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We study the convergence rates of empirical Bayes posterior distributions for nonparametric and high-dimensional inference. We show that as long as the hyperparameter set is discrete, the empirical Bayes posterior distribution induced by…

Minimum Bayes-risk (MBR) decoding has recently gained renewed attention in text generation. MBR decoding considers texts sampled from a model as pseudo-references and selects the text with the highest similarity to the others. Therefore,…

We propose a method for nonparametric density estimation that exhibits robustness to contamination of the training sample. This method achieves robustness by combining a traditional kernel density estimator (KDE) with ideas from classical…

The Mutual Information (MI) is an often used measure of dependency between two random variables utilized in information theory, statistics and machine learning. Recently several MI estimators have been proposed that can achieve parametric…

Statistical modeling of rainfall data is an active research area in agro-meteorology. The most common models fitted to such datasets are exponential, gamma, log-normal, and Weibull distributions. As an alternative to some of these models,…

In real life, we frequently come across data sets that involve some independent explanatory variable(s) generating a set of ordinal responses. These ordinal responses may correspond to an underlying continuous latent variable, which is…

We study empirical Bayes estimation in high-dimensional linear regression. To facilitate computationally efficient estimation of the underlying prior, we adopt a variational empirical Bayes approach, introduced originally in Carbonetto and…

This paper is devoted to the estimation of the common marginal density function of weakly dependent processes. The accuracy of estimation is measured using pointwise risks. We propose a datadriven procedure using kernel rules. The bandwidth…

We solve the problem of estimating the distribution of presumed i.i.d. observations for the total variation loss. Our approach is based on density models and is versatile enough to cope with many different ones, including some density…

Cosmological experiments often employ Bayesian workflows to derive constraints on cosmological and astrophysical parameters from their data. It has been shown that these constraints can be combined across different probes such as Planck and…

In Bayesian inference, we seek to compute information about random variables such as moments or quantiles on the basis of {available data} and prior information. When the distribution of random variables is {intractable}, Monte Carlo (MC)…

Variational inference has been widely used in machine learning literature to fit various Bayesian models. In network analysis, this method has been successfully applied to solve the community detection problems. Although these results are…

In applications of diffusion models, controllable generation is of practical significance, but is also challenging. Current methods for controllable generation primarily focus on modifying the score function of diffusion models, while Mean…

Mendelian randomization (MR) is an instrumental variable (IV) approach to infer causal relationships between exposures and outcomes with genome-wide association studies (GWAS) summary data. However, the multivariable inverse-variance…

We develop an adaptive monotone shrinkage estimator for regression models with the following characteristics: i) dense coefficients with small but important effects; ii) a priori ordering that indicates the probable predictive importance of…

Estimating mutual information between continuous random variables is often intractable and extremely challenging for high-dimensional data. Recent progress has leveraged neural networks to optimize variational lower bounds on mutual…

Estimating the marginal likelihoods is an essential feature of model selection in the Bayesian context. It is especially crucial to have good estimates when assessing the number of planets orbiting stars when the models explain the noisy…

Many unsupervised representation learning methods belong to the class of similarity learning models. While various modality-specific approaches exist for different types of data, a core property of many methods is that representations of…

We consider a non-parametric Bayesian model for conditional densities. The model is a finite mixture of normal distributions with covariate dependent multinomial logit mixing probabilities. A prior for the number of mixture components is…

The ordinary Bayes estimator based on the posterior density suffers from the potential problems of non-robustness under data contamination or outliers. In this paper, we consider the general set-up of independent but non-homogeneous (INH)…