20.760 --> 01:02:22.960
+The Regression tree is learned in the
+
+01:02:22.960 --> 01:02:23.510
+same way.
+
+01:02:24.570 --> 01:02:29.490
+Except that you would use the instead
+
+01:02:29.490 --> 01:02:30.840
+of, sorry.
+
+01:02:32.260 --> 01:02:34.170
+In the Regression tree, it's the same
+
+01:02:34.170 --> 01:02:36.530
+way, but you're typically trying to
+
+01:02:36.530 --> 01:02:38.703
+minimize the sum of squared error of
+
+01:02:38.703 --> 01:02:41.862
+the node instead of minimizing the
+
+01:02:41.862 --> 01:02:42.427
+cross entropy.
+
+01:02:42.427 --> 01:02:44.050
+You could still do it actually based on
+
+01:02:44.050 --> 01:02:45.500
+cross entropy if you're seeing like
+
+01:02:45.500 --> 01:02:47.770
+Gaussian distributions, but here let me
+
+01:02:47.770 --> 01:02:48.900
+show you an example.
+
+01:02:54.540 --> 01:02:55.230
+So.
+
+01:02:57.600 --> 01:02:59.170
+Let's just say I'm doing like one
+
+01:02:59.170 --> 01:03:00.700
+feature, let's say like.
+
+01:03:01.480 --> 01:03:04.610
+This is my feature X and my prediction
+
+01:03:04.610 --> 01:03:05.240
+value.
+
+01:03:06.000 --> 01:03:07.830
+Is the number that I'm putting here.
+
+01:03:18.340 --> 01:03:18.690
+OK.
+
+01:03:19.430 --> 01:03:20.160
+So.
+
+01:03:21.350 --> 01:03:22.980
+I'm trying to predict what this number
+
+01:03:22.980 --> 01:03:25.460
+is given like where I fell on this X
+
+01:03:25.460 --> 01:03:25.950
+axis.
+
+01:03:27.030 --> 01:03:28.940
+So the best split I could do is
+
+01:03:28.940 --> 01:03:30.550
+probably like here, right?
+
+01:03:31.330 --> 01:03:33.800
+And if I take this split, then I would
+
+01:03:33.800 --> 01:03:37.313
+say that if I'm in this side of the
+
+01:03:37.313 --> 01:03:37.879
+split.
+
+01:03:38.640 --> 01:03:42.450
+Then my prediction is 4 out of three,
+
+01:03:42.450 --> 01:03:44.560
+which is the average of the values that
+
+01:03:44.560 --> 01:03:45.690
+are on this side of the split.
+
+01:03:46.510 --> 01:03:48.710
+And if I'm on this side of the split,
+
+01:03:48.710 --> 01:03:51.030
+then my prediction is 6.
+
+01:03:51.800 --> 01:03:53.900
+Which is 18 / 3, right?
+
+01:03:53.900 --> 01:03:55.815
+So it's the average of these values.
+
+01:03:55.815 --> 01:03:58.270
+So if I'm doing Regression, I'm still
+
+01:03:58.270 --> 01:04:00.520
+like I'm choosing a split that's going
+
+01:04:00.520 --> 01:04:03.580
+to give me the best prediction in each
+
+01:04:03.580 --> 01:04:04.390
+side of the split.
+
+01:04:04.980 --> 01:04:06.745
+And then my estimate on each side of
+
+01:04:06.745 --> 01:04:08.170
+the split is just the average of the
+
+01:04:08.170 --> 01:04:10.100
+values after that split.
+
+01:04:11.000 --> 01:04:13.950
+And the scoring, the scoring that I can
+
+01:04:13.950 --> 01:04:16.120
+use is the squared error.
+
+01:04:16.120 --> 01:04:20.464
+So if the squared error would be 1 -, 4
+
+01:04:20.464 --> 01:04:22.536
+thirds squared, plus 2 -, 4 thirds
+
+01:04:22.536 --> 01:04:24.905
+squared plus 1 -, 4 thirds squared plus
+
+01:04:24.905 --> 01:04:29.049
+5 -, 6 ^2 + 8 -, 6 ^2 + 5 -, 6 ^2.
+
+01:04:29.890 --> 01:04:31.665
+And so I could try like every
+
+01:04:31.665 --> 01:04:33.549
+threshold, compute my squared error
+
+01:04:33.550 --> 01:04:35.635
+given every threshold and then choose
+
+01:04:35.635 --> 01:04:37.060
+the one that gives me the lowest
+
+01:04:37.060 --> 01:04:37.740
+squared error.
+
+01:04:41.040 --> 01:04:43.055
+So it's the same algorithm, except that
+
+01:04:43.055 --> 01:04:44.245
+you have a different Criterion.
+
+01:04:44.245 --> 01:04:46.370
+You might use squared error.
+
+01:04:47.820 --> 01:04:49.530
+Because it's continuous values that I'm
+
+01:04:49.530 --> 01:04:50.100
+predicting.
+
+01:04:50.840 --> 01:04:53.030
+And then the output of the node will be
+
+01:04:53.030 --> 01:04:54.390
+the average of the Samples that fall
+
+01:04:54.390 --> 01:04:55.069
+into that node.
+
+01:04:56.480 --> 01:04:58.300
+And for Regression trees, that's
+
+01:04:58.300 --> 01:05:00.020
+especially important to.
+
+01:05:01.330 --> 01:05:03.490
+Stop growing your tree early, because
+
+01:05:03.490 --> 01:05:05.420
+obviously otherwise you're going to
+
+01:05:05.420 --> 01:05:10.090
+always separate your data into one leaf
+
+01:05:10.090 --> 01:05:12.030
+node per data point, since you have
+
+01:05:12.030 --> 01:05:13.995
+like continuous values, unless there's
+
+01:05:13.995 --> 01:05:15.410
+like many of the same value.
+
+01:05:16.020 --> 01:05:17.410
+And so you're going to tend to like
+
+01:05:17.410 --> 01:05:17.870
+overfit.
+
+01:05:23.330 --> 01:05:25.920
+Overfitting, by the way, that's a term
+
+01:05:25.920 --> 01:05:27.060
+that comes up a lot in machine
+
+01:05:27.060 --> 01:05:27.865
+learning.
+
+01:05:27.865 --> 01:05:30.870
+Overfitting means that your model you
+
+01:05:30.870 --> 01:05:32.910
+have a very complex model so that you
+
+01:05:32.910 --> 01:05:34.940
+achieve like really low Training Error.
+
+01:05:35.660 --> 01:05:37.550
+But due to the complexity you're Test
+
+01:05:37.550 --> 01:05:38.740
+error has gone up.
+
+01:05:38.740 --> 01:05:41.570
+So if you plot your.
+
+01:05:42.250 --> 01:05:44.210
+If you plot your Test error as, you
+
+01:05:44.210 --> 01:05:45.510
+increase complexity.
+
+01:05:46.200 --> 01:05:48.000
+You're Test error will go down for some
+
+01:05:48.000 --> 01:05:50.030
+time, but then at some point as your
+
+01:05:50.030 --> 01:05:51.880
+complexity keeps rising, you're Test
+
+01:05:51.880 --> 01:05:53.590
+Error will start to increase.
+
+01:05:53.590 --> 01:05:55.040
+So the point at which you're.
+
+01:05:55.740 --> 01:05:57.650
+You're Test Error increases due to
+
+01:05:57.650 --> 01:05:59.260
+increasing complexity is where you
+
+01:05:59.260 --> 01:06:00.040
+start overfitting.
+
+01:06:00.870 --> 01:06:02.300
+We'll talk about that more at the start
+
+01:06:02.300 --> 01:06:03.000
+of the ensembles.
+
+01:06:04.840 --> 01:06:06.610
+Right, so there's a few variants.
+
+01:06:06.610 --> 01:06:08.620
+You can use different splitting
+
+01:06:08.620 --> 01:06:09.490
+criteria.
+
+01:06:09.490 --> 01:06:12.010
+For example, the genie like impurity or
+
+01:06:12.010 --> 01:06:14.580
+Genie Diversity index is just one minus
+
+01:06:14.580 --> 01:06:17.460
+the sum over all the values of X
+
+01:06:17.460 --> 01:06:18.700
+probability of X ^2.
+
+01:06:19.480 --> 01:06:22.140
+This actually is like almost the same
+
+01:06:22.140 --> 01:06:25.800
+thing as the Entropy.
+
+01:06:26.410 --> 01:06:27.800
+But it's a little bit faster to
+
+01:06:27.800 --> 01:06:29.840
+compute, so it's actually more often
+
+01:06:29.840 --> 01:06:30.740
+used as the default.
+
+01:06:33.830 --> 01:06:35.890
+Most times you split on one attribute
+
+01:06:35.890 --> 01:06:38.460
+at a time, but you can also.
+
+01:06:39.190 --> 01:06:40.820
+They're in some algorithms.
+
+01:06:40.820 --> 01:06:42.790
+You can solve for slices through the
+
+01:06:42.790 --> 01:06:44.600
+feature space you can.
+
+01:06:45.280 --> 01:06:47.490
+Do like linear discriminant analysis or
+
+01:06:47.490 --> 01:06:49.200
+something like that to try to find like
+
+01:06:49.200 --> 01:06:51.970
+a multivariable split that separates
+
+01:06:51.970 --> 01:06:53.870
+the data, but usually it's just single
+
+01:06:53.870 --> 01:06:54.310
+attribute.
+
+01:06:56.180 --> 01:06:57.970
+And as I mentioned a couple of times,
+
+01:06:57.970 --> 01:07:00.010
+you can stop early so you don't need to
+
+01:07:00.010 --> 01:07:02.010
+grow like the full tree until you get
+
+01:07:02.010 --> 01:07:03.025
+perfect Training accuracy.
+
+01:07:03.025 --> 01:07:06.110
+You can stop after you reach a Max
+
+01:07:06.110 --> 01:07:09.475
+depth or stop after you have a certain
+
+01:07:09.475 --> 01:07:11.540
+number of nodes per certain number of
+
+01:07:11.540 --> 01:07:12.620
+data points per node.
+
+01:07:13.710 --> 01:07:15.470
+And the reason that you had stopped
+
+01:07:15.470 --> 01:07:16.920
+early is because you the tree to
+
+01:07:16.920 --> 01:07:18.990
+generalized new data and if you grow
+
+01:07:18.990 --> 01:07:20.450
+like a really big tree, you're going to
+
+01:07:20.450 --> 01:07:23.000
+end up with these like little like
+
+01:07:23.000 --> 01:07:26.240
+micro applicable rules that might not
+
+01:07:26.240 --> 01:07:27.750
+work well when you get new Test
+
+01:07:27.750 --> 01:07:28.270
+Samples.
+
+01:07:29.220 --> 01:07:31.190
+Where if you have a shorter tree that
+
+01:07:31.190 --> 01:07:34.260
+then you might have some uncertainty
+
+01:07:34.260 --> 01:07:36.147
+left in your leaf nodes, but you can
+
+01:07:36.147 --> 01:07:38.300
+have more confidence that will reflect
+
+01:07:38.300 --> 01:07:39.240
+the true distribution.
+
+01:07:42.350 --> 01:07:45.630
+So if we look at Decision trees versus
+
+01:07:45.630 --> 01:07:46.280
+one and north.
+
+01:07:46.980 --> 01:07:49.500
+They're actually kind of similar in a
+
+01:07:49.500 --> 01:07:49.950
+way.
+
+01:07:49.950 --> 01:07:51.620
+They both have piecewise linear
+
+01:07:51.620 --> 01:07:52.120
+decisions.
+
+01:07:52.750 --> 01:07:54.620
+So here's the boundary that I get with
+
+01:07:54.620 --> 01:07:56.420
+one and N in this example.
+
+01:07:57.110 --> 01:08:00.550
+It's going to be based on like if you
+
+01:08:00.550 --> 01:08:03.380
+chop things up into cells where each
+
+01:08:03.380 --> 01:08:05.770
+sample is like everything within the
+
+01:08:05.770 --> 01:08:07.550
+cell is closest to a particular sample.
+
+01:08:08.260 --> 01:08:09.460
+I would get this boundary.
+
+01:08:11.100 --> 01:08:12.915
+And with the Decision tree you tend to
+
+01:08:12.915 --> 01:08:14.440
+get, if you're doing 1 attribute at a
+
+01:08:14.440 --> 01:08:15.980
+time, you get this access to line
+
+01:08:15.980 --> 01:08:16.630
+boundary.
+
+01:08:16.630 --> 01:08:18.832
+So it ends up being like going straight
+
+01:08:18.832 --> 01:08:20.453
+over and then up and then straight over
+
+01:08:20.453 --> 01:08:22.160
+and then down and then a little bit
+
+01:08:22.160 --> 01:08:23.320
+over and then down.
+
+01:08:23.320 --> 01:08:25.226
+But they're kind of similar.
+
+01:08:25.226 --> 01:08:28.220
+So they're the overlap of those spaces
+
+01:08:28.220 --> 01:08:28.690
+is similar.
+
+01:08:31.900 --> 01:08:34.170
+The Decision tree also has the ability
+
+01:08:34.170 --> 01:08:36.042
+for over stopping to improve
+
+01:08:36.042 --> 01:08:36.520
+generalization.
+
+01:08:36.520 --> 01:08:38.530
+While they can and doesn't the K&N you
+
+01:08:38.530 --> 01:08:40.700
+can increase K to try to improve
+
+01:08:40.700 --> 01:08:42.110
+generalization to make it like a
+
+01:08:42.110 --> 01:08:44.506
+smoother boundary, but it doesn't have
+
+01:08:44.506 --> 01:08:46.540
+like as doesn't have very many like
+
+01:08:46.540 --> 01:08:47.930
+controls or knobs to tune.
+
+01:08:50.390 --> 01:08:53.010
+And the true power that Decision trees
+
+01:08:53.010 --> 01:08:54.580
+arise with ensembles.
+
+01:08:54.580 --> 01:08:56.920
+So if you combine lots of these trees
+
+01:08:56.920 --> 01:08:59.250
+together to make a prediction, then
+
+01:08:59.250 --> 01:09:01.050
+suddenly it becomes very effective.
+
+01:09:01.750 --> 01:09:04.430
+In practice, people don't usually use
+
+01:09:04.430 --> 01:09:06.620
+this one Decision tree in machine
+
+01:09:06.620 --> 01:09:07.998
+learning to make an automated
+
+01:09:07.998 --> 01:09:08.396
+prediction.
+
+01:09:08.396 --> 01:09:10.710
+They usually use a whole bunch of them
+
+01:09:10.710 --> 01:09:12.397
+and then average the results or train
+
+01:09:12.397 --> 01:09:14.870
+them in a way that they that they
+
+01:09:14.870 --> 01:09:17.126
+incrementally build up your prediction.
+
+01:09:17.126 --> 01:09:18.850
+And that's what I'll talk about when I
+
+01:09:18.850 --> 01:09:19.730
+talk about ensembles.
+
+01:09:22.360 --> 01:09:23.750
+So Decision trees are really a
+
+01:09:23.750 --> 01:09:26.740
+component in two of the most successful
+
+01:09:26.740 --> 01:09:28.970
+algorithms of all time, but they're not
+
+01:09:28.970 --> 01:09:29.630
+the whole thing.
+
+01:09:30.940 --> 01:09:33.160
+Here's an example of a Regression tree
+
+01:09:33.160 --> 01:09:34.470
+for Temperature prediction.
+
+01:09:35.560 --> 01:09:37.200
+Just so that I can make the tree simple
+
+01:09:37.200 --> 01:09:39.370
+enough to put on a Slide, I set the Min
+
+01:09:39.370 --> 01:09:41.840
+leaf size to 200 so there.
+
+01:09:41.840 --> 01:09:44.000
+So I stopped splitting once the node
+
+01:09:44.000 --> 01:09:44.990
+has 200 points.
+
+01:09:46.120 --> 01:09:49.080
+And then I computed the root mean
+
+01:09:49.080 --> 01:09:50.450
+squared error and the R2.
+
+01:09:51.680 --> 01:09:53.280
+And so you can see for example like.
+
+01:09:54.430 --> 01:09:55.990
+One thing that is interesting to me
+
+01:09:55.990 --> 01:09:58.278
+about this is that I would have thought
+
+01:09:58.278 --> 01:09:59.872
+that the temperature in Cleveland
+
+01:09:59.872 --> 01:10:01.510
+yesterday would be the best predictor
+
+01:10:01.510 --> 01:10:03.150
+of the temperature in Cleveland today,
+
+01:10:03.150 --> 01:10:05.056
+but it's actually not the best
+
+01:10:05.056 --> 01:10:05.469
+predictor.
+
+01:10:05.470 --> 01:10:09.090
+So the best single like criteria is the
+
+01:10:09.090 --> 01:10:11.090
+temperature in Chicago yesterday,
+
+01:10:11.090 --> 01:10:13.590
+because I guess the weather like moves
+
+01:10:13.590 --> 01:10:15.460
+from West to east a bit.
+
+01:10:16.850 --> 01:10:19.665
+And I guess downward, so knowing the
+
+01:10:19.665 --> 01:10:21.477
+weather in Chicago yesterday, whether
+
+01:10:21.477 --> 01:10:23.420
+the weather was less than whether the
+
+01:10:23.420 --> 01:10:25.530
+Temperature was less than 8.4 Celsius
+
+01:10:25.530 --> 01:10:26.950
+or greater than 8.4 Celsius.
+
+01:10:27.590 --> 01:10:29.040
+Is the best single thing that I can
+
+01:10:29.040 --> 01:10:29.290
+know.
+
+01:10:30.480 --> 01:10:31.160
+And then?
+
+01:10:32.290 --> 01:10:34.920
+That reduces my initial squared error
+
+01:10:34.920 --> 01:10:36.400
+was 112.
+
+01:10:38.170 --> 01:10:39.680
+And then if you divide it by number of
+
+01:10:39.680 --> 01:10:41.560
+Samples, then or.
+
+01:10:42.810 --> 01:10:44.720
+Yeah, take divided by number of samples
+
+01:10:44.720 --> 01:10:45.960
+and take square root or something to
+
+01:10:45.960 --> 01:10:47.390
+get the per sample.
+
+01:10:48.300 --> 01:10:51.010
+Then depending on that answer, then I
+
+01:10:51.010 --> 01:10:53.209
+check to see what is the temperature in
+
+01:10:53.210 --> 01:10:55.458
+Milwaukee yesterday or what is the
+
+01:10:55.458 --> 01:10:57.140
+temperature in Grand Rapids yesterday.
+
+01:10:58.060 --> 01:10:59.600
+And then depending on those answers, I
+
+01:10:59.600 --> 01:11:02.040
+check Chicago again, a different value
+
+01:11:02.040 --> 01:11:04.170
+of Chicago, and then I get my final
+
+01:11:04.170 --> 01:11:04.840
+decision here.
+
+01:11:11.120 --> 01:11:13.720
+Yeah, it's like my sister lives in
+
+01:11:13.720 --> 01:11:16.140
+Harrisburg, so I always know that
+
+01:11:16.140 --> 01:11:17.750
+they're going to get our weather like a
+
+01:11:17.750 --> 01:11:18.240
+day later.
+
+01:11:19.020 --> 01:11:20.680
+So it's like, it's really warm here.
+
+01:11:20.680 --> 01:11:22.190
+They're like, it's cold, it's warm
+
+01:11:22.190 --> 01:11:22.450
+here.
+
+01:11:22.450 --> 01:11:23.600
+Well, I guess it will be warm for you
+
+01:11:23.600 --> 01:11:24.930
+tomorrow or in two days.
+
+01:11:26.130 --> 01:11:26.620
+Yeah.
+
+01:11:27.540 --> 01:11:29.772
+But part of the reason that I share
+
+01:11:29.772 --> 01:11:31.300
+this is that the one thing that's
+
+01:11:31.300 --> 01:11:32.890
+really cool about Decision trees is
+
+01:11:32.890 --> 01:11:34.910
+that you get some explanation, like you
+
+01:11:34.910 --> 01:11:37.450
+can understand the data better by
+
+01:11:37.450 --> 01:11:39.600
+looking at the tree like this kind of
+
+01:11:39.600 --> 01:11:41.860
+violated my initial assumption that the
+
+01:11:41.860 --> 01:11:43.340
+best thing to know for the Temperature
+
+01:11:43.340 --> 01:11:44.830
+is your Temperature the previous day.
+
+01:11:45.460 --> 01:11:46.600
+It's actually the temperature of
+
+01:11:46.600 --> 01:11:48.965
+another city the previous day and you
+
+01:11:48.965 --> 01:11:51.100
+can get you can create these rules that
+
+01:11:51.100 --> 01:11:53.030
+help you understand, like how to make
+
+01:11:53.030 --> 01:11:53.740
+predictions.
+
+01:11:56.130 --> 01:11:56.710
+This is.
+
+01:11:56.710 --> 01:11:58.320
+I'm not expecting you to read this now,
+
+01:11:58.320 --> 01:12:00.370
+but this is the code to generate this
+
+01:12:00.370 --> 01:12:00.820
+tree.
+
+01:12:06.080 --> 01:12:07.600
+Right on Summary.
+
+01:12:08.580 --> 01:12:10.800
+The key assumptions of this of the
+
+01:12:10.800 --> 01:12:12.570
+Classification or Regression trees are
+
+01:12:12.570 --> 01:12:15.255
+that Samples with similar features have
+
+01:12:15.255 --> 01:12:16.070
+similar predictions.
+
+01:12:16.070 --> 01:12:17.590
+So it's a similar assumption in Nearest
+
+01:12:17.590 --> 01:12:19.580
+neighbor, except this time we're trying
+
+01:12:19.580 --> 01:12:21.680
+to figure out how to like split up the
+
+01:12:21.680 --> 01:12:23.420
+feature space to define that
+
+01:12:23.420 --> 01:12:25.159
+similarity, rather than using like a
+
+01:12:25.160 --> 01:12:29.090
+preset distance function like Euclidean
+
+01:12:29.090 --> 01:12:29.560
+distance.
+
+01:12:30.970 --> 01:12:32.610
+The model parameters are the split
+
+01:12:32.610 --> 01:12:34.560
+criteria, each internal node, and then
+
+01:12:34.560 --> 01:12:36.630
+the final prediction at each leaf node.
+
+01:12:38.200 --> 01:12:40.020
+The designs are putting limits on the
+
+01:12:40.020 --> 01:12:42.080
+tree growth and what kinds of splits
+
+01:12:42.080 --> 01:12:43.545
+you can consider, like whether to split
+
+01:12:43.545 --> 01:12:45.260
+on one attribute or whole groups of
+
+01:12:45.260 --> 01:12:48.930
+attributes and then choosing their
+
+01:12:48.930 --> 01:12:50.030
+criteria for this split.
+
+01:12:51.520 --> 01:12:52.120
+
+
+01:12:53.300 --> 01:12:56.060
+You Decision trees by themselves are
+
+01:12:56.060 --> 01:12:57.645
+useful if you want some explainable
+
+01:12:57.645 --> 01:12:58.710
+Decision function.
+
+01:12:58.710 --> 01:13:00.270
+So they could be used for like medical
+
+01:13:00.270 --> 01:13:02.090
+diagnosis for example, because you want
+
+01:13:02.090 --> 01:13:03.750
+to be able to tell people like why.
+
+01:13:04.710 --> 01:13:07.324
+Like why I know you have cancer, like
+
+01:13:07.324 --> 01:13:08.840
+you don't want to just be like I use
+
+01:13:08.840 --> 01:13:10.270
+this machine learning algorithm and it
+
+01:13:10.270 --> 01:13:12.070
+says you have like a 93% chance of
+
+01:13:12.070 --> 01:13:13.750
+having cancer and so sorry.
+
+01:13:15.000 --> 01:13:16.785
+You want to be able to say like because
+
+01:13:16.785 --> 01:13:19.086
+of like this thing and because of this
+
+01:13:19.086 --> 01:13:21.099
+thing and because of this thing like
+
+01:13:21.100 --> 01:13:24.919
+out of all these 1500 cases like 90% of
+
+01:13:24.920 --> 01:13:26.750
+them ended up having cancer.
+
+01:13:26.750 --> 01:13:28.180
+So we need to do, we need to do a
+
+01:13:28.180 --> 01:13:29.110
+biopsy, right.
+
+01:13:29.110 --> 01:13:30.305
+So you want some explanation.
+
+01:13:30.305 --> 01:13:31.900
+A lot of times it's not always good
+
+01:13:31.900 --> 01:13:33.600
+enough to have like a good prediction.
+
+01:13:35.590 --> 01:13:37.240
+And they're also like really effective
+
+01:13:37.240 --> 01:13:38.520
+as part of a ensemble.
+
+01:13:38.520 --> 01:13:39.650
+And again, I think we might see a
+
+01:13:39.650 --> 01:13:40.650
+Tuesday instead of Thursday.
+
+01:13:43.150 --> 01:13:44.960
+It's not like a really good predictor
+
+01:13:44.960 --> 01:13:47.320
+by itself, but it is really good as
+
+01:13:47.320 --> 01:13:47.770
+part of an.
+
+01:13:48.500 --> 01:13:48.790
+Alright.
+
+01:13:49.670 --> 01:13:51.250
+So things you remember, Decision
+
+01:13:51.250 --> 01:13:52.690
+Regression trees learn to split up the
+
+01:13:52.690 --> 01:13:54.590
+feature space into partitions into
+
+01:13:54.590 --> 01:13:56.110
+different cells with similar values.
+
+01:13:57.150 --> 01:13:59.070
+And then Entropy is a really important
+
+01:13:59.070 --> 01:13:59.600
+concept.
+
+01:13:59.600 --> 01:14:01.030
+It's a measure of uncertainty.
+
+01:14:02.730 --> 01:14:05.170
+Information gain measures how much
+
+01:14:05.170 --> 01:14:07.090
+particular knowledge reduces the
+
+01:14:07.090 --> 01:14:08.710
+prediction uncertainty, and that's the
+
+01:14:08.710 --> 01:14:10.260
+basis for forming our tree.
+
+01:14:11.630 --> 01:14:13.650
+So on Thursday I'm going to do a bit of
+
+01:14:13.650 --> 01:14:15.680
+review of our concepts and then I think
+
+01:14:15.680 --> 01:14:17.200
+most likely next Tuesday I'll talk
+
+01:14:17.200 --> 01:14:19.730
+about ensembles and random forests and
+
+01:14:19.730 --> 01:14:21.540
+give you an extensive example of how
+
+01:14:21.540 --> 01:14:23.560
+it's used in the Kinect algorithm.
+
+01:14:24.800 --> 01:14:25.770
+Alright, thanks everyone.
+
+01:14:25.770 --> 01:14:26.660
+See you Thursday.
+
+01:19:07.020 --> 01:19:08.790
+Hello.
+
+01:19:10.510 --> 01:19:11.430
+Training an assault.
+