In this post I’m going to prove some results needed to solve the “XOR-sequence” HackerRank problem found here. Spoiler warning…
$\newcommand{\logit}{\operatorname{logit}}$$\newcommand{\y}{\mathbf y}$$\newcommand{\one}{\mathbf 1}$$\newcommand{\e}{\varepsilon}$$\newcommand{\0}{\mathbf 0}$$\newcommand{\Var}{\operatorname{Var}}$$\newcommand{\E}{\operatorname{E}}$In this post I’ll look at the gradient of the loss in logistic regression and explore a…
$\newcommand{\one}{\mathbf 1}$$\newcommand{\0}{\mathbf 0}$$\newcommand{\tr}{\operatorname{tr}}$$\newcommand{\e}{\varepsilon}$In this post I’m going to look at some relationships between the diagonal of a positive semidefinite (PSD)…
$\newcommand{\0}{\mathbf 0}$$\newcommand{\one}{\mathbf 1}$In this post I’m going to work out the distribution of the area of a random parallelogram formed…
$\newcommand{\e}{\varepsilon}$$\newcommand{\one}{\mathbf 1}$Suppose I have collected data $X \in \mathbb R^{n\times p}$ ($n \geq p$ and $X$ is full column rank…
$\newcommand{\X}{\mathcal X}$$\newcommand{\dl}{\,\text d\lambda}$$\newcommand{\dx}{\,\text dx}$$\newcommand{\one}{\mathbf 1}$I’m going to take a look at functional linear regression, where I’ll find the best linear…
$\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…
$\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}$$\newcommand{\a}{\alpha}$In this post I’m going to explore ridge regression as a constrained optimization, and I’ll do…
$\newcommand{\e}{\varepsilon}$$\newcommand{\1}{\mathbf 1}$$\newcommand{\one}{\mathbf 1}$$\newcommand{\0}{\mathbf 0}$In this post I’m going to work with simple linear regression in matrix form. In most places…
In this post I want to take a look at interpolation with a single polynomial. I’ll prove the existence and…