Related papers: Covariance-Informed Subspace: an Adaptive Gradient…

Dimension reduction (DR) aims to learn low-dimensional representations of high-dimensional data with the preservation of essential information. In the context of manifold learning, we define that the representation after…

Variational inference, such as the mean-field (MF) approximation, requires certain conjugacy structures for efficient computation. These can impose unnecessary restrictions on the viable prior distribution family and further constraints on…

In the application of Bayesian methods to metrology, pre-data probabilities play a critical role in the estimation of the model uncertainty. Following the observation that distributions form Riemann's manifolds, methods of differential…

While Bayesian neural networks (BNNs) hold the promise of being flexible, well-calibrated statistical models, inference often requires approximations whose consequences are poorly understood. We study the quality of common variational…

Bayesian inversion generates a posterior distribution of model parameters from an observation equation and prior information both weighted by hyperparameters. The prior is also introduced for the hyperparameters in fully Bayesian inversions…

Variational inference is a technique that approximates a target distribution by optimizing within the parameter space of variational families. On the other hand, Wasserstein gradient flows describe optimization within the space of…

This paper focuses on the contextual optimization problem where a decision is subject to some uncertain parameters and covariates that have some predictive power on those parameters are available before the decision is made. More…

Uncertainty quantification of groundwater (GW) aquifer parameters is critical for efficient management and sustainable extraction of GW resources. These uncertainties are introduced by the data, model, and prior information on the…

Gaussian covariance graph model is a popular model in revealing underlying dependency structures among random variables. A Bayesian approach to the estimation of covariance structures uses priors that force zeros on some off-diagonal…

Covariate-dependent graph learning has gained increasing interest in the graphical modeling literature for the analysis of heterogeneous data. This task, however, poses challenges to modeling, computational efficiency, and interpretability.…

It is now practically the norm for data to be very high dimensional in areas such as genetics, machine vision, image analysis and many others. When analyzing such data, parametric models are often too inflexible while nonparametric…

Dimension reduction techniques, such as Sufficient Dimension Reduction (SDR), are indispensable for analyzing high-dimensional datasets. This paper introduces a novel SDR method named Principal Square Response Forward Regression (PSRFR) for…

We propose a likelihood ratio based inferential framework for high dimensional semiparametric generalized linear models. This framework addresses a variety of challenging problems in high dimensional data analysis, including incomplete…

Although deep learning (DL) methods are powerful for solving inverse problems, their reliance on high-quality training data is a major hurdle. This is significant in high-dimensional (dynamic/volumetric) magnetic resonance imaging (MRI),…

We perform scalable approximate inference in continuous-depth Bayesian neural networks. In this model class, uncertainty about separate weights in each layer gives hidden units that follow a stochastic differential equation. We demonstrate…

Three different inferential problems related to a two dimensional categorical data from a Bayesian perspective have been discussed in this article. Conjugate prior distribution with symmetric and asymmetric hyper parameters are considered.…

As its name suggests, sufficient dimension reduction (SDR) targets to estimate a subspace from data that contains all information sufficient to explain a dependent variable. Ample approaches exist to SDR, some of the most recent of which…

Accurate simulation of complex physical systems enables the development, testing, and certification of control strategies before they are deployed into the real systems. As simulators become more advanced, the analytical tractability of the…

Gradient-based solvers risk convergence to local optima, leading to incorrect researcher inference. Heuristic-based algorithms are able to ``break free" of these local optima to eventually converge to the true global optimum. However, given…

Uncertainty quantification is essential when dealing with ill-conditioned inverse problems due to the inherent nonuniqueness of the solution. Bayesian approaches allow us to determine how likely an estimation of the unknown parameters is…