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In Part I (arXiv:1911.00619) of this article, we proposed an importance sampling algorithm to compute rare-event probabilities in forward uncertainty quantification problems. The algorithm, which we termed the "Bayesian Inverse Monte Carlo…

Reliability updating refers to a problem that integrates Bayesian updating technique with structural reliability analysis and cannot be directly solved by structural reliability methods (SRMs) when it involves equality information. The…

We consider an active learning setting where the algorithm has access to a large pool of unlabeled data and a small pool of labeled data. In each iteration, the algorithm chooses few unlabeled data points and obtains their labels from an…

Early in an infectious disease outbreak, timely and accurate estimation of the basic reproduction number ($R_0$) and the serial interval (SI) is critical for understanding transmission dynamics and informing public health responses. While…

Random sampling has become a critical tool in solving massive matrix problems. For linear regression, a small, manageable set of data rows can be randomly selected to approximate a tall, skinny data matrix, improving processing time…

Biclustering is an unsupervised machine-learning approach aiming to cluster rows and columns simultaneously in a data matrix. Several biclustering algorithms have been proposed for handling numeric datasets. However, real-world data mining…

In this article, we construct a numerical method for a stochastic version of the Susceptible Infected Susceptible (SIS) epidemic model, expressed by a suitable stochastic differential equation (SDE), by using the semi-discrete method to a…

Importance sampling has been successfully used to accelerate stochastic optimization in many convex problems. However, the lack of an efficient way to calculate the importance still hinders its application to Deep Learning. In this paper,…

As a specific proportional hazard rates model, sequential order statistics can be used to describe the lifetimes of load-sharing systems. Inference for these systems needs to account for small sample sizes, which are prevalent in…

We consider the problem of estimating rare event probabilities, focusing on systems whose evolution is governed by differential equations with uncertain input parameters. If the system dynamics is expensive to compute, standard sampling…

Popular statistical software provides Bayesian information criterion (BIC) for multilevel models or linear mixed models. However, it has been observed that the combination of statistical literature and software documentation has led to…

Ordinal Regression (OR) aims to model the ordering information between different data categories, which is a crucial topic in multi-label learning. An important class of approaches to OR models the problem as a linear combination of basis…

For obtaining optimal first-order convergence guarantee for stochastic optimization, it is necessary to use a recurrent data sampling algorithm that samples every data point with sufficient frequency. Most commonly used data sampling…

This paper proposes a scalable binary CUR low-rank approximation algorithm that leverages parallel selection of representative rows and columns within a deterministic framework. By employing a blockwise adaptive cross approximation…

There has been significant interest and progress recently in algorithms that solve regression problems involving tall and thin matrices in input sparsity time. These algorithms find shorter equivalent of a n*d matrix where n >> d, which…

We prove an asymptotic estimate for the number of mxn non-negative integer matrices (contingency tables) with prescribed row and column sums and, more generally, for the number of integer feasible flows in a network. Similarly, we estimate…

We propose bandit importance sampling (BIS), a powerful importance sampling framework tailored for settings in which evaluating the target density is computationally expensive. BIS facilitates accurate sampling while minimizing the required…

Analysis of high-dimensional data has led to increased interest in both single index models (SIMs) and the best-subset selection. SIMs provide an interpretable and flexible modeling framework for high-dimensional data, while the best-subset…

Bayesian methods have received increasing attention in medical research, where sensitivity analysis of prior distributions is essential. Such analyses typically require the evaluation of the posterior distribution of a parameter under…

We develop new tools in the theory of nonlinear random matrices and apply them to study the performance of the Sum of Squares (SoS) hierarchy on average-case problems. The SoS hierarchy is a powerful optimization technique that has achieved…