Assume that we are given a matrix $X \in \mathbb{R}^{n \times p}$. Each row of the matrix $X$ is considered to be an observation represented by a data vector that measures $p$ features of some phenomenon. We can think of Principal Component Analysis (PCA) as trying to trying to solve two related problems. Read more...
Thanks to Prof. Larry for this problem! Consider the following binary classification problem. Every individual of a population is associated with an independent replicate of the pair $(\mathbf{X}, Y)$, having known joint distribution and where the (observed) covariate $\mathbf{X}$ has a (marginal) distribution $\pi$, and the (unobserved) response $Y \in \{-1, 1\}$. Suppose the costs of misclassifying an individual with $Y = 1$ and $Y = -1$ are $a > 0$ and $b > 0$, respectively. What’s the Bayes decision rule? Read more...