Two Strange Facts
Here are two strange facts about matrices, which I can prove but not in a
satisfying way.
1. If $A$ and $B$ are symmetric matrices satisfying $0 \preceq A \preceq B$,
then $A^
Difficulty of Predicting the Maximum of Gaussians
Suppose that we have a random variable $X \in \mathbb{R}^d$, such that
$\mathbb{E}[XX^{\top}] = I_{d \times d}$. Now take k independent Gaussian random
variables $Z_1, \ldots, Z_
Maximal Maximum-Entropy Sets
Consider a probability distribution ${p(y)}$ on a space ${\mathcal{Y}}$. Suppose
we want to construct a set ${\mathcal{P}}$ of probability distributions on
${\mathcal{Y}}$ such that ${p(y)}$ is the maximum-
Long-Term and Short-Term Challenges to Ensuring the Safety of AI Systems
Introduction
There has been much recent discussion about AI risk, meaning specifically the
potential pitfalls (both short-term and long-term) that AI with improved
capabilities could create for society. Discussants include AI
A Fervent Defense of Frequentist Statistics
[Highlights for the busy: de-bunking standard "Bayes is optimal" arguments;
frequentist Solomonoff induction; and a description of the online learning
framework.]
Short summary. This essay makes many points, each of