Related papers: Fast Mixing of Data Augmentation Algorithms: Bayes…
We study the convergence properties of a class of data augmentation algorithms targeting posterior distributions of Bayesian lasso models with log-concave likelihoods. Leveraging isoperimetric inequalities, we derive a generic convergence…
We investigate the convergence properties of popular data-augmentation samplers for Bayesian probit regression. Leveraging recent results on Gibbs samplers for log-concave targets, we provide simple and explicit non-asymptotic bounds on the…
In this article, we consider Markov chain Monte Carlo(MCMC) algorithms for exploring the intractable posterior density associated with Bayesian probit linear mixed models under improper priors on the regression coefficients and variance…
Data Augmentation (DA) has become an essential tool to improve robustness and generalization of modern machine learning. However, when deciding on DA strategies it is critical to choose parameters carefully, and this can be a daunting task…
The reversible Markov chains that drive the data augmentation (DA) and sandwich algorithms define self-adjoint operators whose spectra encode the convergence properties of the algorithms. When the target distribution has uncountable…
Deep Learning (DL) methods have emerged as one of the most powerful tools for functional approximation and prediction. While the representation properties of DL have been well studied, uncertainty quantification remains challenging and…
The logistic linear mixed model (LLMM) is one of the most widely used statistical models. Generally, Markov chain Monte Carlo algorithms are used to explore the posterior densities associated with the Bayesian LLMMs. Polson, Scott and…
The standard Gibbs sampler of Mixed Multinomial Logit (MMNL) models involves sampling from conditional densities of utility parameters using Metropolis-Hastings (MH) algorithm due to unavailability of conjugate prior for logit kernel. To…
The application of the lasso is espoused in high-dimensional settings where only a small number of the regression coefficients are believed to be nonzero. Moreover, statistical properties of high-dimensional lasso estimators are often…
The logistic regression model is the most popular model for analyzing binary data. In the absence of any prior information, an improper flat prior is often used for the regression coefficients in Bayesian logistic regression models. The…
Data augmentation (DA) is indispensable in modern machine learning and deep neural networks. The basic idea of DA is to construct new training data to improve the model's generalization by adding slightly disturbed versions of existing data…
Let $\pi$ denote the intractable posterior density that results when the likelihood from a multivariate linear regression model with errors from a scale mixture of normals is combined with the standard non-informative prior. There is a…
The use of MCMC algorithms in high dimensional Bayesian problems has become routine. This has spurred so-called convergence complexity analysis, the goal of which is to ascertain how the convergence rate of a Monte Carlo Markov chain scales…
Gaussian errors are sometimes inappropriate in a multivariate linear regression setting because, for example, the data contain outliers. In such situations, it is often assumed that the error density is a scale mixture of multivariate…
Data augmentation (DA) algorithms are widely used for Bayesian inference due to their simplicity. In massive data settings, however, DA algorithms are prohibitively slow because they pass through the full data in any iteration, imposing…
Deep Convolutional Neural Networks have made an incredible progress in many Computer Vision tasks. This progress, however, often relies on the availability of large amounts of the training data, required to prevent over-fitting, which in…
There has been considerable interest in making Bayesian inference more scalable. In big data settings, most literature focuses on reducing the computing time per iteration, with less focused on reducing the number of iterations needed in…
Data augmentation (DA) is a widely used technique for enhancing the training of deep neural networks. Recent DA techniques which achieve state-of-the-art performance always meet the need for diversity in augmented training samples. However,…
Data augmentation (DA) is commonly used during model training, as it significantly improves test error and model robustness. DA artificially expands the training set by applying random noise, rotations, crops, or even adversarial…
Data Augmentation (DA) is a technique to increase the quantity and diversity of the training data, and by that alleviate overfitting and improve generalisation. However, standard DA produces synthetic data for augmentation with limited…