• ## Notes on Machine Learning 9: Linear regression

(ML 9.1) Linear regression - Nonlinearity via basis functions “It’s truly a workhorse of statistics!” “It’s not just about lines & planes!” Setup. Given $D = ((x_1, y_1), \ldots, (x_n, y_n))$ with $x_i \in \mathbb{R}^d$ and $y_i \in \mathbb{R}$. Goal. Select “good” $f : \mathbb{R} \rightarrow \mathbb{R}$ for predicting $y$...

• ## Notes on Probability Primer 5: Multiple random variables

(PP 5.1) Multiple discrete random variables Definition. Given $(\Omega, \mathscr{A}, P)$, a random vector is a measurable function where $d \in \mathbb{N}$. Definition. A discrete random vector $X \in \mathbb{R}^d$ is s.t. $X(\Omega)$ is countable. Definition. The (joint) PMF (or joint distribution) of a discrete random vector $X \in \mathbb{R}^d$...