## 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_

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_

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

(This is available in pdf form here
[http://web.mit.edu/jsteinha/www/stats-essay.pdf].)
If you are a newly initiated student into the field of machine learning, it
won't be long before

Humans are very good at correctly generalizing rules across categories (at
least, compared to computers). In this post I will examine mechanisms that would
allow us to do this in a reasonably rigorous

What happens when you are uncertain about observations you made? For instance,
you remember something happening, but you don't remember who did it. Or you
remember some fact you read on wikipedia, but