Bayesian Inference for Latent Biologic Structure with Determinantal Point Processes (DPP)

TL;DR

This paper explores the application of determinantal point processes (DPP) as priors for latent biological structures, demonstrating their advantages in interpretability and inference through case studies in biomedical data analysis.

Contribution

It introduces the use of DPP priors for latent structure modeling in biomedical applications and develops efficient posterior simulation methods for inference.

Findings

DPP priors improve interpretability of latent features in biomedical models.

Application to MRI and gene expression data shows effective inference.

Reversible jump MCMC methods facilitate inference with DPP priors.

Abstract

We discuss the use of the determinantal point process (DPP) as a prior for latent structure in biomedical applications, where inference often centers on the interpretation of latent features as biologically or clinically meaningful structure. Typical examples include mixture models, when the terms of the mixture are meant to represent clinically meaningful subpopulations (of patients, genes, etc.). Another class of examples are feature allocation models. We propose the DPP prior as a repulsive prior on latent mixture components in the first example, and as prior on feature-specific parameters in the second case. We argue that the DPP is in general an attractive prior model for latent structure when biologically relevant interpretation of such structure is desired. We illustrate the advantages of DPP prior in three case studies, including inference in mixture models for magnetic resonance images (MRI) and for protein expression, and a feature allocation model for gene expression using data from The Cancer Genome Atlas. An important part of our argument are efficient and straightforward posterior simulation methods. We implement a variation of reversible jump Markov chain Monte Carlo simulation for inference under the DPP prior, using a density with respect to the unit rate Poisson process.