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We consider the problems of hypothesis testing and model comparison under a flexible Bayesian linear regression model whose formulation is closely connected with the linear mixed effect model and the parametric models for SNP set analysis…

A central issue lying at the heart of online reinforcement learning (RL) is data efficiency. While a number of recent works achieved asymptotically minimal regret in online RL, the optimality of these results is only guaranteed in a…

In this paper, we propose an improved online confidence bound for multinomial logistic (MNL) models and apply this result to MNL bandits, achieving variance-dependent optimal regret. Recently, Lee & Oh (2024) established an online…

Markov Chain Monte Carlo (MCMC) algorithms do not scale well for large datasets leading to difficulties in Neural Network posterior sampling. In this paper, we propose Penalty Bayesian Neural Networks - PBNNs, as a new algorithm that allows…

Learning latent variable models with stochastic variational inference is challenging when the approximate posterior is far from the true posterior, due to high variance in the gradient estimates. We propose a novel rejection sampling step…

The study of network formation is pervasive in economics, sociology, and many other fields. In this paper, we model network formation as a `choice' that is made by nodes in a network to connect to other nodes. We study these `choices' using…

Marginalising out uncertain quantities within the internal representations or parameters of neural networks is of central importance for a wide range of learning techniques, such as empirical, variational or full Bayesian methods. We set…

Traditional LLM alignment methods are vulnerable to heterogeneity in human preferences. Fitting a na\"ive probabilistic model to pairwise comparison data (say over prompt-completion pairs) yields an inconsistent estimate of the…

We generalize the approach of Liu and Lawrence (1999) for multiple changepoint problems where the number of changepoints is unknown. The approach is based on dynamic programming recursion for efficient calculation of the marginal…

Importance sampling is a popular technique in Bayesian inference: by reweighting samples drawn from a proposal distribution we are able to obtain samples and moment estimates from a Bayesian posterior over latent variables. Recent work,…

Nonparametric two-sample tests such as the Maximum Mean Discrepancy (MMD) are often used to detect differences between two distributions in machine learning applications. However, the majority of existing literature assumes that error-free…

We consider a sequential subset selection problem under parameter uncertainty, where at each time step, the decision maker selects a subset of cardinality $K$ from $N$ possible items (arms), and observes a (bandit) feedback in the form of…

Existing multilevel quasi-Monte Carlo (MLQMC) methods often rely on multiple independent randomizations of a low-discrepancy (LD) sequence to estimate statistical errors on each level. While this approach is standard, it can be less…

Many Bayesian inference problems involve high dimensional models for which only a subset of the model variables are of actual interest. All other variables are just nuisance parameters that one would ideally like to integrate out…

Large-scale undirected weighted networks are usually found in big data-related research fields. It can naturally be quantified as a symmetric high-dimensional and incomplete (SHDI) matrix for implementing big data analysis tasks. A…

I define a natural measure of the complexity of a parametric distribution relative to a given true distribution called the {\it razor} of a model family. The Minimum Description Length principle (MDL) and Bayesian inference are shown to…

In contrastive self-supervised learning, positive samples are typically drawn from the same image but in different augmented views, resulting in a relatively limited source of positive samples. An effective way to alleviate this problem is…

We propose a novel Bayesian model selection technique on linear mixed-effects models to compare multiple treatments with a control. A fully Bayesian approach is implemented to estimate the marginal inclusion probabilities that provide a…

Missing values in covariates due to censoring by signal interference or lack of sensitivity in the measuring devices are common in industrial problems. We propose a full Bayesian solution to the prediction problem with an efficient Markov…

It is known that the Thresholded Lasso (TL), SCAD or MCP correct intrinsic estimation bias of the Lasso. In this paper we propose an alternative method of improving the Lasso for predictive models with general convex loss functions which…