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This paper investigates two prominent probabilistic neural modeling paradigms: Bayesian Neural Networks (BNNs) and Mixture Density Networks (MDNs) for uncertainty-aware nonlinear regression. While BNNs incorporate epistemic uncertainty by…

The Distributional Random Forest (DRF) is a recently introduced Random Forest algorithm to estimate multivariate conditional distributions. Due to its general estimation procedure, it can be employed to estimate a wide range of targets such…

Deep Neural Networks (DNNs) are known to be vulnerable to adversarial attacks, i.e., an imperceptible perturbation to the input can mislead DNNs trained on clean images into making erroneous predictions. To tackle this, adversarial training…

This paper is motivated by addressing open questions in distributionally robust chance-constrained programs (DRCCP) using the popular Wasserstein ambiguity sets. Specifically, the computational techniques for those programs typically place…

The competition between local and global driving forces is significant in a wide variety of naturally occurring branched networks. We have investigated the impact of a global minimization criterion versus a local one on the structure of…

Graph Convolutional Networks (GCNs) have recently attracted vast interest and achieved state-of-the-art performance on graphs, but its success could typically hinge on careful training with amounts of expensive and time-consuming labeled…

Distributed parameter identification for large-scale multi-agent networks encounters challenges due to nonlinear dynamics and partial observations. Simultaneously, ensuring the stability is crucial for the robust identification of dynamic…

Controlling the false discovery rate (FDR) is a powerful approach to multiple testing. In many applications, the tested hypotheses have an inherent hierarchical structure. In this paper, we focus on the fixed sequence structure where the…

Well-mixed chemical reaction networks (CRNs) contain many distinct chemical species with copy numbers that fluctuate in correlated ways. While those correlations are typically monitored via Monte Carlo sampling of stochastic trajectories,…

Numerical methods based on tensor networks have been extensively explored in the research of quantum many-body systems in recent years. It has been recognized that the ability of tensor networks to describe a quantum many-body state…

Given an undirected, weighted graph, the minimum spanning tree (MST) is a tree that connects all of the vertices of the graph with minimum sum of edge weights. In real world applications, network designers often seek to quickly find a…

We establish sharp upper and lower bounds for distortion risk metrics under distributional uncertainty. The uncertainty sets are characterized by four key features of the underlying distribution: mean, variance, unimodality, and Wasserstein…

Mixed linear regression (MLR) is a powerful model for characterizing nonlinear relationships by utilizing a mixture of linear regression sub-models. The identification of MLR is a fundamental problem, where most of the existing results…

Given a spatio-temporal network (ST network) where edge properties vary with time, a time-sub-interval minimum spanning tree (TSMST) is a collection of minimum spanning trees of the ST network, where each tree is associated with a time…

Deep learning (DL) networks have recently been shown to outperform other segmentation methods on various public, medical-image challenge datasets [3,11,16], especially for large pathologies. However, in the context of diseases such as…

We present a novel method for quantifying dependencies in multivariate datasets, based on estimating the R\'{e}nyi entropy by minimum spanning trees (MSTs). The length of the MSTs can be used to order pairs of variables from strongly to…

Wood increment is critical information in forestry management. Previous studies used mathematics models to describe complex growing pattern of forest stand, in order to determine the dynamic status of growing forest stand in multiple…

We study complex networks under random matrix theory (RMT) framework. Using nearest-neighbor and next-nearest-neighbor spacing distributions we analyze the eigenvalues of adjacency matrix of various model networks, namely, random,…

Selecting relevant features associated with a given response variable is an important issue in many scientific fields. Quantifying quality and uncertainty of a selection result via false discovery rate (FDR) control has been of recent…

To improve the uncertainty quantification of variance networks, we propose a novel tree-structured local neural network model that partitions the feature space into multiple regions based on uncertainty heterogeneity. A tree is built upon…