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This article tackles the old problem of prediction via a nonparametric transformation model (NTM) in a new Bayesian way. Estimation of NTMs is known challenging due to model unidentifiability though appealing because of its robust…

In this paper, we study structured quasi-Newton methods for optimization problems with orthogonality constraints. Note that the Riemannian Hessian of the objective function requires both the Euclidean Hessian and the Euclidean gradient. In…

Bayesian method is capable of capturing real world uncertainties/incompleteness and properly addressing the over-fitting issue faced by deep neural networks. In recent years, Bayesian Neural Networks (BNNs) have drawn tremendous attentions…

A common problem in natural sciences is the comparison of competing models in the light of observed data. Bayesian model comparison provides a statistically sound framework for this comparison based on the evidence each model provides for…

Model-based sequential approaches to discrete "black-box" optimization, including Bayesian optimization techniques, often access the same points multiple times for a given objective function in interest, resulting in many steps to find the…

In recent years, neural networks have revolutionized various domains, yet challenges such as hyperparameter tuning and overfitting remain significant hurdles. Bayesian neural networks offer a framework to address these challenges by…

Approximate Bayesian Computation has been successfully used in population genetics to bypass the calculation of the likelihood. These methods provide accurate estimates of the posterior distribution by comparing the observed dataset to a…

In Bayesian nonparametric models, Gaussian processes provide a popular prior choice for regression function estimation. Existing literature on the theoretical investigation of the resulting posterior distribution almost exclusively assume a…

Many cosmological models have only a finite number of parameters of interest, but a very expensive data-generating process and an intractable likelihood function. We address the problem of performing likelihood-free Bayesian inference from…

Many statistical models can be simulated forwards but have intractable likelihoods. Approximate Bayesian Computation (ABC) methods are used to infer properties of these models from data. Traditionally these methods approximate the posterior…

Quasi-Bayesian theory uses convex sets of probability distributions and expected loss to represent preferences about plans. The theory focuses on decision robustness, i.e., the extent to which plans are affected by deviations in subjective…

We formulate in this paper the mini-bucket algorithm for approximate inference in terms of exact inference on an approximate model produced by splitting nodes in a Bayesian network. The new formulation leads to a number of theoretical and…

In this paper, we present a novel approach to accelerate the Bayesian inference process, focusing specifically on the nested sampling algorithms. Bayesian inference plays a crucial role in cosmological parameter estimation, providing a…

We introduce a Fourier-based fast algorithm for Gaussian process regression in low dimensions. It approximates a translationally-invariant covariance kernel by complex exponentials on an equispaced Cartesian frequency grid of $M$ nodes.…

Divide-and-conquer based methods for Bayesian inference provide a general approach for tractable posterior inference when the sample size is large. These methods divide the data into smaller subsets, sample from the posterior distribution…

As machine learning tasks continue to evolve, the trend has been to gather larger datasets and train increasingly larger models. While this has led to advancements in accuracy, it has also escalated computational costs to unsustainable…

Recursive Bayesian inference, in which posterior beliefs are updated in light of accumulating data, is a tool for implementing Bayesian models in applications with streaming and/or very large data sets. As the posterior of one iteration…

We consider a novel Bayesian approach to estimation, uncertainty quantification, and variable selection for a high-dimensional linear regression model under sparsity. The number of predictors can be nearly exponentially large relative to…

Due to the growing adoption of deep neural networks in many fields of science and engineering, modeling and estimating their uncertainties has become of primary importance. Despite the growing literature about uncertainty quantification in…

In this paper, we consider stochastic second-order methods for minimizing a finite summation of nonconvex functions. One important key is to find an ingenious but cheap scheme to incorporate local curvature information. Since the true…