[Paper Review] CrossCat: a fully Bayesian nonparametric method for analyzing heterogeneous, high dimensional data

Vikash K. Mansinghka, Patrick Shafto+4 more|arXiv (Cornell University)|Jan 1, 2016

Bayesian Methods and Mixture Models47 references12 citations

TL;DR

CrossCat is a fully Bayesian nonparametric method for analyzing heterogeneous, high-dimensional data by inferring multiple non-overlapping views, each modeled with a nonparametric mixture. It uses scalable Gibbs sampling to achieve predictive accuracy competitive with state-of-the-art methods on datasets up to 10 million cells, capturing structure consistent with domain knowledge.

ABSTRACT

There is a widespread need for statistical methods that can analyze high-dimensional datasets without imposing restrictive or opaque modeling assumptions. This paper describes a domain-general data analysis method called CrossCat. CrossCat infers multiple non-overlapping views of the data, each consisting of a subset of the variables, and uses a separate nonparametric mixture to model each view. CrossCat is based on approximately Bayesian inference in a hierarchical, nonparametric model for data tables. This model consists of a Dirichlet process mixture over the columns of a data table in which each mixture component is itself an independent Dirichlet process mixture over the rows; the inner mixture components are simple parametric models whose form depends on the types of data in the table. CrossCat combines strengths of mixture modeling and Bayesian network structure learning. Like mixture modeling, CrossCat can model a broad class of distributions by positing latent variables, and produces representations that can be efficiently conditioned and sampled from for prediction. Like Bayesian networks, CrossCat represents the dependencies and independencies between variables, and thus remains accurate when there are multiple statistical signals. Inference is done via a scalable Gibbs sampling scheme; this paper shows that it works well in practice. This paper also includes empirical results on heterogeneous tabular data of up to 10 million cells, such as hospital cost and quality measures, voting records, unemployment rates, gene expression measurements, and images of handwritten digits. CrossCat infers structure that is consistent with accepted findings and common-sense knowledge in multiple domains and yields predictive accuracy competitive with generative, discriminative, and model-free alternatives.

Motivation & Objective

• Address the need for statistical methods that analyze high-dimensional data without restrictive or opaque modeling assumptions.
• Enable robust inference in heterogeneous tabular datasets with mixed data types and complex dependencies.
• Develop a method that combines the strengths of mixture modeling and Bayesian network structure learning for accurate representation and prediction.
• Provide a fully Bayesian, nonparametric approach capable of handling data with unknown structure and dimensionality.
• Ensure scalability and practical applicability to real-world datasets with up to 10 million cells.

Proposed method

• CrossCat models data tables using a hierarchical, nonparametric Bayesian model with a Dirichlet process mixture over columns.
• Each column's mixture component is an independent Dirichlet process mixture over rows, with parametric components tailored to data types.
• The method infers multiple non-overlapping views of the data, each representing a subset of variables with shared conditional dependencies.
• It employs a scalable Gibbs sampling scheme for approximate Bayesian inference, enabling practical application to large datasets.
• The model captures conditional independence and dependence structures between variables, akin to Bayesian networks.
• Predictive inference is performed by conditioning on observed variables and sampling from the posterior predictive distribution.

Experimental results

Research questions

• RQ1 Can a fully Bayesian, nonparametric method effectively model high-dimensional, heterogeneous data without strong parametric assumptions?
• RQ2 How well can CrossCat infer meaningful, interpretable data structure across diverse domains such as healthcare, social science, and genomics?
• RQ3 To what extent does CrossCat outperform or match generative, discriminative, and model-free approaches in predictive accuracy?
• RQ4 Can CrossCat scale to large datasets with up to 10 million cells while maintaining accuracy and interpretability?
• RQ5 Does CrossCat's view-based decomposition improve modeling fidelity when multiple statistical signals coexist in the data?

Key findings

• CrossCat successfully infers data structure consistent with accepted findings and common-sense knowledge across diverse domains, including healthcare, voting records, and gene expression.
• The method achieves predictive accuracy competitive with both generative and discriminative models on high-dimensional, heterogeneous datasets.
• CrossCat demonstrates scalability, effectively analyzing datasets with up to 10 million cells using Gibbs sampling.
• The view-based decomposition enables accurate modeling of multiple statistical signals by isolating dependencies within subsets of variables.
• The inferred structure reflects known domain relationships, such as correlations between hospital quality measures and cost data.
• CrossCat’s nonparametric nature allows it to adapt to unknown data complexity without requiring prior specification of model dimensionality.