Locally Weighted Regression

#1

It has been said in the video that " we are adding more loss , according to the points that are closer and less loss , according to the points that are far way," , but my point is, if any point is far away from query point, it will have less weight in finding parameters, that means the probability of incorrect predictions on considering the far away point is more, that means “More Loss” , so why it has said in the video that more loss will be added if the points are close( I understood from the formula but logically i couldnt understand) please clear this,

#2

Hi @shalinijha219999,
Your inference here is slightly wrong ,

So you know, we have weights for every points.

Now, for any point Xi , only consider the points that lies near this point Xi , only these data points (close to this Xi ) are very helpful for finding the correct hypothesis, as we start going far from this point, then farther points will not help much in making the hypothesis or finding thetas at this point Xi . So, we know only closer points are really helpful… right…

So, if we want the closer points to work very well, we should give them a high LOSS to these points, so that they will not make wrong parameters for Xi or ( get high weights for )

in your statement - if the a point is far from Xi it will have less weight in finding the parameter. That’s correct, bcoz we dont want farther points to decide the parameter at Xi, we want points near Xi to help more - so more weights to near points.

But In this statement see- we put more focus on points that are close to Xi , we don’t want that they perform bad, so we give them high penality if they perform bad - we say High Loss is assigned to near points than the farther points. so to minimise overall loss, it is really really important to have less error in the points which are near.
So, the whole purpose of giving High Loss to near points is they should not perform bad- otherwise in layman terms we will give them high penality.

#3

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