On the inferential implications of decreasing weight structures in mixture models

Blasi, Pierpaolo De; Martínez, Asael Fabian; Mena, Ramsés H.; Prünster, Igor

doi:10.1016/j.csda.2020.106940

Cited by 11 publications

(7 citation statements)

References 34 publications

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“…It is well known that, under the DP specification, the expected number of clusters induced in the novelty term grows as γ log M. We choose the DP mostly for computational convenience: if more flexibility is required, Brand can easily be adapted to accommodate different nonparametric priors, such as the Pitman-Yor process (Pitman 1995;Pitman and Yor 1997) or the geometric process and its extensions (De Blasi et al 2020). To facilitate posterior inference given the specification in (4), we consider the following complete likelihood:…”

Section: Stage Ii: Bnp Novelty Detection In Test Datamentioning

confidence: 99%

A two-stage Bayesian semiparametric model for novelty detection with robust prior information

2021

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Novelty detection methods aim at partitioning the test units into already observed and previously unseen patterns. However, two significant issues arise: there may be considerable interest in identifying specific structures within the novelty, and contamination in the known classes could completely blur the actual separation between manifest and new groups. Motivated by these problems, we propose a two-stage Bayesian semiparametric novelty detector, building upon prior information robustly extracted from a set of complete learning units. We devise a general-purpose multivariate methodology that we also extend to handle functional data objects. We provide insights on the model behavior by investigating the theoretical properties of the associated semiparametric prior. From the computational point of view we, propose, a suitable $$\varvec{\xi }$$ ξ : $$\varvec{\xi }$$ ξ -sequence to construct an independent slice-efficient sampler that takes into account the difference between manifest and novelty components. We showcase our model performance through an extensive simulation study and applications on both multivariate and functional datasets, in which diverse and distinctive unknown patterns are discovered.

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Section: Stage Ii: Bnp Novelty Detection In Test Datamentioning

confidence: 99%

A two-stage Bayesian semiparametric model for novelty detection with robust prior information

2021

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“…Theorem 2.2, explains how to compute these expectations when the length variables are driven by a species sampling process. Hence, the following result is a straight-forward consequence of the aforementioned Theorem and equation (7).…”

Section: Exchangeable Length Variables Driven By Species Sampling Pro...mentioning

confidence: 76%

“…. ., as in (7). It is clear that this probabilities can be written in terms of the expectation of power products of the length variables.…”

Section: Exchangeable Length Variables Driven By Species Sampling Pro...mentioning

confidence: 99%

“…Searching for competitive alternatives to the canonical model, different constructions of random probability measures have been developed. Some of the most notable are through the normalization of homogeneous completely random measures [22,29,19,17], through the prediction rule of exchangeable partitions [5,28], by means of the stick-breaking decomposition a sequence of weights [30,18,10], and most recently by virtue of latent random subsets of the natural numbers [31,12,7]. All of these, as well as other popular models, fall into the class of species sampling processes [28,20,4], which are random probability measures whose atomic decomposition specialize to the form,…”

Section: Introductionmentioning

confidence: 99%

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Stick-breaking processes with exchangeable length variables

Gil–Leyva¹,

Mena²

2020

Preprint

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We investigate the general class of stick-breaking processes with exchangeable length variables. These generalize well-known Bayesian non-parametric priors in an unexplored direction. We give conditions to assure the respective species sampling process is discrete almost surely and the corresponding prior has full support. For a rich sub-class we find the probability that the stick-breaking weights are decreasingly ordered. A general formulae for the distribution of the latent allocation variables is derived and an MCMC algorithm is proposed for density estimation purposes.

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“…It is well known that, under the DP specification, the number of clusters induced in the novelty term grows as γ log M . We choose the DP mostly for computational convenience: if more flexibility is required BRAND can easily be adapted to accomodate different nonparametric priors, such as the Pitman-Yor process (Pitman, 1995;Pitman and Yor, 1997) or the geometric process and its extensions (De Blasi et al, 2020). To facilitate posterior inference given the specification in (4), we consider the following complete likelihood:…”

Section: Stage Ii: Bnp Novelty Detection In Test Datamentioning

confidence: 99%

A Two-Stage Bayesian Semiparametric Model for Novelty Detection with Robust Prior Information

Denti,

Cappozzo,

Greselin

2020

Preprint

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Standard novelty detection methods aim at bi-partitioning the test units into already observed and previously unseen patterns. However, two significant issues arise: there may be considerable interest in identifying specific structures within the latter subset, and contamination in the known classes could completely blur the actual separation between manifest and new groups. Motivated by these problems, we propose a two-stage Bayesian nonparametric novelty detector, building upon prior information robustly extracted from a set of complete learning units. A general-purpose multivariate methodology, as well as an extension suitable for functional data objects, are devised. Some theoretical properties of the associated semi-parametric prior are investigated. Moreover, we propose a suitable ξ-sequence to construct an independent slice-efficient sampler that takes into account the difference between manifest and novelty components. We showcase our model performance through an extensive simulation study and applications on both multivariate and functional datasets, in which diverse and distinctive unknown patterns are discovered.

show abstract

On the inferential implications of decreasing weight structures in mixture models

Cited by 11 publications

References 34 publications

A two-stage Bayesian semiparametric model for novelty detection with robust prior information

A two-stage Bayesian semiparametric model for novelty detection with robust prior information

Stick-breaking processes with exchangeable length variables

A Two-Stage Bayesian Semiparametric Model for Novelty Detection with Robust Prior Information

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