StaRAI - Semantics and Symmetries in Exact Lifted Inference

A tutorial on Statistical Relational AI (StaRAI) at the ECAI 2020

24th European Conference on Artificial Intelligence, August 29th - September 2nd 2020, Santiago de Compostela, Spain

Abstract

Symmetries in a probabilistic graphical model with a known number of constants allow for lifted inference to perform tractable problem solving given a liftable model and a liftable query. In this tutorial, we show how to retain properties of lifted inference even with an unknown set of constants as well as how to retain a liftable model by approximating symmetries while performing inference.

Objectives

Relational modelling allows for representing knowledge and reasoning under uncertainty (KRR and UAI), which are main topics of the ECAI 2020 call for papers. The goal of this tutorial is two-fold:

  1. to provide an overview about recent developments in probabilistic relational mod- elling and reasoning with a focus on obtaining/restoring a lifted model and their semantics and
  2. to discuss new directions for investigation.

Therefore, this tutorial on the one hand provides an introduction to novices to a major topic within AI as well as discusses a topic of emerging importance for AI.

The tutorial will be mostly self-contained. While we assume familiarity with probabilistic graphical models, like Bayesian networks, we will revisit all necessary definitions.

Contents

  1. Motivation
  2. Probabilistic relational modelling
    • Propositional models
    • Algorithms to identify symmetries
    • Relational models
    • Inference tasks
    • Algorithms, systems, problems
  3. Inference in probabilistic relational models
    • Exact inference in probabilistic relational models
    • Inference with unknown numbers of constants
    • Exact inference in dynamic probabilistic relational models
    • Restoring symmetries while performing inference
  4. Summary

Selected References and Further Reading

  • David Poole: First-order Probabilistic Inference, IJCAI-03.
  • Mathias Niepert and Guy Van den Broeck: Tractability through Exchangeability: A New Perspective on Efficient Probabilistic Inference, AAAI-14
  • Guy Van den Broeck and Mathias Niepert: Lifted Probabilistic Inference for Asymmetric Graphical Models, AAAI-15.
  • Mathias Niepert: Symmetry-aware Marginal Density Estimation, AAAI-13.
  • Parag Singla and Pedro Domingos: Markov Logic in Infinite Domains, UAI-07.
  • Babak Ahmadi, Kristian Kersting, Martin Mladenov, and Sriraam Natarajan: Exploiting Symmetries for Scaling Loopy Belief Propagation and Relational Training, Machine Learning 92(1).
  • Tanya Braun and Ralf Möller: Exploring Unknown Universes in Probabilistic Relational Models, AI-19.
  • Marcel Gehrke, Tanya Braun, and Ralf Möller: Taming Reasoning in Temporal Probabilistic Relational Models, ECAI-20.

Download Presentations

Will be made available as soon as possible, with beginning of ECAI2020 at the latest