# 一起啃PRML - 1.1 Example: Polynomial Curve Fitting 多项式曲线拟合

We begin by introducing a simple regression problem, 用一个例子穿起这些零碎的知识点。

@define 我们用x ≡ (x1 , . . . , xN )T 表示我们的training set，t ≡ (t1, . . . , tN )T表示对应值。

The input data set x in this chart was generated by choosing values of Xn, for n = 1,...,N, spaced uniformly in range [0,1], and the target data set t was obtained by first computing the corresponding values of the function sin(2πx) and then adding a small level of random noise.

@define polynomial function

Ps.有一大堆公式的文档真的慎用pages

@define error function

@define (RMS) error function

Furthermore, we might suppose that the best predictor of new data would be the function sin(2πx) from which the data was generated (and we shall see later that this is indeed the case). We know that a power series expansion of the function sin(2πx) contains terms of all orders, so we might expect that results should improve monotonically as we increase M.

posted @ 2016-02-19 15:16  AI_Believer  阅读(1010)  评论(1编辑  收藏  举报