Bayesian Analysis

Determinantal Point Process Mixtures Via Spectral Density Approach

Ilaria Bianchini, Alessandra Guglielmi, and Fernando A. Quintana

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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 partially available, we adopt a spectral representation from which approximations to the DPP density 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. Supplementary materials for this article are available online (Bianchini et al., 2019).

Article information

Source
Bayesian Anal., Advance publication (2018), 28 pages.

Dates
First available in Project Euclid: 26 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.ba/1551150619

Digital Object Identifier
doi:10.1214/19-BA1150

Keywords
density estimation nonparametric regression repulsive mixtures reversible jumps

Rights
Creative Commons Attribution 4.0 International License.

Citation

Bianchini, Ilaria; Guglielmi, Alessandra; Quintana, Fernando A. Determinantal Point Process Mixtures Via Spectral Density Approach. Bayesian Anal., advance publication, 26 February 2019. doi:10.1214/19-BA1150. https://projecteuclid.org/euclid.ba/1551150619


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Supplemental materials

  • Supplementary Material for “Determinantal Point Process Mixtures Via Spectral Density Approach”. Supplementary materials for this article are available online. In particular, the document contains a description of the two Gibbs samplers used for posterior inference under the DPP mixture model (Sections 1 and 3), without and with covariate dependence, respectively. Moreover, a new test on the Galaxy dataset when different spectral densities are considered (Section 2). Finally, supplemental figures that did not fit in the paper and additional analysis of an Air Quality Index dataset are provided.