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Determinantal point process mixtures via spectral density approach. (English) Zbl 1437.62136
Summary: 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 [I. Bianchini et al., “Supplementary material for ‘Determinantal point process mixtures via spectral density approach’”, Bayesian Anal. (2019; doi:10.1214/19-BA1150.187)].

MSC:
62G08 Nonparametric regression and quantile regression
62H30 Classification and discrimination; cluster analysis (statistical aspects)
62G07 Density estimation
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
62M15 Inference from stochastic processes and spectral analysis
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