# Hierarchical Infinite Relational Model

arXiv: https://arxiv.org/abs/2108.07208 · HTML: https://mlsanity.com/paper/2108.07208/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 60 references that are in the map.
- First posted on arXiv 16 Aug 2021.

## Builds on (most cited first, 14 of 14)

- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [GMNN: Graph Markov Neural Networks](https://mlsanity.com/paper/1905.06214/) (2019)
- [Stochastic Blockmodels meet Graph Neural Networks](https://mlsanity.com/paper/1905.05738/) (2019)
- [Bayesian Models of Graphs, Arrays and Other Exchangeable Random Structures](https://mlsanity.com/paper/1312.7857/) (2013)
- [Bayesian Synthesis of Probabilistic Programs for Automatic Data Modeling](https://mlsanity.com/paper/1907.06249/) (2019)
- [SPPL: Probabilistic Programming with Fast Exact Symbolic Inference](https://mlsanity.com/paper/2010.03485/) (2020)
- [Object-Oriented Bayesian Networks](https://mlsanity.com/paper/1302.1554/) (2013)
- [CrossCat: A Fully Bayesian Nonparametric Method for Analyzing Heterogeneous, High Dimensional Data](https://mlsanity.com/paper/1512.01272/) (2015)
- [The Binary Space Partitioning-Tree Process](https://mlsanity.com/paper/1903.09343/) (2019)
- [Bayesian Nonparametric Space Partitions: A Survey](https://mlsanity.com/paper/2002.11394/) (2020)
- [Detecting Dependencies in Sparse, Multivariate Databases Using Probabilistic Programming and Non-parametric Bayes](https://mlsanity.com/paper/1611.01708/) (2016)
- [Automatic discovery of cell types and microcircuitry from neural connectomics](https://mlsanity.com/paper/1407.4137/) (2014)
- [Probabilistic Search for Structured Data via Probabilistic Programming and Nonparametric Bayes](https://mlsanity.com/paper/1704.01087/) (2017)
- [Scalable Deep Generative Relational Models with High-Order Node Dependence](https://mlsanity.com/paper/1911.01535/) (2019)

## Built on by (most cited first, 2 of 2)

- [Sequential Monte Carlo Learning for Time Series Structure Discovery](https://mlsanity.com/paper/2307.09607/) (2023)
- [Hierarchical Blockmodelling for Knowledge Graphs](https://mlsanity.com/paper/2408.15649/) (2024)

## Abstract (arXiv)

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.