Bayesian inference for latent biologic structure with determinantal point processes (DPP).

Area of Science:

• Biomedical data analysis
• Statistical modeling
• Machine learning

Background:

• Biomedical research often requires interpreting latent features as meaningful biological or clinical structures.
• Existing models like mixture models and feature allocation models face challenges in representing complex latent structures.

Purpose of the Study:

• To propose and evaluate the determinantal point process (DPP) as a repulsive prior for latent structure in biomedical applications.
• To demonstrate the DPP's utility in enhancing the interpretability of latent features.

Main Methods:

• The study proposes using DPP as a repulsive prior for latent mixture components and feature-specific parameters.
• Efficient posterior simulation methods, including a variation of reversible jump Markov chain Monte Carlo, are implemented.
• The DPP prior is applied using a density with respect to the unit rate Poisson process.

Main Results:

• The DPP prior effectively models latent structures in mixture models for magnetic resonance images (MRI) and protein expression data.
• The DPP prior demonstrates advantages in a feature allocation model for gene expression data from The Cancer Genome Atlas.
• The proposed simulation methods facilitate straightforward inference under the DPP prior.

Conclusions:

• The determinantal point process (DPP) is an attractive prior for latent structure when biological interpretation is desired.
• DPPs enhance the interpretability of latent structures in various biomedical models.
• The study provides efficient computational methods for DPP-based inference in biomedical applications.