# Inference in Statistical Relational AI

## 1. Abstract

In recent years, a need for efficient inference algorithms on compact representations of large relational databases became apparent, e.g., in natural language understanding, machine learning, or decision making. This need has lead to advances in probabilistic relational modeling for artificial intelligence (also called statistical relational AI). Probabilistic relational models combine the fields of reasoning under uncertainty and modeling
incorporating relations and objects in the vain of first-order logic. After briefly introducing basics about probability theory and Bayesian or Markovian networks, we present specific probabilistic relational modelling approaches and focus on exact and approximative inference algorithms.

## 4. Outline (tentative)

1. Introduction
2. Probabilistic (relational) modeling
• Semantics
• Inference problems and applications
• Algorithms and systems
• Scalability
3. Scalability by lifting
• Exact lifted inference
• Approximate lifted inference
4. Summary

# Practical introduction to Formal Concept Analysis and using conexp-clj

## 1. Abstract

Formal Concept Analysis is a mathematical theory for deriving a concept hierarchy or formal ontology from a collection of objects and their properties. It builds on the mathematical theory of lattices and ordered sets. The conceptual view on data enables qualitative data analysis purely based on relational properties. Furthermore, there is a close relation to the analysis of bipartite graphs nourishing both fields. Conexp-clj is a stand-alone software as well as a library for computational tasks in the realm of Formal Concept Analysis. Its main purpose is to enable nontrivial examples and ideas to be
computed easily.

This tutorial will provide a brief and compact introduction the basic notions of FCA. This will include the computation of implicational bases in data as well as a demonstration of the attribute exploration algorithm. We will also show how to overcome computational limitations for large data setst hrough the application of approximative methods.

## 3. Outline

1. Foundations of FCA
2. Simple FCA tasks and how to solve them with conexp-clj
3. Learning via the exploration algorithm
4. Measures and metrics in concept lattices
5. Probably approximately correct learning and FCA
6. State of the art and what to come in concept-clj