About me

I am a Postdoctoral Researcher at the Interdisciplinary Hub for Security, Privacy and Data Governance (iHub) at Radboud University Nijmegen.

Here is a short overview of my CV

• DPhil in Computer Science with Sam Staton, University of Oxford, England 2021
• MASt in Pure Mathematics, Part III of the Mathematical Tripos at University of Cambridge, England 2017
• Bachelor in Mathematics, University of Hamburg, Germany

You can find my complete CV here.

Research Interests

My research interests concern the interplay of

• Category Theory
• Probability Theory
• Programming Language Semantics

I apply these insights to the design of probabilistic programming languages, Bayesian machine learning and causal inference. I am also interested in interactive theorem proving, functional programming with effects, string-diagrammatic methods, quantum computation, type theory, universal algebra.

Projects

Are you a motivated student looking for a project? Write me an email! I am keen on (co)supervising BSc and MSc Projects as well as Research Internships.

BSc Thesis Topics:

• Presentations of Convex Spaces: Convex spaces are an algebraic axiomatization (like vector spaces) of convex subsets of Euclidean space, which are useful in the study of probabilistic computation. You will investigate some algebraic questions about convex spaces, related to free algebras and presentations.
• Reflections into Free Algebras: Free algebras are the basic building blocks of algebraic structures. You will investigate algebras which can be approximated by free algebras in a certain sense, or prove why such an approximation is impossible.
• Uniqueness of Retrodiction: You will study the monoid of relations from a set X to itself, and try to classify automorphisms of this monoid.

MSc Thesis Topics or Research Internships:

• Nominal Sets and Probability: Nominal sets are a mathematical formalism for dealing with names such as variable names or memory locations in programming languages. It doesn't matter what these names are -- we only care whether two names are equal or not. For example, variables bindings are often considered up to α-equivalence. In this project, you'll investigate various formal similarities between fresh name generation (choosing a new variable name, or allocating a memory location), and probability.
• Random Variables and Iso-sets: How can the formalism of random variables be captured or generalized categorically? This project will involve sheaves over categories of sample spaces. A concrete variant are Iso-sets, a continuous generalization of nominal sets using isometries of Euclidean space
• A Type Theory for Equivariance: Group actions are a fundamental language for describing mathematical structures with symmetries. How would a type theory look where everything that typechecks is automatically equivariant?
• Causality and do-calculus: Various topics related to causal inference, causal probabilistic programming languages, and formalization
• Formalization of String Diagrams There are various tools for string diagrams, but the support in type-theoretic theorem provers (Coq/Lean) is still limited. There are various formalization challanges, e.g. Markov categories, causal inference, ...

Publications

You can find my DPhil Thesis here: Structural Foundations for Probabilistic Programming Languages

• Random Variables, Conditional Independence and Categories of Abstract Sample Spaces
  Dario Stein
• Combs, Causality and Contractions in Atomic Markov Categories
  Dario Stein, Márk Széles, EPTCS 2024 (ACT)
• A Categorical Treatment of Open Linear Systems
  Dario Stein, Richard Samuelson
• Graphical Quadratic Algebra
  Dario Stein, Fabio Zanasi, Richard Samuelson, Robin Piedeleu
• Towards a Compositional Framework for Convex Analysis (with Applications to Probability Theory)
  Dario Stein, Richard Samuelson, FoSSaCS 2024
• Absolute continuity, supports and idempotent splitting in categorical probability
  Tobias Fritz, Tomáš Gonda, Antonio Lorenzin, Paolo Perrone, Dario Stein
• Overdrawing Urns with Signed Probabilities
  Bart Jacobs, Dario Stein, EPTCS 2023 (ACT)
• Pearl's and Jeffrey's Update as Modes of Learning in Probabilistic Programming
  Bart Jacobs, Dario Stein, MFPS 2023
• A Category for unifying Gaussian Probability and Nondeterminism
  Dario Stein, Richard Samuelson, CALCO 2023
• Dilations and information flow axioms in categorical probability
  Tobias Fritz, Tomáš Gonda, Nicholas Gauguin Houghton-Larsen, Paolo Perrone, Dario Stein. MSCS, 2023
• Counting and Matching
  Bart Jacobs, Dario Stein, CSL 2023
• Probabilistic Programming with Exact Conditions
  Dario Stein, Sam Staton. Invited Article, Journal of the ACM, 2023
• Compositional Semantics for Probabilistic Programs with Exact Conditioning
  Dario Stein, Sam Staton. LICS 2021 Distinguished Paper
• Probabilistic Programming Semantics for Name Generation
  Marcin Sabok, Sam Staton, Dario Stein, Michael Wolman. POPL 2021
• The Beta-Bernoulli process and Algebraic Effects
  Sam Staton, Dario Stein, Hongseok Yang, Nathanael L. Ackerman, Cameron E. Freer, Daniel M. Roy. ICALP 2018

Teaching

• Spring 24, Lecturer for Category Theory and Coalgebra, Radboud University Nijmegen
• Winter 2023-24, MFoCS Seminar at Radboud University Nijmegen
• Spring 23, Lecturer for Category Theory and Coalgebra, Radboud University Nijmegen
• Winter 2022-23, MFoCS Seminar at Radboud University Nijmegen
• Spring 2022, Tutor for Category Theory and Coalgebra at Radboud University Nijmegen
• Michaelmas 2020, Tutor for Categories, Proofs and Processes at University of Oxford
• Hilary 2020, Tutor for Quantum Information at University of Oxford
• Michaelmas 2019, Tutor for Principles of Programming Languages at University of Oxford.
• Hilary 2019, Tutor for Probability and Computing at University of Oxford.

Talks

• Sep 2024, ItaCa Fest 2024, Online
• Jul 2024, SWS Seminar, RU Nijmegen
• Jun 2024, DutchCATS 2024, Leiden
• Apr 2024, FoSSaCS 2024, Luxembourg
• Nov 2023, DutchCATS 2023, Radboud Universiteit Nijmegen
• Jul 2023, ACT 2023, University of Maryland
• Jun 2023, MFPS 2023, Bloomington, Indiana
• Jun 2023, CALCO 2023, Bloomington, Indiana
• May 2023, Southern Logic Seminar, UCL
• Feb 2023, CSL 2023, University of Warsaw
• Jan 2023, Inn'formal Probability Seminar, Universität Innsbruck
• Aug 2022, Introduction to Probabilistic Programming, SWS Seminar, Radboud University Nijmegen
• Jul 2022, "A Hypergraph Category for Exact Gaussian Inference", Applied Category Theory 22 (slides, video), Strathclyde
• Jul 2022, Tutorial on Probabilistic Programming, iHub, Radboud University Nijmegen
• Jul 2021, Mathematical Foundations Seminar, Bath
• Jul 2021, VeriProP 2021
• Jun 2021, LICS 2021
• Jan 2021, Oxford Quantum Group Workshop
• Jan 2021, POPL 2021 (View on Clowdr)
• Jan 2021, LAFI. Slides
• Oct 2020, ProbProg workshop, MIT/Online
• Feb 2020, PIHOC workshop, IRIF, Paris. Slides
• Jan 2020, LAFI workshop, POPL, New Orleans. Slides
• 2019, Junior Semantics Seminar x 2, Oxford
• Jul 2018, ICALP 2018, Prague.
• 2018, Quantum Lunch, Quantum Group, Oxford

Service

• PC for ProbProg'21, LAFI'23, ACT 2023, ACT 2024, MFPS 2025
• Reviewer for Compositionality, MSCS, FSCD, ProbProg'21 PC, LICS'22, MFCS 2022, FoSSaCS 2023, ESOP 2023, FoSSaCS 2024, LICS 2024

Supervision

• PhD: Márk Széles (cosupervision)
• BSc: Gideon de Hoop (daily supervisor)
• MFoCS Seminar: Tjitske Koster, Sergio Dominguez Cabrera, Dick Blankvoort, Bas van der Linden