Efficiently estimating the trace \(\textrm{tr}(A) = \sum_{i=1}^d A_{ii}\) of a square matrix \(A \in \mathbb{R}^{d \times d}\) is an important problem required in a number of recent deep learning and machine learning models. In those cases the matrix \(A\) is typically positive-definite, large …

TLDR: Yes, and there are precise results, although they are not as well known as they perhaps should be.

Over the last few years I had many conversations in which the statement was made that Bayesians methods are generally immune to overfitting, or at least, robust against overfitting, or---everybody would …

This post continues the previous post, part 1 on scoring rules. However, today we will be more hands on, testing your skill of making good and well-calibrated predictions.

To this end, I will ask you several questions about numerical quantities and I would like to hear an answer stated as …

This article is the first of two on proper scoring rules, a specific type of loss function defined on probability distributions or functions of probability distributions.

If this article sparks your interest, I recommend the gentle introduction to scoring rules in the context of decision theory in Chapter 10 of …

In this article we will look at a practically important measure of efficiency in importance sampling, the so called effective sample size (ESS) estimate. This measure was proposed by Augustine Kong in 1992 in a technical report which until recently has been difficult to locate online, but after getting in …