Correlated Discrete Random Variables

$\newcommand{\bern}{\text{Bern}}$$\newcommand{\vp}{\varphi}$$\newcommand{\e}{\varepsilon}$$\newcommand{\P}{\mathcal P}$$\newcommand{\Cov}{\text{Cov}}$$\newcommand{\E}{\text{E}}$$\newcommand{\one}{\mathbf 1}$$\newcommand{\s}{\mathbf s}$$\newcommand{\Disc}{\text{Disc}}$In this post I’m going to explore correlations between finitely-supported discrete variables. Bernoulli case I’ll begin with…

Continue Reading →

Ridge regression as a constrained optimization

$\newcommand{\hb}{\hat\beta}$$\newcommand{\hbl}{\hat\beta_\lambda}$$\newcommand{\tb}{\tilde \beta}$$\newcommand{\L}{\mathcal L}$$\newcommand{\l}{\lambda}$$\newcommand{\e}{\varepsilon}$$\newcommand{\0}{\mathbf 0}$$\newcommand{\Lam}{\Lambda}$$\newcommand{\g}{\gamma}$$\newcommand{\D}{\mathcal D}$$\newcommand{\ht}{\hat\theta}$$\newcommand{\a}{\alpha}$In this post I’m going to explore ridge regression as a constrained optimization, and I’ll do…

Continue Reading →