WEBVTT 00:01.250 --> 00:04.640 In this session, we will discuss about the based algorithm. 00:06.100 --> 00:12.220 So first of all, before getting into my base, we need to understand a few concepts of probability. 00:13.160 --> 00:19.100 So let us discuss about this particular data here, we have different fruits. 00:20.330 --> 00:27.980 And out of these frauds, if we need to find out the probability of getting apples or oranges or bananas, 00:28.250 --> 00:32.060 we will be having to find out the ratio of these. 00:32.240 --> 00:33.320 So how would we do that? 00:33.620 --> 00:36.160 To find out the probability of apples? 00:36.500 --> 00:43.300 The probability of apples will be the number of apples divided by the total number of fruit. 00:44.540 --> 00:48.080 Similarly, the probability of oranges would be. 00:49.460 --> 00:58.100 The number of oranges divided by the total number of fruit and the probability of getting a banana would 00:58.100 --> 01:02.450 be the number of banana divided by the total number of fruit. 01:03.900 --> 01:11.460 Now, by this condition, if they want to find out the probability of getting E, then the probability 01:11.460 --> 01:18.650 of getting it will be the number, the models of E divided by the models of the universe. 01:18.660 --> 01:23.910 That is the number of a divided by the number of elements in the entire universe. 01:25.130 --> 01:31.490 Now, if you want to find out the probability of getting the then the probability of getting the will 01:31.490 --> 01:38.050 be the number of elements and in divide divided by the number of all the elements present in the universe. 01:38.960 --> 01:42.590 So this is the statement for both of these. 01:43.230 --> 01:45.000 Now, let us get further. 01:45.800 --> 01:55.810 Now let us see that A and B actually intersect at a B, and we have some common elements named as Ebby. 01:56.540 --> 02:04.730 Then what will be the probability of getting Aebi the probability of getting a will again be the problem, 02:04.880 --> 02:13.100 the amount of the number of elements of a B divided by the number of elements in the universe. 02:14.830 --> 02:23.470 Now, let us assume let us see that what is the probability of getting A, given that B is already two? 02:24.400 --> 02:31.150 Now, if you want to find out the probability of a given vs already through, then the probability will 02:31.150 --> 02:40.670 be the area which is both a B divided by the universe b, B, because these already through. 02:40.900 --> 02:44.230 So we know that the universe for this is the. 02:46.750 --> 02:55.390 So here, because the universe is V, so the probability of A given B is already through will be A B 02:55.540 --> 02:57.100 divided by B. 02:58.010 --> 03:09.860 Now, we can also write it up on the as a given universe and be given universe, so probability of A 03:09.860 --> 03:12.200 given B will be equal to. 03:13.360 --> 03:21.820 A B divided by universe, I'm B divided by Univers now this storm can also be written as. 03:23.760 --> 03:25.500 Probability of a. 03:26.830 --> 03:34.720 And similarly be given, Univers can also be written as probability of being. 03:35.560 --> 03:44.320 From this, we can derive that probability of A given B is equal to probability of any given problem 03:44.740 --> 03:46.960 divided by the probability of B. 03:48.590 --> 03:53.120 Now, can we derive the probability of being given a using this? 03:54.770 --> 04:00.990 So the probability of A, given B is probability of Ebbie divided by probability of me. 04:01.490 --> 04:04.370 So just swapping all the envy's. 04:04.550 --> 04:05.610 So what do we get? 04:05.810 --> 04:13.340 We get probability of be given e- equal to probability of A B divided by the probability of A. 04:14.980 --> 04:24.040 Now, let us try to replace the probability of EBE here with the probability of evacuation, which we 04:24.040 --> 04:25.070 get from this one. 04:25.810 --> 04:26.780 So what do we get? 04:27.190 --> 04:36.700 We will get a probability of Ebbe and probability of V is equal to probability of being in probability 04:36.700 --> 04:36.970 of. 04:37.840 --> 04:46.800 A not as probability of a given be in the probability of B, equal to probability of being given, E 04:46.990 --> 04:48.670 in the probability of A. 04:49.710 --> 04:59.400 Hence, we can see the probability of A given B is equal to probability of be given E in the probability 04:59.400 --> 05:02.820 of E divided by probability of B. 05:05.330 --> 05:14.420 So we are treating probability of a given me is equal to probability of be given a Endou probability 05:14.420 --> 05:16.250 of E that is. 05:17.360 --> 05:23.270 What we are trying to find out, divided by the probability of V, which is given here. 05:24.050 --> 05:25.420 So how do we do that? 05:27.480 --> 05:27.930 Now. 05:29.010 --> 05:36.480 What are the values here, probability of a human being is equal to probability of a intersection B 05:36.870 --> 05:38.460 A born probability of B. 05:39.430 --> 05:45.580 That is equal to probability of the probability of being given a divided by probability of the. 05:46.470 --> 05:55.650 Here, the probability of a probability of a probability of these probability of the probability of 05:55.650 --> 05:57.060 a human being is. 05:58.550 --> 05:59.870 Probability of a given. 06:00.470 --> 06:07.910 This means that probability of being given A and B of A intersection B, this is the probability of 06:07.910 --> 06:09.620 both A and B occurring. 06:13.250 --> 06:19.340 Now, let us try to relate this to the problem which we have. 06:20.510 --> 06:27.020 Now, the statement which we have just created, this is called the Nijhuis Equation. 06:29.190 --> 06:37.020 Now, let us have a look at this and try to relate it to the type of problem that we have now, usually 06:37.290 --> 06:39.510 let us take the loan data example. 06:40.320 --> 06:50.440 Now we want to find out the probability of a person defaulting on a loan given certain conditions. 06:50.490 --> 06:51.700 What are those conditions? 06:51.960 --> 06:55.860 Those conditions are different values of those features. 06:56.160 --> 06:58.130 That is different attributes. 06:58.440 --> 07:07.230 So we have to find out if someone will default on the loan or not based on what is the salary of the 07:07.230 --> 07:09.670 person, how many children he has. 07:09.870 --> 07:11.570 What are the number of dependents? 07:11.730 --> 07:13.140 What is the FICO range? 07:13.260 --> 07:15.510 So based on all of these criteria? 07:16.830 --> 07:23.080 We want to find out the probability of it, so now you can relate to this, right? 07:23.340 --> 07:31.650 This is actually the value by which we want to predict and B, are the X values, that is the input 07:31.650 --> 07:36.810 values that are features or attributes or the independent variables. 07:37.780 --> 07:46.720 Now thinking about independent variables, so the property of independent variables is that we are trying 07:46.720 --> 07:54.700 to find the intersection of all these, when all of these things are true, then all of these intersection 07:54.700 --> 08:01.810 is true that this we want to find out the probability of E for different combinations of these one be 08:01.840 --> 08:02.980 to be three before. 08:04.100 --> 08:06.930 Now, what are these be1 B to be three, four? 08:07.370 --> 08:14.090 So these will be if the someone has the number of children as one, if someone has a number of dependents 08:14.720 --> 08:17.480 do and then what is the salary of the person? 08:17.510 --> 08:23.150 So these good ideas together will become a condition. 08:23.480 --> 08:27.200 And that condition has been depicted by this intersection. 08:29.000 --> 08:37.760 Now we will have the same thing and all the places that is probability of a given BE1 be to be investigated. 08:38.980 --> 08:45.870 Is equal to probability of an intersection between the Section B, the intersection before given E and 08:45.880 --> 08:52.420 the probability of A divided by probability of one intersection, probability of BIDU intersection, 08:52.420 --> 08:54.040 probability of B three and so on. 08:55.650 --> 08:58.260 Now, can we record this? 08:59.910 --> 09:09.690 Can we re establish this particular thing to reestablish this week and also write this as probability 09:09.690 --> 09:17.070 of BE1 given E in into probability, agree to give an E in to probability of victory given and so on? 09:17.570 --> 09:18.570 And why is that? 09:18.570 --> 09:26.790 So if they are to find out the probability of multiple endives, given one condition, then if the. 09:27.960 --> 09:35.380 Different conditions are independent of each other, then they could be said to be multiplied. 09:35.670 --> 09:41.880 So when we are finding out probability and different conditions are occurring together, then we can 09:42.090 --> 09:46.700 find out the probability of one thing and multiplied with the probability of the other one. 09:47.400 --> 09:54.140 That is how we calculate probabilities so we can subdivide this and find out probability of given the 09:54.420 --> 10:01.050 probability of being given a probability of ubani and hence find out the probability of a given we when 10:01.050 --> 10:01.730 be do be three. 10:03.270 --> 10:07.830 So to saw this kind of problem, we can use this. 10:08.960 --> 10:17.840 Particular formula, which we have from the ninth base equation and VI is the base equation. 10:17.870 --> 10:22.270 Why is this particular algorithm called Knife? 10:22.730 --> 10:32.870 The equation is based Hürrem, but this algorithm is called Navys because it assumes that all these 10:32.870 --> 10:35.560 BE1 V to be three are independent. 10:36.470 --> 10:44.510 That is the reason why the first thing which we do while creating the data for this particular algorithm 10:44.510 --> 10:47.840 is we remove all the correlations. 10:49.050 --> 10:56.520 Which we have already learned during our data preparation, that is we will remove all the related variables 10:56.670 --> 11:05.100 and we will remove all the variables will have to be present so that all of these attributes be one 11:05.100 --> 11:07.970 be to be three are independent of each other. 11:10.730 --> 11:12.740 So what is Meyvis? 11:14.220 --> 11:22.500 The night vision classifier is based on the beast Hürrem, with the independence assumption between 11:22.500 --> 11:29.280 the predictors, so between the predictors, these are the predictors X one extra extra X for values. 11:29.490 --> 11:36.240 It is assuming that all of these predictors are independent from each other. 11:37.260 --> 11:43.130 A NIMBY's model is easy to break with, the more complicated. 11:43.140 --> 11:51.360 If I drew the barometer estimation, which makes it particularly useful for a large dataset now for 11:51.360 --> 11:53.030 knives, we don't have to. 11:53.060 --> 11:57.330 I daily find out values for different Fatah leaders. 11:57.330 --> 11:59.540 We just need to find out probabilities. 11:59.820 --> 12:03.900 So that is easily done for a very large dataset. 12:05.190 --> 12:13.590 Now, although it is simple knives in classified, it often does surprisingly well and is widely used 12:13.590 --> 12:21.810 because it often outperforms the more sophisticated classification methods, so it might outperform 12:21.960 --> 12:24.430 random forest or extra boost. 12:24.680 --> 12:29.400 So that is why Nijhuis is one of the favorite algorithms. 12:31.780 --> 12:35.760 So what about the Elgort and what do we have in the algorithm? 12:36.040 --> 12:45.250 So for this algorithm, the base theorem provides a way of calculating the posterior probability that 12:45.250 --> 12:55.000 this probability of C given X or probability of Vivan human X from the prior prior is what data we already 12:55.000 --> 12:55.270 have. 12:55.270 --> 13:02.050 That is probability of C operating independently, probability of X acting independently, and probability 13:02.050 --> 13:04.680 of X given C.. 13:05.320 --> 13:13.480 So we already have this data and using all this data, we just want to find out the probability of C 13:13.480 --> 13:17.140 given X or probability of Y given X. 13:18.310 --> 13:26.800 The prior probability is the probability of an event before new data is collected and posterior probability 13:26.800 --> 13:33.070 is the revised probability of an event occurring after taking into consideration new information. 13:33.490 --> 13:41.890 OK, now posterior probability is the probability of event e occurring given that event, event B has 13:41.890 --> 13:42.830 already occurred. 13:43.060 --> 13:46.000 So what are these event B, these events? 13:46.030 --> 13:54.460 These are nothing but the predictors, the probabilities of the features and the attribute having those 13:54.460 --> 13:56.240 values which they already have. 13:56.590 --> 14:05.080 Now the Navy's classifier assumes that the effect of the value of a predictor on a given Class C is 14:05.080 --> 14:08.920 independent of the values of other predictors. 14:09.840 --> 14:19.290 So for one column, that is let's say we have three features age, gender and salary, then the impact 14:19.290 --> 14:26.010 of age is independent of the impact of salary or the impact of gender. 14:26.160 --> 14:31.280 So that is the main assumption, and that is why it is called knife tuto. 14:32.470 --> 14:39.850 Now, this assumption is called conditional independence, and it is called because of the glass conditional 14:39.850 --> 14:41.000 independence only. 14:41.470 --> 14:45.400 So that is why the Navy's got the name in. 14:47.160 --> 14:53.490 OK, so the main task here is to find out the probability of E! 14:53.700 --> 14:56.840 That is why Vidi got a good value. 14:56.850 --> 15:04.980 The probability of a class having occurred with respect to the different feature and attribute values 15:05.220 --> 15:07.410 already have been occurring. 15:07.860 --> 15:09.950 So how do we do that? 15:10.140 --> 15:13.200 So let us solve this problem first. 15:13.860 --> 15:15.680 So we have this data. 15:16.380 --> 15:22.250 This is the data that you would have already seen during the decision tree creation. 15:22.440 --> 15:31.350 So we looked at the data where we had our rainy, overcast and sunny and the first split which we had 15:31.350 --> 15:35.970 made was using rainy, overcast and sunny. 15:36.450 --> 15:42.000 And then we have temperature, different temperature values, different humidity values and different 15:42.000 --> 15:42.900 Vendy values. 15:43.080 --> 15:49.260 And based on this, we actually decided if the Chinese should play or not. 15:51.200 --> 15:59.990 So how do we do this, so we have this data, so from this particular data, we will create a frequency 15:59.990 --> 16:03.170 table that is the number of occurrences of these values. 16:03.440 --> 16:05.810 So we will check the frequencies. 16:06.080 --> 16:13.500 So the frequency table for our different outlook values will be for Sunee play. 16:13.520 --> 16:19.640 Golf has three yeses and doulos for overcast play. 16:19.640 --> 16:24.610 Golf has for yes and zero news for me. 16:25.010 --> 16:28.520 Play Golf has two yes and three no's. 16:29.530 --> 16:33.340 Now, from this, we will create the likelihood. 16:34.180 --> 16:37.690 How do we create that so we have three values here. 16:39.320 --> 16:41.960 And the total number of values I. 16:42.970 --> 16:43.480 Nine. 16:44.590 --> 16:46.510 Three plus four plus two. 16:46.750 --> 16:52.350 That is nine, so we see three by nine, four by nine, two by nine. 16:52.750 --> 17:00.440 So Sonny has three by nine of yesses, overcast has four by nine of us, and really has to by nine orfeus. 17:02.140 --> 17:10.090 So we get nine by 14, so nine items out of 14 have yes, in our. 17:11.440 --> 17:17.380 Similarly, we find out the similar table for no, we calculate the same thing for No. 17:18.940 --> 17:28.260 And we have to find out the probability of X given or probability of it being Sunee given, it is yes. 17:29.020 --> 17:33.580 So probability of having Sunee given it is yesses three by nine. 17:36.430 --> 17:36.850 Right. 17:38.090 --> 17:39.940 Dorville, yes, nine. 17:41.190 --> 17:50.220 And there are three entities with Sunny, so the probability of getting sunny as a result, given it 17:50.220 --> 17:53.110 is yes, is three by nine. 17:53.940 --> 18:00.660 Similarly, we can find out the ratios for overcast, rainy and. 18:02.630 --> 18:09.440 From this, we can calculate the probability of yes and the probability of sunny, so the probability 18:09.440 --> 18:13.230 of yes is nine by 14, that is nine times. 18:13.250 --> 18:18.020 It is, yes, and hopefully 14 data points out there. 18:19.090 --> 18:24.580 Then the probability of it being sunny is five by 40. 18:25.610 --> 18:31.910 Similarly, we can find out the probability of it being overcast, probability of it being rainy. 18:33.230 --> 18:36.100 That is four by 14, five by 14. 18:37.550 --> 18:46.730 Now, what is the probability, the probability is probability of yes, given it is sunny, so what 18:46.730 --> 18:48.040 how will we find this out? 18:48.260 --> 18:51.410 We will find this out by multiplying the values. 18:52.070 --> 19:00.950 So it comes out to be zero point three three in zero point six four in zero point, divided by zero 19:00.950 --> 19:01.970 point three six. 19:03.920 --> 19:12.850 That is probability of yes, given it is sunny is equal to probability of sunny, given it is, yes. 19:13.150 --> 19:16.750 And the probability of it being. 19:18.630 --> 19:22.350 Yes, divided by the probability of. 19:23.210 --> 19:28.850 Sunny, this is just the simplest implementation of the nine best. 19:29.830 --> 19:32.740 Formula, the simplest implementation of this formula. 19:34.470 --> 19:41.190 You can pause the slide and have a look at this, how this is performing, because it is very important 19:41.190 --> 19:47.880 to understand so you can pause any time and have a look at this table and understand how this has been 19:47.880 --> 19:48.750 constructed. 19:51.830 --> 19:59.270 Next, we will find out the probability of no, given it is sunny, so the probability of no, given 19:59.270 --> 20:07.310 it is sunny, will be the probability of sunny, given it is no end to the probability of no divided 20:07.310 --> 20:09.560 by probability of it being sunny. 20:13.560 --> 20:21.270 Similarly, we will create different likely would be moods and frequency tables for humidity, temperature 20:21.270 --> 20:21.940 and windy. 20:22.140 --> 20:26.460 So for all all four of the features, we will create the stable. 20:28.660 --> 20:35.410 Now, when we want to find out if someone has to play, then how would we do that? 20:35.680 --> 20:43.370 We will do that using we will be finding all probability of yes, given different X values. 20:43.510 --> 20:45.060 So what are the X values? 20:45.070 --> 20:45.560 Let's see. 20:45.590 --> 20:48.960 We want to find out for the rainy outlook. 20:48.970 --> 20:51.340 Temperature, cool, humidity, high and windy. 20:51.610 --> 20:53.460 So how will we find this out? 20:53.740 --> 20:58.510 So probability of yes, given X will be probability of. 21:04.860 --> 21:15.150 So probability of a given certain conditions is equal to probability of condition, one, given a probability 21:15.150 --> 21:22.690 of condition to give given be given a probability of condition to be given in to probability of a.. 21:23.060 --> 21:24.330 So let us get to that. 21:26.350 --> 21:33.910 So probability of condition given, yes, probability of another condition given in the probability 21:33.910 --> 21:35.350 of another condition given. 21:35.350 --> 21:42.310 Yes, in all probability of next condition, that is probability of rule given. 21:42.310 --> 21:43.850 Yes, indeed. 21:43.900 --> 21:45.790 Probability of yes. 21:54.770 --> 22:04.190 So what do we get from this weekend, probability of yes, given X as zero point zero zero five two 22:04.190 --> 22:04.490 nine. 22:05.520 --> 22:09.510 Now, we will divide this value by. 22:10.610 --> 22:12.980 The probability of. 22:15.170 --> 22:17.060 Intersection of all of these. 22:18.760 --> 22:21.880 So the probability of intersection of all of these will be. 22:23.120 --> 22:26.780 This some value, so this is what the result will be. 22:27.020 --> 22:30.930 Similarly, we can calculate the probability of no given XL's. 22:31.810 --> 22:33.460 And you can see it is. 22:35.560 --> 22:41.290 Contrasting to this one, so the probability of us given X is zero point two and the probability of 22:41.290 --> 22:44.080 no given exists zero point eight. 22:46.960 --> 22:54.730 So this is the end of my base, I will be providing another example question to you so that you can 22:54.730 --> 23:01.170 practice that and find out the values of probabilities using the base formula. 23:01.180 --> 23:02.470 And I visited him. 23:02.980 --> 23:11.020 And in the next session, we will be implementing my base algorithm using Escalon.