Learning high-level causal representations together with a causal model from unstructured
low-level data such as pixels is impossible from observational data alone. We prove under …

We develop Markov categories as a framework for synthetic probability and statistics,
following work of Golubtsov as well as Cho and Jacobs. This means that we treat the …

The notions of disintegration and Bayesian inversion are fundamental in conditional
probability theory. They produce channels, as conditional probabilities, from a joint state, or …

The d-separation criterion detects the compatibility of a joint probability distribution with a
directed acyclic graph through certain conditional independences. In this work, we study this …

Markov categories are a recent categorical approach to the mathematical foundations of
probability and statistics. Here, this approach is advanced by stating and proving equivalent …

Categorical probability has recently seen significant advances through the formalism of
Markov categories, within which several classical theorems have been proven in entirely …

Artificial intelligence (AI) is currently based largely on black-box machine learning models
which lack interpretability. The field of eXplainable AI (XAI) strives to address this major …

Extracting causal relationships from observed correlations is a growing area in probabilistic
reasoning, originating with the seminal work of Pearl and others from the early 1990s. This …

We spell out the paradigm of exact conditioning as an intuitive and powerful way of
conditioning on observations in probabilistic programs. This is contrasted with likelihood …

This document is an elementary introduction to string diagrams. It takes a computer science
perspective: rather than using category theory as a starting point, we build on intuitions from …