Convexity counterexample
Here's a fun counterexample: a function $\mathbb{R}^n \to \mathbb{R}$ that is
jointly convex in any $n-1$ of the variables, but not in all variables at once.
The function
Probabilistic Abstractions I
(This post represents research in progress. I may think about these concepts
entirely differently a few months from now, but for my own benefit I'm trying to
exposit on them in
Pairwise Independence vs. Independence
For collections of independent random variables, the Chernoff bound and related
bounds give us very sharp concentration inequalities --- if $X_1,\ldots,X_n$ are
independent, then their sum has a distribution
A Fun Optimization Problem
I spent the last several hours trying to come up with an efficient algorithm to
the following problem:
Problem:Suppose that we have a sequence of $l$ pairs of non-negative numbers
$(a_1,
Eigenvalue Bounds
While grading homeworks today, I came across the following bound:
Theorem 1: If A and B are symmetric $n\times n$ matrices with eigenvalues
$\lambda_1 \geq \lambda_2 \geq \ldots \geq \lambda_