Related papers: Multiscale Shrinkage and L\'evy Processes

Compressive sensing is a technique to sample signals well below the Nyquist rate using linear measurement operators. In this paper we present an algorithm for signal reconstruction given such a set of measurements. This algorithm…

Existing techniques to reconstruct tree models of progression for accumulative processes, such as cancer, seek to estimate causation by combining correlation and a frequentist notion of temporal priority. In this paper, we define a novel…

Few Bayesian methods for analyzing high-dimensional sparse survival data provide scalable variable selection, effect estimation and uncertainty quantification. Such methods often either sacrifice uncertainty quantification by computing…

We introduce a new shrinkage variable selection operator for linear models which we term the \emph{adaptive ridge selector} (ARiS). This approach is inspired by the \emph{relevance vector machine} (RVM), which uses a Bayesian hierarchical…

Learning latent representations that are simultaneously expressive, geometrically well-structured, and reliably calibrated remains a central challenge for Variational Autoencoders (VAEs). Standard VAEs typically assume a diagonal Gaussian…

The multiple measurement vector (MMV) problem addresses the identification of unknown input vectors that share common sparse support. Even though MMV problems had been traditionally addressed within the context of sensor array signal…

Despite recent advances, sampling-based inference for Bayesian Neural Networks (BNNs) remains a significant challenge in probabilistic deep learning. While sampling-based approaches do not require a variational distribution assumption,…

We study the rate of Bayesian consistency for hierarchical priors consisting of prior weights on a model index set and a prior on a density model for each choice of model index. Ghosal, Lember and Van der Vaart [2] have obtained general…

Macroeconomists using large datasets often face the choice of working with either a large Vector Autoregression (VAR) or a factor model. In this paper, we develop methods for combining the two using a subspace shrinkage prior. Subspace…

We survey a new paradigm in signal processing known as "compressive sensing". Contrary to old practices of data acquisition and reconstruction based on the Shannon-Nyquist sampling principle, the new theory shows that it is possible to…

We introduce a general algorithm for the computation of the scale functions of a spectrally negative L\'evy process $X$, based on a natural weak approximation of $X$ via upwards skip-free continuous-time Markov chains with stationary…

Approximate Bayesian inference for models with computationally expensive, black-box likelihoods poses a significant challenge, especially when the posterior distribution is complex. Many inference methods struggle to explore the parameter…

Hidden Markov models provide a natural statistical framework for the detection of the copy number variations (CNV) in genomics. In this paper, we consider a Hidden Markov Model involving several correlated hidden processes at the same time.…

We propose a scalable inference algorithm for Bayes posteriors defined on a reproducing kernel Hilbert space (RKHS). Given a likelihood function and a Gaussian random element representing the prior, the corresponding Bayes posterior measure…

This article describes a full Bayesian treatment for simultaneous fixed-effect selection and parameter estimation in high-dimensional generalized linear mixed models. The approach consists of using a Bayesian adaptive Lasso penalty for…

We propose a novel algorithm for compressive imaging that exploits both the sparsity and persistence across scales found in the 2D wavelet transform coefficients of natural images. Like other recent works, we model wavelet structure using a…

Many problems of low-level computer vision and image processing, such as denoising, deconvolution, tomographic reconstruction or super-resolution, can be addressed by maximizing the posterior distribution of a sparse linear model (SLM). We…

Modeled along the truncated approach in Panigrahi (2016), selection-adjusted inference in a Bayesian regime is based on a selective posterior. Such a posterior is determined together by a generative model imposed on data and the selection…

Portfolio balancing requires estimates of covariance between asset returns. Returns data have histories which greatly vary in length, since assets begin public trading at different times. This can lead to a huge amount of missing data--too…

This paper develops a spatially resolved perturbation theory for singular vectors under high-dimensional separable noise and applies it to data-driven matrix recovery. In the asymptotic regime where the matrix dimensions are proportional…