numerical optimization

Note: full code is on my github. 1. Abstract In this article, I will derive SMO algorithm and the Fourier kernel approximation which are well-known algorithm for kernel machine. SMO can solve optimization problem of SVM efficiently and the Fourier kernel approximation is a kind of kernel approximation that can speed up the computation of the kernel matrix. In the last section, I will conduct a evaluation of my manual SVM on the simulation dataset and “Women’s Clothing E-Commerce Review Dataset”....

Gaussian Process Big Picture and Background Intuitively, Gaussian distribution define the state space, while Gaussian Process define the function space Before we introduce Gaussian process, we should understand Gaussian distriution at first. For a RV(random variable) $X$ that follow Gaussian Distribution $\mathcal{N}(0, 1)$ should be following image: The P.D.F should be $$x \sim \mathcal{N}(\mu, \sigma) = \frac{1}{\sigma \sqrt{2 \pi}} e^{- \frac{1}{2} (\frac{- \mu}{\sigma})^2}$$ As for Multivariate Gaussian Distribution, given 2 RV $x$, $y$ both 2 RV follow Gaussian Distribution $\mathcal{N}(0, 1)$ we can illustrate it as...