arXiv research

The study assesses sensitivity to prior choices in Bayesian nonparametric models.

Bayesian nonparametric models improve OOD detection, especially with complex covariance structures.

Bayesian neural networks with nonparametric noise models for system identification.

An implementation of a nonparametric Bayesian approach to solving binary classification problems on graphs is described. A hierarchical Bayesian approach with a randomly scaled Gaussian prior is considered. The prior uses the graph Laplacian to take into account the underlying geometry of the graph. A method based on a…

This article describes an implementation of a nonparametric Bayesian approach to solving binary classification problems on graphs. We consider a hierarchical Bayesian approach with a prior that is constructed by truncating a series expansion of the soft label function using the graph Laplacian eigenfunctions as basis f…

This paper introduces the Indian Chefs Process (ICP), a Bayesian nonparametric prior on the joint space of infinite directed acyclic graphs (DAGs) and orders that generalizes Indian Buffet Processes. As our construction shows, the proposed distribution relies on a latent Beta Process controlling both the orders and out…

Bayesian methods improve causal effect estimation, offering shrinkage and sensitivity analysis.

Enhances CMS with Bayesian nonparametrics for better low-frequency token estimation.

The recently developed variational autoencoders (VAEs) have proved to be an effective confluence of the rich representational power of neural networks with Bayesian methods. However, most work on VAEs use a rather simple prior over the latent variables such as standard normal distribution, thereby restricting its appli…

This article introduces a Bayesian nonparametric method for quantifying the relative evidence in a dataset in favour of the dependence or independence of two variables conditional on a third. The approach uses Polya tree priors on spaces of conditional probability densities, accounting for uncertainty in the form of th…

New method for density estimation without approximating posterior distributions.

Given discrete time observations over a fixed time interval, we study a nonparametric Bayesian approach to estimation of the volatility coefficient of a stochastic differential equation. We postulate a histogram-type prior on the volatility with piecewise constant realisations on bins forming a partition of the time in…

Bayesian methods improve tracking multiple objects through dynamic dependencies.

Bayesian nonparametric models improve tracking in cluttered environments.

Unsupervised image segmentation aims at clustering the set of pixels of an image into spatially homogeneous regions. We introduce here a class of Bayesian nonparametric models to address this problem. These models are based on a combination of a Potts-like spatial smoothness component and a prior on partitions which is…

Bayesian analysis shows unlabeled data improve graph-based semi-supervised learning.

Deep model learns complex latent codes without assuming factor structure.

We characterize conjugate nonparametric Bayesian models as projective limits of conjugate, finite-dimensional Bayesian models. In particular, we identify a large class of nonparametric models representable as infinite-dimensional analogues of exponential family distributions and their canonical conjugate priors. This c…

A Bayesian nonparametric approach for continual learning using neural networks.

Metalearned neural circuit performs inference over open classes.

Existing Bayesian models, especially nonparametric Bayesian methods, rely on specially conceived priors to incorporate domain knowledge for discovering improved latent representations. While priors can affect posterior distributions through Bayes' rule, imposing posterior regularization is arguably more direct and in s…

Statistical machine learning methods, especially nonparametric Bayesian methods, have become increasingly popular to infer clonal population structure of tumors. Here we describe the treeCRP, an extension of the Chinese restaurant process (CRP), a popular construction used in nonparametric mixture models, to infer the …

Dependent nonparametric processes extend distributions over measures, such as the Dirichlet process and the beta process, to give distributions over collections of measures, typically indexed by values in some covariate space. Such models are appropriate priors when exchangeability assumptions do not hold, and instead …

Deep-HGP uses Bayesian nonparametric approach for complex data regression.

Bayesian deep learning with heavy-tailed weights achieves near-optimal performance.

Detecting anomalies in multivariate functional data using Bayesian nonparametric methods.

We develop a Bayesian nonparametric extension of the popular Plackett-Luce choice model that can handle an infinite number of choice items. Our framework is based on the theory of random atomic measures, with the prior specified by a gamma process. We derive a posterior characterization and a simple and effective Gibbs…

Bayesian posterior contraction rates improve with decreasing tails

Bayesian methods estimate regression functions on submanifolds using graph Laplacian eigenbasis.

Bayesian approach learns nonparametric mixture components from heterogeneous data.

Bayesian method clusters time series with varying dynamics.

The paper introduces a method for learning nonparametric Volterra kernels using Gaussian processes.

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 right. Current inference schemes for models involving the gamma process are restricted to MCMC-based …

Beta process is the standard nonparametric Bayesian prior for latent factor model. In this paper, we derive a structured mean-field variational inference algorithm for a beta process non-negative matrix factorization (NMF) model with Poisson likelihood. Unlike the linear Gaussian model, which is well-studied in the non…

In this paper, we introduce a method for segmenting time series data using tools from Bayesian nonparametrics. We consider the task of temporal segmentation of a set of time series data into representative stationary segments. We use Gaussian process (GP) priors to impose our knowledge about the characteristics of the …

In this work, we study the problem of learning the volatility under market microstructure noise. Specifically, we consider noisy discrete time observations from a stochastic differential equation and develop a novel computational method to learn the diffusion coefficient of the equation. We take a nonparametric Bayesia…

Bayesian model improves classification performance with flexible uncertainty modeling.

Bayesian method estimates coverage from sketching imperfect data.

Increasingly complex datasets pose a number of challenges for Bayesian inference. Conventional posterior sampling based on Markov chain Monte Carlo can be too computationally intensive, is serial in nature and mixes poorly between posterior modes. Further, all models are misspecified, which brings into question the val…

Bayesian nonparametrics enables dynamic skill discovery from expert data.

Bayesian Additive Distribution Regression (DistBART) predicts distributions from grouped data.

We develop a scoring and classification procedure based on the PAC-Bayesian approach and the AUC (Area Under Curve) criterion. We focus initially on the class of linear score functions. We derive PAC-Bayesian non-asymptotic bounds for two types of prior for the score parameters: a Gaussian prior, and a spike-and-slab p…

Nonparametric extension of tensor regression is proposed. Nonlinearity in a high-dimensional tensor space is broken into simple local functions by incorporating low-rank tensor decomposition. Compared to naive nonparametric approaches, our formulation considerably improves the convergence rate of estimation while maint…

Bayesian framework for sphere regression using Gaussian fields.

Bayesian method improves estimation of unseen species.

In this paper we propose a Bayesian nonparametric model for clustering partial ranking data. We start by developing a Bayesian nonparametric extension of the popular Plackett-Luce choice model that can handle an infinite number of choice items. Our framework is based on the theory of random atomic measures, with the pr…

Nonparametric Bayesian models are often based on the assumption that the objects being modeled are exchangeable. While appropriate in some applications (e.g., bag-of-words models for documents), exchangeability is sometimes assumed simply for computational reasons; non-exchangeable models might be a better choice for a…

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 Process (IBP) is used as a prior on $\mathbf{G}$ to incorporate sparsity and to …