Related papers: Optimal projection of observations in a Bayesian s…

We consider the problem of estimating the parameters of a Gaussian or binary distribution in such a way that the resulting undirected graphical model is sparse. Our approach is to solve a maximum likelihood problem with an added l_1-norm…

In statistical inference, a discrepancy between the parameter-to-observable map that generates the data and the parameter-to-observable map that is used for inference can lead to misspecified likelihoods and thus to incorrect estimates. In…

Bayesian methods feature useful properties for solving inverse problems, such as tomographic reconstruction. The prior distribution introduces regularization, which helps solving the ill-posed problem and reduces overfitting. In practice,…

Bayesian inference typically relies on specifying a parametric model that approximates the data-generating process. However, misspecified models can yield poor convergence rates and unreliable posterior calibration. Bayesian empirical…

Statistical inference on the mean of a Poisson distribution is a fundamentally important problem with modern applications in, e.g., particle physics. The discreteness of the Poisson distribution makes this problem surprisingly challenging,…

We develop a Bayesian approach called Bayesian projected calibration to address the problem of calibrating an imperfect computer model using observational data from a complex physical system. The calibration parameter and the physical…

We address the problem of fitting parametric curves on the Grassmann manifold for the purpose of intrinsic parametric regression. As customary in the literature, we start from the energy minimization formulation of linear least-squares in…

This paper addresses the problem of summarizing the posterior distributions that typically arise, in a Bayesian framework, when dealing with signal decomposition problems with unknown number of components. Such posterior distributions are…

The Busemann function has recently found much interest in a variety of geometric machine learning problems, as it naturally defines projections onto geodesic rays of Riemannian manifolds and generalizes the notion of hyperplanes. As several…

We consider optimal design of infinite-dimensional Bayesian linear inverse problems governed by partial differential equations that contain secondary reducible model uncertainties, in addition to the uncertainty in the inversion parameters.…

Spatial regression of random fields based on potentially biased sensing information is proposed in this paper. One major concern in such applications is that since it is not known a-priori what the accuracy of the collected data from each…

Big data is ubiquitous in practices, and it has also led to heavy computation burden. To reduce the calculation cost and ensure the effectiveness of parameter estimators, an optimal subset sampling method is proposed to estimate the…

In many statistical settings, two types of data are available: coupled data, which preserve the joint structure among variables but are limited in size due to cost or privacy constraints, and marginal data, which are available at larger…

The intrinsic dimensionality of an inverse problem is affected by prior information, the accuracy and number of observations, and the smoothing properties of the forward operator. From a Bayesian perspective, changes from the prior to the…

In data assimilation, the model may be subject to uncertainties and errors. The weak-constraint data assimilation framework enables incorporating model uncertainty in the dynamics of the governing equations. We propose a new framework for…

This PhD thesis presents a distributional view of optimization in place of a worst-case perspective. We motivate this view with an investigation of the failure point of classical optimization. Subsequently we consider the optimization of a…

The key distinguishing property of a Bayesian approach is marginalization, rather than using a single setting of weights. Bayesian marginalization can particularly improve the accuracy and calibration of modern deep neural networks, which…

In this paper, we investigate the problem of learning disentangled representations. Given a pair of images sharing some attributes, we aim to create a low-dimensional representation which is split into two parts: a shared representation…

Bayesian Neural Networks (BNNs) are trained to optimize an entire distribution over their weights instead of a single set, having significant advantages in terms of, e.g., interpretability, multi-task learning, and calibration. Because of…

Sparse stealth attack constructions that minimize the mutual information between the state variables and the observations are proposed. The attack construction is formulated as the design of a multivariate Gaussian distribution that aims to…