Derivation of polynomial-fitting bias function in machine learning-statistical learning method

Recently Learning machine learning, saw Andrew Ng's public class, while studying Dr. Hangyuan Li's "Statistical learning method" in this record.

On page 12th There is a question about polynomial fitting. Here, the author gives a direct derivative of the request. Here's a detailed derivation.

，

In this paper, we first look at the definition of biased derivative of the function model.

Because here is, so except WJ outside the Xi,yi can be regarded as constant. To solve this problem.

After derivation we will find that the formula is different from the answer given by the author.

, but the author also gives corrections

But we found that the answer was different from the one I deduced. The X on the author's denominator is labeled j+1, and I deduced the superscript as 2j, referring to the author's misunderstanding that the numerator X's superscript added a

J, if the molecule is also missing a J, then it can be figured out.

This post is the first posting, style undecided, flawed, there may be errors, welcome to correct me. Only as a personal learning record, can be a little reference for everyone.

Please indicate the source, thank you.

Derivation of polynomial-fitting bias function in machine learning-statistical learning method