Mathematix

Making sense of PCA

Here we look at the universality-based definition of the tensor product

We are trying to make sense of tensors and the tensor product of vector spaces

Sufficient statistics

The Cramér-Rao Bound is a lower bound on the variance of an unbiased estimator. Here we focus on one-parameter models.

Introduction of the notion of Fisher information: a quantity of central importance in statistics.

Statistics and Estimators: definitions of statisics and an introduction to the concepts of bias and variance of an estimator; several examples.

We study the class of sub-Gaussian random variables: those random variables whose tails are dominated by a Gaussian. Such random variables satisfy Hoeffding-type bounds and possess several interesting properties. We also define the sub-Gaussian norm and study its properties.

A result on the convergence of sample mean and notes on some standard concentration inequalities such as the Markov, Chernoff, Hoeffding, and Chernoff’s bounds

How to project on the epigraph of the squared Euclidean norm