Related papers: Bayesian orthogonal component analysis for sparse …
A nonparanormal graphical model is a semiparametric generalization of a Gaussian graphical model for continuous variables in which it is assumed that the variables follow a Gaussian graphical model only after some unknown smooth monotone…
Statistical tasks such as density estimation and approximate Bayesian inference often involve densities with unknown normalising constants. Score-based methods, including score matching, are popular techniques as they are free of…
In dictionary learning, also known as sparse coding, the algorithm is given samples of the form $y = Ax$ where $x\in \mathbb{R}^m$ is an unknown random sparse vector and $A$ is an unknown dictionary matrix in $\mathbb{R}^{n\times m}$…
Bayesian learning in undirected graphical models|computing posterior distributions over parameters and predictive quantities is exceptionally difficult. We conjecture that for general undirected models, there are no tractable MCMC (Markov…
A Bayesian approach to the classification problem is proposed in which random partitions play a central role. It is argued that the partitioning approach has the capacity to take advantage of a variety of large-scale spatial structures, if…
Inverse problems involving partial differential equations (PDEs) are widely used in science and engineering. Although such problems are generally ill-posed, different regularisation approaches have been developed to ameliorate this problem.…
In compressive sensing, sparse signals are recovered from underdetermined noisy linear observations. One of the interesting problems which attracted a lot of attention in recent times is the support recovery or sparsity pattern recovery…
Motivated by distributed machine learning settings such as Federated Learning, we consider the problem of fitting a statistical model across a distributed collection of heterogeneous data sets whose similarity structure is encoded by a…
Statistical models for multivariate data often include a semi-orthogonal matrix parameter. In many applications, there is reason to expect that the semi-orthogonal matrix parameter satisfies a structural assumption such as sparsity or…
Variable selection techniques have become increasingly popular amongst statisticians due to an increased number of regression and classification applications involving high-dimensional data where we expect some predictors to be unimportant.…
This work studies the problem of simultaneously separating and reconstructing signals from compressively sensed linear mixtures. We assume that all source signals share a common sparse representation basis. The approach combines classical…
Undirected graphical models are applied in genomics, protein structure prediction, and neuroscience to identify sparse interactions that underlie discrete data. Although Bayesian methods for inference would be favorable in these contexts,…
Regularization is a common tool in variational inverse problems to impose assumptions on the parameters of the problem. One such assumption is sparsity, which is commonly promoted using lasso and total variation-like regularization.…
This paper presents an improved implicit sampling method for hierarchical Bayesian inverse problems. A widely used approach for sampling posterior distribution is based on Markov chain Monte Carlo (MCMC). However, the samples generated by…
Mixture models are widely used to fit complex and multimodal datasets. In this paper we study mixtures with high dimensional sparse latent parameter vectors and consider the problem of support recovery of those vectors. While parameter…
Matrix completion and robust principal component analysis have been widely used for the recovery of data suffering from missing entries or outliers. In many real-world applications however, the data is also time-varying, and the naive…
This paper presents Sparse Partitioning, a Bayesian method for identifying predictors that either individually or in combination with others affect a response variable. The method is designed for regression problems involving binary or…
In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is,…
Signal modeling lies at the core of numerous signal and image processing applications. A recent approach that has drawn considerable attention is sparse representation modeling, in which the signal is assumed to be generated as a…
Gaussian graphical models are widely used to infer dependence structures. Bayesian methods are appealing to quantify uncertainty associated with structural learning, i.e., the plausibility of conditional independence statements given the…