相关论文: Scalable Bayes via Barycenter in Wasserstein Space

Divide-and-conquer Bayesian methods consist of three steps: dividing the data into smaller computationally manageable subsets, running a sampling algorithm in parallel on all the subsets, and combining parameter draws from all the subsets.…

Bayesian computational algorithms tend to scale poorly as data size increases. This has motivated divide-and-conquer-based approaches for scalable inference. These divide the data into subsets, perform inference for each subset in parallel,…

Efficiently aggregating data from different sources is a challenging problem, particularly when samples from each source are distributed differently. These differences can be inherent to the inference task or present for other reasons:…

We propose a three-step divide-and-conquer strategy within the Bayesian paradigm that delivers massive scalability for any spatial process model. We partition the data into a large number of subsets, apply a readily available Bayesian…

The United States Bureau of Labor Statistics collects data using survey instruments under informative sampling designs that assign probabilities of inclusion to be correlated with the response. The bureau extensively uses Bayesian…

Wasserstein Barycenter is a principled approach to represent the weighted mean of a given set of probability distributions, utilizing the geometry induced by optimal transport. In this work, we present a novel scalable algorithm to…

Bayesian inference typically requires the computation of an approximation to the posterior distribution. An important requirement for an approximate Bayesian inference algorithm is to output high-accuracy posterior mean and uncertainty…

Approximate Bayesian Computation (ABC) is a popular method for approximate inference in generative models with intractable but easy-to-sample likelihood. It constructs an approximate posterior distribution by finding parameters for which…

Divide-and-conquer methods use large-sample approximations to provide frequentist guarantees when each block of data is both small enough to facilitate efficient computation and large enough to support approximately valid inferences. When…

Wasserstein barycenters provide a principled approach for aggregating probability measures, while preserving the geometry of their ambient space. Existing discrete methods are not scalable as they assume access to the complete set of…

We propose a novel approach to Bayesian analysis that is provably robust to outliers in the data and often has computational advantages over standard methods. Our technique is based on splitting the data into non-overlapping subgroups,…

We develop a general theory to address a consensus-based combination of estimations in a parallelized or distributed estimation setting. Taking into account the possibility of very discrepant estimations, instead of a full consensus we…

Two major bottlenecks to the solution of large-scale Bayesian inverse problems are the scaling of posterior sampling algorithms to high-dimensional parameter spaces and the computational cost of forward model evaluations. Yet incomplete or…

Divide-and-conquer strategies for Monte Carlo algorithms are an increasingly popular approach to making Bayesian inference scalable to large data sets. In its simplest form, the data are partitioned across multiple computing cores and a…

We introduce and study a novel model-selection strategy for Bayesian learning, based on optimal transport, along with its associated predictive posterior law: the Wasserstein population barycenter of the posterior law over models. We first…

Data sets for statistical analysis become extremely large even with some difficulty of being stored on one single machine. Even when the data can be stored in one machine, the computational cost would still be intimidating. We propose a…

This paper proposes Bayesian mosaic, a parallelizable composite posterior, for scalable Bayesian inference on a broad class of multivariate discrete data models. Sampling is embarrassingly parallel since Bayesian mosaic is a multiplication…

We propose a distributed computing framework, based on a divide and conquer strategy and hierarchical modeling, to accelerate posterior inference for high-dimensional Bayesian factor models. Our approach distributes the task of…

We develop Bayesian predictive stacking for geostatistical models, where the primary inferential objective is to provide inference on the latent spatial random field and conduct spatial predictions at arbitrary locations. We exploit…

The Wasserstein barycenter is a geometric construct which captures the notion of centrality among probability distributions, and which has found many applications in machine learning. However, most algorithms for finding even an approximate…