A tutorial on Dynamic Models and Statistical Relational AI at the KI 2019

42nd German Conference on Artificial Intelligence, September 23rd-26th 2019, University Kassel

In recent years, a need for compact representations of large databases became apparent, e.g., in natural language understanding, machine learning, or decision making, accompanied by a need for efficient inference algorithms. Representations need to incorporate objects, relations between them, and uncertainties about object attribute values, object identity, or even existence of objects or relations. Explicitly modelling objects and relations enable algorithms to exploit repeated structures for efficiency gains during inference. Instead of grounding such a relational model, which incurs an exponential blowup and makes inference infeasible, one can answer queries on the model directly and in a stable and scalable way.

Unfortunately, our world is not static, changing and evolving over time. Thus, objects and relations are not only relevant for snapshots but also for reasoning in temporal, or more general, sequential models. Handling sequential influences explicitly allows algorithms to efficiently answer queries regarding previous, present, and future states. Representing objects and relations under uncertainty in a temporal model also enables query answering in a scalable and stable way given growing object numbers. But, a sequential model brings about various new problems like temporal evidence, which may destroy compact representations, inhibiting stable query answering.

This tutorial is a continuation of previous tutorials, with dynamic modelling and reasoning taking centre stage for the first time.

• Tanya Braun
• Marcel Gehrke
• Ralf Möller

1. Probabilistic relational models (PRMs) and dynamic models
   
   • Application example
   • Semantics, static vs. dynamic
   • Exact multi-query answering
2. Answering static queries in PRMs
   
   • Lifting
   • Junction trees
   • Colour passing
3. Answering continuous queries in dynamic models
   
   • Lifted dynamic junction tree algorithm
   • Relational interfaces
   • Taming reasoning w.r.t. evidence over time
4. Take-home messages

1. Introduction
2. Static queries
3. Continuous queries
4. Wrap-up