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Multivariate, heteroscedastic errors complicate statistical inference in many large-scale denoising problems. Empirical Bayes is attractive in such settings, but standard parametric approaches rest on assumptions about the form of the prior…
This work deals with a regularization method enforcing solution sparsity of linear ill-posed problems by appropriate discretization in the image space. Namely, we formulate the so called least error method in an $\ell^1$ setting and perform…
The available probes of the large scale structure in the Universe have distinct properties: galaxies are a high resolution but biased tracer of mass, while weak lensing avoids such biases but, due to low signal-to-noise ratio, has poor…
We have previously reported a Bayesian algorithm for determining the coordinates of points in three-dimensional space from uncertain constraints. This method is useful in the determination of biological molecular structure. It is limited,…
The completion of a Euclidean distance matrix (EDM) from sparse and noisy observations is a fundamental challenge in signal processing, with applications in sensor network localization, acoustic room reconstruction, molecular conformation,…
Given the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, the goal of this paper is to establish deterministic conditions under which exact recovery of the low-rank and sparse…
Many imaging science tasks can be modeled as a discrete linear inverse problem. Solving linear inverse problems is often challenging, with ill-conditioned operators and potentially non-unique solutions. Embedding prior knowledge, such as…
In the general signal+noise model we construct an empirical Bayes posterior which we then use for uncertainty quantification for the unknown, possibly sparse, signal. We introduce a novel excessive bias restriction (EBR) condition, which…
Equivariant models leverage prior knowledge on symmetries to improve predictive performance, but misspecified architectural constraints can harm it instead. While work has explored learning or relaxing constraints, selecting among…
A greedy algorithm called Bayesian multiple matching pursuit (BMMP) is proposed to estimate a sparse signal vector and its support given $m$ linear measurements. Unlike the maximum a posteriori (MAP) support detection, which was proposed by…
Undoing the image formation process and therefore decomposing appearance into its intrinsic properties is a challenging task due to the under-constraint nature of this inverse problem. While significant progress has been made on inferring…
Recently it has become popular to learn sparse Gaussian graphical models (GGMs) by imposing l1 or group l1,2 penalties on the elements of the precision matrix. Thispenalized likelihood approach results in a tractable convex optimization…
We present a general linear algorithm for measuring the surface mass density 1-\kappa from the observable reduced shear g=\gamma/(1-\kappa) in the strong lensing regime. We show that in general, the observed polarization field can be…
We consider the problem of upper bounding the expected log-likelihood sub-optimality of the maximum likelihood estimate (MLE), or a conjugate maximum a posteriori (MAP) for an exponential family, in a non-asymptotic way. Surprisingly, we…
Marginal MAP inference involves making MAP predictions in systems defined with latent variables or missing information. It is significantly more difficult than pure marginalization and MAP tasks, for which a large class of efficient and…
In the sparse normal means model, convergence of the Bayesian posterior distribution associated to spike and slab prior distributions is considered. The key sparsity hyperparameter is calibrated via marginal maximum likelihood empirical…
We present a parametric deterministic formulation of Bayesian inverse problems with input parameter from infinite dimensional, separable Banach spaces. In this formulation, the forward problems are parametric, deterministic elliptic partial…
The proliferation of automated inference algorithms in Bayesian statistics has provided practitioners newfound access to fast, reproducible data analysis and powerful statistical models. Designing automated methods that are also both…
The observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise…
Building on ideas from Castillo and Nickl [Ann. Statist. 41 (2013) 1999-2028], a method is provided to study nonparametric Bayesian posterior convergence rates when "strong" measures of distances, such as the sup-norm, are considered. In…