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 …

Artificial Intelligence (AI) systems such as autonomous vehicles, facial recognition, and
speech recognition systems are increasingly integrated into our daily lives. However …

Over the past two decades machine learning has permeated almost every realm of
technology. At the same time, many researchers have begun using category theory as a …

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 …

We propose a category-theoretic definition of retrodiction and use it to exhibit a time-reversal
symmetry for all quantum channels. We do this by introducing retrodiction families and …

Markov categories are a novel framework to describe and treat problems in probability and
information theory. In this work we combine the categorical formalism with the traditional …

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 …

We present a novel proof of de Finetti's Theorem characterizing permutation-invariant
probability measures of infinite sequences of variables, so-called exchangeable measures …

We present Lilac, a separation logic for reasoning about probabilistic programs where
separating conjunction captures probabilistic independence. Inspired by an analogy with …

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 …