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Many real-world datasets contain missing entries and mixed data types including categorical and ordered (e.g. continuous and ordinal) variables. Imputing the missing entries is necessary, since many data analysis pipelines require complete…
Missing data theory deals with the statistical methods in the occurrence of missing data. Missing data occurs when some values are not stored or observed for variables of interest. However, most of the statistical theory assumes that data…
Gaussian graphical regression is a powerful means that regresses the precision matrix of a Gaussian graphical model on covariates, permitting the numbers of the response variables and covariates to far exceed the sample size. Model fitting…
Bayesian hierarchical Poisson models are an essential tool for analyzing count data. However, designing efficient algorithms to sample from the posterior distribution of the target parameters remains a challenging task for this class of…
The logistic and probit link functions are the most common choices for regression models with a binary response. However, these choices are not robust to the presence of outliers/unexpected observations. The robit link function, which is…
There is wide interest in studying how the distribution of a continuous response changes with a predictor. We are motivated by environmental applications in which the predictor is the dose of an exposure and the response is a health…
Underlying data structures, such as symmetries or invariances to transformations, are often exploited to improve the solution of learning tasks. However, embedding these properties in models or learning algorithms can be challenging and…
The Gaussian graphical model is a widely used tool for learning gene regulatory networks with high-dimensional gene expression data. Most existing methods for Gaussian graphical models assume that the data are homogeneous, i.e., all samples…
When statistical analyses consider multiple data sources, Markov melding provides a method for combining the source-specific Bayesian models. Markov melding joins together submodels that have a common quantity. One challenge is that the…
Imbalanced regression arises when the target distribution is skewed, causing models to focus on dense regions and struggle with underrepresented (minority) samples. Despite its relevance across many applications, few methods have been…
We present a data augmentation scheme to perform Markov chain Monte Carlo inference for models where data generation involves a rejection sampling algorithm. Our idea, which seems to be missing in the literature, is a simple scheme to…
Hierarchical parametric models consisting of observable and latent variables are widely used for unsupervised learning tasks. For example, a mixture model is a representative hierarchical model for clustering. From the statistical point of…
Gaussian graphical models with sparsity in the inverse covariance matrix are of significant interest in many modern applications. For the problem of recovering the graphical structure, information criteria provide useful optimization…
We study high-dimensional regression with missing entries in the covariates. A common strategy in practice is to \emph{impute} the missing entries with an appropriate substitute and then implement a standard statistical procedure acting as…
Deploying machine learning systems in the real world requires both high accuracy on clean data and robustness to naturally occurring corruptions. While architectural advances have led to improved accuracy, building robust models remains…
Heavy-tailed distributions are widely used in robust mixture modelling due to possessing thick tails. As a computationally tractable subclass of the stable distributions, sub-Gaussian $\alpha$-stable distribution received much interest in…
Bayesian regression remains a simple but effective tool based on Bayesian inference techniques. For large-scale applications, with complicated posterior distributions, Markov Chain Monte Carlo methods are applied. To improve the well-known…
Additive-interactive regression has recently been shown to offer attractive minimax error rates over traditional nonparametric multivariate regression in a wide variety of settings, including cases where the predictor count is much larger…
Finite element model updating is challenging because 1) the problem is oftentimes underdetermined while the measurements are limited and/or incomplete; 2) many combinations of parameters may yield responses that are similar with respect to…
This paper proposes a flexible Bayesian approach to multiple imputation using conditional Gaussian mixtures. We introduce novel shrinkage priors for covariate-dependent mixing proportions in the mixture models to automatically select the…