Solomonoff induction is a computational formalization of Bayesianism; a method for inductive inference and prediction [2]. It provides a formal framework for predicting the next observation in a sequence by weighing all computable hypotheses, with a bias towards those of lower Kolmogorov complexity—a principle that rigorously formalises Occam’s Razor [1] [4]. In this talk, we explore these concepts by building from their foundational mathematical underpinnings.

We present the measure-theoretic concepts required to rigorously develop Bayesian probability theory, thereby laying the groundwork for a formal and unambiguous treatment of Bayesian inference. Our objective is to directly address the prerequisites for a deeper analysis of the theory of Universal Artificial Intelligence [3], algorithmic probability [2], and to provide a comprehensive understanding of Solomonoff induction.

1. Andrey Nikolaevich Kolmogorov, Three Approaches to the Quantitative Definition of Information, Problems of Information Transmission, vol.1 (1965), no.1, pp.1–7.
2. Ray J. Solomonoff, A Formal Theory of Inductive Inference: Part 1 and 2, Information and Control, vol.7 (1964), pp.1–22 and 224–254.
3. Marcus Hutter, David Quarel and Elliot Catt, An Introduction to Universal Artificial Intelligence, Chapman and Hall/CRC, 2024.
4. Ming Li and Paul Vit´anyi, An Introduction to Kolmogorov Complexity and Its Applications, Springer, 2008.