arXiv subjects

Alessandra Guglielmi

Publications and source records attributed to Alessandra Guglielmi.

23 records · Page 2Linked to original sources

arXiv2019

Bayesian nonparametric temporal dynamic clustering via autoregressive Dirichlet priors

In this paper we consider the problem of dynamic clustering, where cluster memberships may change over time and clusters may split and merge over time, thus creating new clusters and destroying existing ones. We propose a Bayesian nonparametric approach to dynamic clustering via mixture modeling. Our approach relies on a novel time-dependent nonparametric prior defined by combining: i) a copula-based transformation of a Gaussian autoregressive process; ii) the stick-breaking construction of the Dirichlet process. Posterior inference is performed through a particle Markov chain Monte Carlo algorithm which is simple, computationally efficient and scalable to massive datasets. Advantages of the proposed approach include flexibility in applications, ease of computations and interpretability. We present an application of our dynamic Bayesian nonparametric mixture model to the study the temporal dynamics of gender stereotypes in adjectives and occupations in the 20th and 21st centuries in the United States. Moreover, to highlight the flexibility of our model we present additional applications to time-dependent data with covariates and with spatial structure.

stat.ME↗

arXiv2017

Determinantal point process mixtures via spectral density approach

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 available, we adopt a spectral representation from which approximations to the DPP intensity 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.

stat.ME↗

arXiv2016

Bayesian Nonparametric Modelling of Joint Gap Time Distributions for Recurrent Event Data

We propose autoregressive Bayesian semi-parametric models for waiting times between recurrent events. The aim is two-fold: inference on the effect of possibly time-varying covariates on the gap times and clustering of individuals based on the time trajectory of the recurrent event. Time-dependency between gap times is taken into account through the specification of an autoregressive component for the random effects parameters influencing the response at different times. The order of the autoregression may be assumed unknown and object of inference and we consider two alternative approaches to perform model selection under this scenario. Covariates may be easily included in the regression framework and censoring and missing data are easily accounted for. As the proposed methodologies lies within the class of Dirichlet process mixtures, posterior inference can be performed through efficient MCMC algorithms. We illustrate the approach through simulations and medical applications involving recurrent hospitalizations of cancer patients and successive urinary tract infections.

stat.AP↗

arXiv2015

A priori truncation method for posterior sampling from homogeneous normalized completely random measure mixture models

This paper adopts a Bayesian nonparametric mixture model where the mixing distribution belongs to the wide class of normalized homogeneous completely random measures. We propose a truncation method for the mixing distribution by discarding the weights of the unnormalized measure smaller than a threshold. We prove convergence in law of our approximation, provide some theoretical properties and characterize its posterior distribution so that a blocked Gibbs sampler is devised. The versatility of the approximation is illustrated by two different applications. In the first the normalized Bessel random measure, encompassing the Dirichlet process, is introduced; goodness of fit indexes show its good performances as mixing measure for density estimation. The second describes how to incorporate covariates in the support of the normalized measure, leading to a linear dependent model for regression and clustering.

math.ST↗

arXiv2012

A class of measure-valued Markov chains and Bayesian nonparametrics

Measure-valued Markov chains have raised interest in Bayesian nonparametrics since the seminal paper by (Math. Proc. Cambridge Philos. Soc. 105 (1989) 579--585) where a Markov chain having the law of the Dirichlet process as unique invariant measure has been introduced. In the present paper, we propose and investigate a new class of measure-valued Markov chains defined via exchangeable sequences of random variables. Asymptotic properties for this new class are derived and applications related to Bayesian nonparametric mixture modeling, and to a generalization of the Markov chain proposed by (Math. Proc. Cambridge Philos. Soc. 105 (1989) 579--585), are discussed. These results and their applications highlight once again the interplay between Bayesian nonparametrics and the theory of measure-valued Markov chains.

math.ST↗