文章基本信息

标题：Determinantal Point Process Mixtures Via Spectral Density Approach
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作者：Ilaria Bianchini ; Alessandra Guglielmi ; Fernando A. Quintana 等
期刊名称：Bayesian Analysis
印刷版ISSN：1931-6690
电子版ISSN：1936-0975
出版年度：2020
卷号：15
期号：1
页码：187-214
DOI：10.1214/19-BA1150
语种：English
出版社：International Society for Bayesian Analysis
摘要：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).
关键词：density estimation; nonparametric regression; repulsive mixtures; reversible jumps