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Activity Number: 230 - Recent Advances in Nonexchangeable, Dependent, Random Partition and Feature Allocation Models
Type: Topic Contributed
Date/Time: Monday, July 30, 2018 : 2:00 PM to 3:50 PM
Sponsor: International Society for Bayesian Analysis (ISBA)
Abstract #328678 Presentation
Title: Determinantal Point Process Mixtures via Spectral Density Approach
Author(s): Fernando Quintana* and Alessandra Guglielmi and Ilaria Bianchini
Companies: Pontificia Universidad Catolica De Chile and Politecnico de Milano and Politecnico de Milano
Keywords: Density Estimation; Nonparametric Regression; Repulsive Mixtures; Reversible Jumps

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.

Authors who are presenting talks have a * after their name.

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