1 00:00:01,100 --> 00:00:09,260 ‫In this video we will discuss about the bias media straight off so as I told you indeed a strange split 2 00:00:09,320 --> 00:00:10,370 ‫lecture. 3 00:00:10,560 --> 00:00:19,140 ‫Our agenda is to find the model that lowest test at a now fundamentally there are three contributors 4 00:00:19,260 --> 00:00:28,230 ‫to the expected test added these three contributors are called variants bias and the variance of errata 5 00:00:28,710 --> 00:00:38,350 ‫which is represented by either this third term comes from the fact that there is some inherent randomness 6 00:00:38,470 --> 00:00:48,190 ‫in the process and the given sample observations also do not follow the intended true function. 7 00:00:48,300 --> 00:00:56,010 ‫So this is an irreducible error and since we cannot do much about it we will not focus on it will focus 8 00:00:56,010 --> 00:01:05,060 ‫on these two other terms and let us talk about them one by one towards variance variance refers to the 9 00:01:05,060 --> 00:01:07,810 ‫amount by which effort change. 10 00:01:07,970 --> 00:01:16,390 ‫If we change our training dataset and bias therefore to that part of it which is introduced by approximating 11 00:01:16,390 --> 00:01:26,380 ‫a complicated real life relationship with a simpler model so let's look at them one by one so as I told 12 00:01:26,370 --> 00:01:32,590 ‫you variance therefore to the amount by which the predicted function would change if I change my training 13 00:01:32,600 --> 00:01:40,570 ‫dataset if you remember when we talked about simple linear regression I told you that there is this 14 00:01:40,660 --> 00:01:47,170 ‫true population line even by this recall which is the best line. 15 00:01:47,170 --> 00:01:55,880 ‫If we were putting the line on the whole population but when we are putting it on a sample the sample 16 00:01:55,880 --> 00:02:02,540 ‫regression line is different from the population regression line and if my sample data changes the sample 17 00:02:02,540 --> 00:02:05,250 ‫regression line also changes. 18 00:02:05,310 --> 00:02:08,750 ‫So basically variance is capturing the part of error. 19 00:02:08,960 --> 00:02:17,320 ‫Is just coming from that particular sample so if we have two models one of them is more flexible than 20 00:02:17,320 --> 00:02:26,020 ‫the other which one will have more variance and the more flexible method we'll be trying to that each 21 00:02:26,020 --> 00:02:33,090 ‫and every point even if I change one or two points it will give all the completely different than the 22 00:02:33,090 --> 00:02:36,910 ‫triple function to accommodate this small change. 23 00:02:36,910 --> 00:02:40,600 ‫This means that more flexible methods of high variance 24 00:02:43,260 --> 00:02:45,320 ‫This is shown graphically as well. 25 00:02:45,420 --> 00:02:47,040 ‫This first graph on the left. 26 00:02:47,640 --> 00:02:55,840 ‫We are trying to predict this relationship with a straight line straight line is a very less flexible 27 00:02:55,880 --> 00:03:01,120 ‫method even if I change one or two data points. 28 00:03:01,370 --> 00:03:10,730 ‫This Blue Point these lope and the intercept of this line will not change as much however if you look 29 00:03:10,730 --> 00:03:13,450 ‫at the function on the date. 30 00:03:13,490 --> 00:03:20,800 ‫If I change even one or two points on this go the predicted output function will be very different. 31 00:03:23,070 --> 00:03:26,910 ‫So you can see that the variance is very high. 32 00:03:27,200 --> 00:03:36,810 ‫If the flexibility in the covers I seem more flexible the matter I will be the variance this phenomenon 33 00:03:37,290 --> 00:03:39,400 ‫of following the data too closely. 34 00:03:39,540 --> 00:03:46,980 ‫As you see in the right graph that we are even following the error in the observations is called overweighting 35 00:03:48,220 --> 00:03:49,130 ‫when we overdo it. 36 00:03:49,420 --> 00:03:55,980 ‫We do get low training error but the test data increases. 37 00:03:55,990 --> 00:04:04,150 ‫Now let's talk about bias bias refers to that part of data which is introduced by approximating a complicated 38 00:04:04,150 --> 00:04:07,720 ‫real life relationship with a simpler model. 39 00:04:07,750 --> 00:04:15,270 ‫For example we may be trying to fit a linear model between dependent and independent variables where 40 00:04:15,270 --> 00:04:17,390 ‫a linear relationship is highly unlikely. 41 00:04:18,790 --> 00:04:26,180 ‫You can see in this graph the points can never be fitted with a straight line much still but still if 42 00:04:26,180 --> 00:04:30,410 ‫we select a linear model it is always going to have some error. 43 00:04:30,740 --> 00:04:33,080 ‫And that part of it is called bias 44 00:04:35,750 --> 00:04:39,550 ‫and how is bias related flexibility of model. 45 00:04:39,580 --> 00:04:46,750 ‫You can see that linear model which is less flexible is enabled offered this data if I increased flexibility 46 00:04:46,870 --> 00:04:51,380 ‫and allow it to go then it will better fit the point. 47 00:04:51,460 --> 00:04:59,230 ‫So generally if we increase flexibility the bias error reduces so you can see where the bias variance 48 00:04:59,240 --> 00:05:08,360 ‫tradeoff is coming from as we increase flexibility error due to variance increases and error due to 49 00:05:08,360 --> 00:05:17,840 ‫bias decreases although we want to decrease both but when we try to decrease one the other one starts 50 00:05:17,840 --> 00:05:27,160 ‫to increase so the challenge is to find that point where this summer's minimum this is depicted graphically 51 00:05:27,160 --> 00:05:27,430 ‫here. 52 00:05:28,340 --> 00:05:34,640 ‫This orange line is showing us the variance which is increasing with flexibility and this blue line 53 00:05:34,760 --> 00:05:42,850 ‫is for bias which is decreasing with flexibility and this red line it is some of the of these two others. 54 00:05:43,100 --> 00:05:49,870 ‫We want to find this minimum point where the sum is the minimum although we will not be able to compute 55 00:05:50,050 --> 00:05:52,690 ‫bias and variance what our model. 56 00:05:52,690 --> 00:05:59,350 ‫This concept will be used when we will be comparing different models and the potential accuracy in predicting 57 00:05:59,350 --> 00:06:00,400 ‫dependent variables.