Open Access
March 2020 Determinantal Point Process Mixtures Via Spectral Density Approach
Ilaria Bianchini, Alessandra Guglielmi, Fernando A. Quintana
Bayesian Anal. 15(1): 187-214 (March 2020). DOI: 10.1214/19-BA1150


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).


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Ilaria Bianchini. Alessandra Guglielmi. Fernando A. Quintana. "Determinantal Point Process Mixtures Via Spectral Density Approach." Bayesian Anal. 15 (1) 187 - 214, March 2020.


Published: March 2020
First available in Project Euclid: 26 February 2019

zbMATH: 1437.62136
MathSciNet: MR4050882
Digital Object Identifier: 10.1214/19-BA1150

Keywords: Density estimation , Nonparametric regression , repulsive mixtures , reversible jumps

Vol.15 • No. 1 • March 2020
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