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I encountered this problem in a book "Pattern Recognition and Machine Learning" by Christopher M. Bishop. I excerpt it below: screenshot of the book In the excerpt, the big-O notation $O(\xi^...

Let $I$ be the ideal of smooth germs vanishing at zero. Let $I^{k+1}$ be the ideal generated by $(k+1)$-fold product of such germs. Write $F_k$ for the ideal of $k$-flat germs at zero. By the product ...

problem statement For any $x \in R^d$, consider the function $$\phi(x,a) = \min_{1\leq j \leq k} \|x-a_j\|^2,$$ where $a = (a_1, \dots, a_k) \in R^{kd}$ and $\| \cdot \|$ is the $L_p$ norm for any $p ...

I'm trying to derive some weights expression for a boosting algorithm on a L2-ISE loss function, and i have trouble with the taylor expension. Suppose that $f$ and $g$ are two densities from $\...

I have an integral of the form $$ I=\int_0^{\infty}{dx}\ln \bigg(1+\exp(-\frac{f(x)}{a})\bigg) $$ where $a$ is a positive constant and $f(x)$ is a regular and positive function such that $I$ is finite ...