Generalized Species Sampling Priors with Latent Beta reinforcements
Many popular Bayesian nonparametric priors can be characterized in terms of exchangeable species sampling sequences. However, in some applications, exchangeability may not be appropriate. We introduce a {novel and probabilistically coherent family of non-exchangeable species sampling sequences characterized by a tractable predictive probability function with weights driven by a sequence of independent Beta random variables. We compare their theoretical clustering properties with those of the Dirichlet Process and the two parameters Poisson-Dirichlet process. The proposed construction provides a complete characterization of the joint process, differently from existing work. We then propose the use of such process as prior distribution in a hierarchical Bayes modeling framework, and we describe a Markov Chain Monte Carlo sampler for posterior inference. We evaluate the performance of the prior and the robustness of the resulting inference in a simulation study, providing a comparison with popular Dirichlet Processes mixtures and Hidden Markov Models. Finally, we develop an application to the detection of chromosomal aberrations in breast cancer by leveraging array CGH data.
Code (0)
등록된 구현이 없습니다.
Tasks
ClusteringSimilar Papers 제목 키워드 기반
Generalized Beta Mixtures of Gaussians
In recent years, a rich variety of shrinkage priors have been proposed that have great promise in addressing massive regression problems. In general, these new priors can be expressed as scale mixtures of normals, but h…
regressionDynamic $β$-VAEs for quantifying biodiversity by clustering optically recorded insect signals
While insects are the largest and most diverse group of terrestrial animals, constituting ca. 80% of all known species, they are difficult to study due to their small size and similarity between species. Conventional mon…
ClusteringGamma Processes, Stick-Breaking, and Variational Inference
While most Bayesian nonparametric models in machine learning have focused on the Dirichlet process, the beta process, or their variants, the gamma process has recently emerged as a useful nonparametric prior in its own r…
Variational InferenceGeneralized Gaussian Model for Learned Image Compression
In learned image compression, probabilistic models play an essential role in characterizing the distribution of latent variables. The Gaussian model with mean and scale parameters has been widely used for its simplicity …
Image CompressionmodelSparse Estimation with Generalized Beta Mixture and the Horseshoe Prior
In this paper, the use of the Generalized Beta Mixture (GBM) and Horseshoe distributions as priors in the Bayesian Compressive Sensing framework is proposed. The distributions are considered in a two-layer hierarchical m…
Compressive Sensing