Related papers: Spatially-dependent Indian Buffet Processes
Analyzing multivariate time series data is important to predict future events and changes of complex systems in finance, manufacturing, and administrative decisions. The expressiveness power of Gaussian Process (GP) regression methods has…
We introduce a Bayesian non-parametric spatial factor analysis model with spatial dependency induced through a prior on factor loadings. For each column of the loadings matrix, spatial dependency is encoded using a probit stick-breaking…
We characterize the combinatorial structure of conditionally-i.i.d. sequences of negative binomial processes with a common beta process base measure. In Bayesian nonparametric applications, such processes have served as models for latent…
Latent feature models are a powerful tool for modeling data with globally-shared features. Nonparametric exchangeable models such as the Indian Buffet Process offer modeling flexibility by letting the number of latent features be unbounded.…
Modeling sparse count data, which arise across numerous scientific fields, presents significant statistical challenges. This chapter addresses these challenges in the context of infectious disease prediction, with a focus on predicting…
This paper presents a Bayesian nonparametric latent feature model specially suitable for exploratory analysis of high-dimensional count data. We perform a non-negative doubly sparse matrix factorization that has two main advantages: not…
We study random families of subsets of $\mathbb{N}$ that are similar to exchangeable random partitions, but do not require constituent sets to be disjoint: Each element of ${\mathbb{N}}$ may be contained in multiple subsets. One class of…
Indian Buffet Process based models are an elegant way for discovering underlying features within a data set, but inference in such models can be slow. Inferring underlying features using Markov chain Monte Carlo either relies on an…
We investigate a class of feature allocation models that generalize the Indian buffet process and are parameterized by Gibbs-type random measures. Two existing classes are contained as special cases: the original two-parameter Indian buffet…
Quantifying spatial and/or temporal associations in multivariate geolocated data of different types is achievable via spatial random effects in a Bayesian hierarchical model, but severe computational bottlenecks arise when spatial…
We introduce a flexible and scalable class of Bayesian geostatistical models for discrete data, based on the class of nearest neighbor mixture transition distribution processes (NNMP), referred to as discrete NNMP. The proposed class…
Prediction is a classic challenge in spatial statistics and the inclusion of spatial covariates can greatly improve predictive performance when incorporated into a model with latent spatial effects. It is desirable to develop flexible…
A nonparametric Bayesian extension of Factor Analysis (FA) is proposed where observed data $\mathbf{Y}$ is modeled as a linear superposition, $\mathbf{G}$, of a potentially infinite number of hidden factors, $\mathbf{X}$. The Indian Buffet…
In this paper, we establish a high-dimensional CLT for the sample mean of $p$-dimensional spatial data observed over irregularly spaced sampling sites in $\mathbb{R}^d$, allowing the dimension $p$ to be much larger than the sample size $n$.…
In this paper we concentrate on an alternative modeling strategy for positive data that exhibit spatial or spatio-temporal dependence. Specifically we propose to consider stochastic processes obtained trough a monotone transformation of…
Feature allocation models are an extension of Bayesian nonparametric clustering models, where individuals can share multiple features. We study a broad class of models whose probability distribution has a product form, which includes the…
Spatial statistics often rely on Gaussian processes (GPs) to capture dependencies across locations. However, their computational cost increases rapidly with the number of locations, potentially needing multiple hours even for moderate…
We develop the distance dependent Chinese restaurant process (CRP), a flexible class of distributions over partitions that allows for non-exchangeability. This class can be used to model many kinds of dependencies between data in infinite…
This article introduces novel and practicable Bayesian factor analysis frameworks that are computationally feasible for moderate to large spatiotemporal data. Previous Bayesian analysis of spatiotemporal data has utilized a Bayesian factor…
Bayesian spatial modeling provides a flexible framework for whole-brain fMRI analysis by explicitly incorporating spatial dependencies, overcoming the limitations of traditional massive univariate approaches that lead to information waste.…