# Determinantal point process mixtures via spectral density approach

## TL;DR

This paper introduces a spectral density approach to DPP mixture models that encourages well-separated location parameters, extends to covariate incorporation, and develops Bayesian inference with empirical validation.

## Contribution

It proposes a general spectral representation for DPP mixture models, allowing flexible approximation and extension to covariate-dependent settings, with comprehensive Bayesian inference.

## Key findings

- Effective separation of mixture components demonstrated
- Model extensions incorporate covariate information
- Bayesian inference performs well in simulations and data examples

## Abstract

We consider mixture models where location parameters are a priori encouraged to be well separated. We explore a class of determinantal point process (DPP) mixture models, which provide the desired notion of separation or repulsion. Instead of using the rather restrictive case where analytical results are available, we adopt a spectral representation from which approximations to the DPP intensity functions can be readily computed. For the sake of concreteness the presentation focuses on a power exponential spectral density, but the proposed approach is in fact quite general. We later extend our model to incorporate covariate information in the likelihood and also in the assignment to mixture components, yielding a trade-off between repulsiveness of locations in the mixtures and attraction among subjects with similar covariates. We develop full Bayesian inference, and explore model properties and posterior behavior using several simulation scenarios and data illustrations.