Operator Calculus for Information Field Theory

TL;DR

This paper introduces an operator calculus approach for information field theory, simplifying complex expectation calculations in non-Gaussian signal inference problems, demonstrated through a new self-calibrating algorithm tested on mock data.

Contribution

It presents a novel operator calculus framework for information field theory, enabling easier computation of expectation values in non-Gaussian posteriors, and introduces a self-calibrating algorithm.

Findings

Operator calculus simplifies expectation value calculations.

The self-calibrating algorithm performs well on mock data.

The method extends to log-normal priors and complex inference tasks.

Abstract

Signal inference problems with non-Gaussian posteriors can be hard to tackle. Through using the concept of Gibbs free energy these posteriors are rephrased as Gaussian posteriors for the price of computing various expectation values with respect to a Gaussian distribution. We present a new way of translating these expectation values to a language of operators which is similar to that in quantum mechanics. This simplifies many calculations, for instance such involving log-normal priors. The operator calculus is illustrated by deriving a novel self-calibrating algorithm which is tested with mock data.