Hierarchical Infinite Relational Model

TL;DR

The Hierarchical Infinite Relational Model (HIRM) is a probabilistic framework that captures complex relational data structures, enabling tasks like clustering and density estimation in noisy, sparse datasets through Bayesian inference.

Contribution

HIRM extends the infinite relational model by introducing a hierarchical structure for relation clustering and domain partitioning, with new Gibbs sampling algorithms for inference.

Findings

Effective density estimation on large datasets with 18 million cells.

Successful discovery of relational structures in political and genomic data.

Outperforms existing models in handling heterogeneous relational data.

Abstract

This paper describes the hierarchical infinite relational model (HIRM), a new probabilistic generative model for noisy, sparse, and heterogeneous relational data. Given a set of relations defined over a collection of domains, the model first infers multiple non-overlapping clusters of relations using a top-level Chinese restaurant process. Within each cluster of relations, a Dirichlet process mixture is then used to partition the domain entities and model the probability distribution of relation values. The HIRM generalizes the standard infinite relational model and can be used for a variety of data analysis tasks including dependence detection, clustering, and density estimation. We present new algorithms for fully Bayesian posterior inference via Gibbs sampling. We illustrate the efficacy of the method on a density estimation benchmark of twenty object-attribute datasets with up to 18 million cells and use it to discover relational structure in real-world datasets from politics and genomics.