Related papers: Convergence analysis of data augmentation algorith…

In this paper, we suggest using a skew Gaussian-log Gaussian model for the analysis of spatial censored data from a Bayesian point of view. This approach furnishes an extension of the skew log Gaussian model to accommodate to both skewness…

We consider three Bayesian penalized regression models and show that the respective deterministic scan Gibbs samplers are geometrically ergodic regardless of the dimension of the regression problem. We prove geometric ergodicity of the…

We develop a Bayesian framework for variable selection in linear regression with autocorrelated errors, accommodating lagged covariates and autoregressive structures. This setting occurs in time series applications where responses depend on…

Regression models for dichotomous data are ubiquitous in statistics. Besides being useful for inference on binary responses, these methods serve also as building blocks in more complex formulations, such as density regression, nonparametric…

Combining predictions from different models is a central problem in Bayesian inference and machine learning more broadly. Currently, these predictive distributions are almost exclusively combined using linear mixtures such as Bayesian model…

The LASSO is a recent technique for variable selection in the regression model \bean y & = & X\beta + z, \eean where $X\in \R^{n\times p}$ and $z$ is a centered gaussian i.i.d. noise vector $\mathcal N(0,\sigma^2I)$. The LASSO has been…

We study the mixing time of Metropolis-Adjusted Langevin algorithm (MALA) for sampling a target density on $\mathbb{R}^d$. We assume that the target density satisfies $\psi_\mu$-isoperimetry and that the operator norm and trace of its…

The Lasso is one of the most important approaches for parameter estimation and variable selection in high dimensional linear regression. At the heart of its success is the attractive rate of convergence result even when $p$, the dimension…

Though data augmentation has rapidly emerged as a key tool for optimization in modern machine learning, a clear picture of how augmentation schedules affect optimization and interact with optimization hyperparameters such as learning rate…

Finite mixture models have become a popular tool for clustering. Amongst other uses, they have been applied for clustering longitudinal data and clustering high-dimensional data. In the latter case, a latent Gaussian mixture model is…

Ordinal categorical data are routinely encountered in many practical applications. When the primary goal is to construct a regression model for ordinal outcomes, cumulative link models represent one of the most popular choices to link the…

This work presents a fast and scalable algorithm for incremental learning of Gaussian mixture models. By performing rank-one updates on its precision matrices and determinants, its asymptotic time complexity is of \BigO{NKD^2} for $N$ data…

We study the convergence behavior of the Expectation Maximization (EM) algorithm on Gaussian mixture models with an arbitrary number of mixture components and mixing weights. We show that as long as the means of the components are separated…

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…

The emergence of big data has led to a growing interest in so-called convergence complexity analysis, which is the study of how the convergence rate of a Monte Carlo Markov chain (for an intractable Bayesian posterior distribution) scales…

In this paper, we examine the computational complexity of sampling from a Bayesian posterior (or pseudo-posterior) using the Metropolis-adjusted Langevin algorithm (MALA). MALA first employs a discrete-time Langevin SDE to propose a new…

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…

A Bayesian filtering algorithm is developed for a class of state-space systems that can be modelled via Gaussian mixtures. In general, the exact solution to this filtering problem involves an exponential growth in the number of mixture…

Univariate and multivariate general linear regression models, subject to linear inequality constraints, arise in many scientific applications. The linear inequality restrictions on model parameters are often available from phenomenological…

We study the rate of convergence of posterior distributions in density estimation problems for log-densities in periodic Sobolev classes characterized by a smoothness parameter p. The posterior expected density provides a nonparametric…