Related papers: Bayesian Inversion, Uncertainty Analysis and Inter…
We study data-driven decision-making problems in the Bayesian framework, where the expectation in the Bayes risk is replaced by a risk-sensitive entropic risk measure. We focus on problems where calculating the posterior distribution is…
A common task in experimental sciences is to fit mathematical models to real-world measurements to improve understanding of natural phenomenon (reverse-engineering or inverse modeling). When complex dynamical systems are considered, such as…
In statistical applications, it is common to encounter parameters supported on a varying or unknown dimensional space. Examples include the fused lasso regression, the matrix recovery under an unknown low rank, etc. Despite the ease of…
Variational Bayes (VB) is rapidly becoming a popular tool for Bayesian inference in statistical modeling. However, the existing VB algorithms are restricted to cases where the likelihood is tractable, which precludes the use of VB in many…
For predictive modeling relying on Bayesian inversion, fully independent, or ``mean-field'', Gaussian distributions are often used as approximate probability density functions in variational inference since the number of variational…
Due to their uncertainty quantification, Bayesian solutions to inverse problems are the framework of choice in applications that are risk averse. These benefits come at the cost of computations that are in general, intractable. New advances…
Stability selection is a versatile framework for structure estimation and variable selection in high-dimensional setting, primarily grounded in frequentist principles. In this paper, we propose an enhanced methodology that integrates…
In variational inference (VI), the practitioner approximates a high-dimensional distribution $\pi$ with a simple surrogate one, often a (product) Gaussian distribution. However, in many cases of practical interest, Gaussian distributions…
Covariance estimation and selection for multivariate datasets in a high-dimensional regime is a fundamental problem in modern statistics. Gaussian graphical models are a popular class of models used for this purpose. Current Bayesian…
In order to predict future performance of subsurface fluid reservoirs under possible operating scenarios, a dynamic, porous-medium flow simulation model must be tuned to include representative properties of the reservoir. Estimating…
Bayesian imaging inverse problems in astrophysics and cosmology remain challenging, particularly in low-data regimes, due to complex forward operators and the frequent lack of well-motivated priors for non-Gaussian signals. In this paper,…
Variational inference is computationally challenging in models that contain both conjugate and non-conjugate terms. Methods specifically designed for conjugate models, even though computationally efficient, find it difficult to deal with…
Future wireless networks are envisioned to provide ubiquitous sensing services, which also gives rise to a substantial demand for high-dimensional non-convex parameter estimation, i.e., the associated likelihood function is non-convex and…
In many practices, scientists are particularly interested in detecting which of the predictors are truly associated with a multivariate response. It is more accurate to model multiple responses as one vector rather than separating each…
We formulate, and present a numerical method for solving, an inverse problem for inferring parameters of a deterministic model from stochastic observational data (quantities of interest). The solution, given as a probability measure, is…
The tilted-wave interferometer is a promising technique for the development of a reference measurement system for the highly accurate form measurement of aspheres and freeform surfaces. The technique combines interferometric measurements,…
Bayesian inference is used extensively to quantify the uncertainty in an inferred field given the measurement of a related field when the two are linked by a mathematical model. Despite its many applications, Bayesian inference faces…
The choice of approximate posterior distribution is one of the core problems in variational inference. Most applications of variational inference employ simple families of posterior approximations in order to allow for efficient inference,…
While Bayesian inference provides a principled framework for reasoning under uncertainty, its widespread adoption is limited by the intractability of exact posterior computation, necessitating the use of approximate inference. However,…
Gaussian mixture models are a popular tool for model-based clustering, and mixtures of factor analyzers are Gaussian mixture models having parsimonious factor covariance structure for mixture components. There are several recent extensions…