‫In this video we will discuss about the bias media straight off so as I told you indeed a strange split
‫lecture.
‫Our agenda is to find the model that lowest test at a now fundamentally there are three contributors
‫to the expected test added these three contributors are called variants bias and the variance of errata
‫which is represented by either this third term comes from the fact that there is some inherent randomness
‫in the process and the given sample observations also do not follow the intended true function.
‫So this is an irreducible error and since we cannot do much about it we will not focus on it will focus
‫on these two other terms and let us talk about them one by one towards variance variance refers to the
‫amount by which effort change.
‫If we change our training dataset and bias therefore to that part of it which is introduced by approximating
‫a complicated real life relationship with a simpler model so let's look at them one by one so as I told
‫you variance therefore to the amount by which the predicted function would change if I change my training
‫dataset if you remember when we talked about simple linear regression I told you that there is this
‫true population line even by this recall which is the best line.
‫If we were putting the line on the whole population but when we are putting it on a sample the sample
‫regression line is different from the population regression line and if my sample data changes the sample
‫regression line also changes.
‫So basically variance is capturing the part of error.
‫Is just coming from that particular sample so if we have two models one of them is more flexible than
‫the other which one will have more variance and the more flexible method we'll be trying to that each
‫and every point even if I change one or two points it will give all the completely different than the
‫triple function to accommodate this small change.
‫This means that more flexible methods of high variance
‫This is shown graphically as well.
‫This first graph on the left.
‫We are trying to predict this relationship with a straight line straight line is a very less flexible
‫method even if I change one or two data points.
‫This Blue Point these lope and the intercept of this line will not change as much however if you look
‫at the function on the date.
‫If I change even one or two points on this go the predicted output function will be very different.
‫So you can see that the variance is very high.
‫If the flexibility in the covers I seem more flexible the matter I will be the variance this phenomenon
‫of following the data too closely.
‫As you see in the right graph that we are even following the error in the observations is called overweighting
‫when we overdo it.
‫We do get low training error but the test data increases.
‫Now let's talk about bias bias refers to that part of data which is introduced by approximating a complicated
‫real life relationship with a simpler model.
‫For example we may be trying to fit a linear model between dependent and independent variables where
‫a linear relationship is highly unlikely.
‫You can see in this graph the points can never be fitted with a straight line much still but still if
‫we select a linear model it is always going to have some error.
‫And that part of it is called bias
‫and how is bias related flexibility of model.
‫You can see that linear model which is less flexible is enabled offered this data if I increased flexibility
‫and allow it to go then it will better fit the point.
‫So generally if we increase flexibility the bias error reduces so you can see where the bias variance
‫tradeoff is coming from as we increase flexibility error due to variance increases and error due to
‫bias decreases although we want to decrease both but when we try to decrease one the other one starts
‫to increase so the challenge is to find that point where this summer's minimum this is depicted graphically
‫here.
‫This orange line is showing us the variance which is increasing with flexibility and this blue line
‫is for bias which is decreasing with flexibility and this red line it is some of the of these two others.
‫We want to find this minimum point where the sum is the minimum although we will not be able to compute
‫bias and variance what our model.
‫This concept will be used when we will be comparing different models and the potential accuracy in predicting
‫dependent variables.