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Probabilistic graphical models are a powerful concept for modeling high-dimensional distributions. Besides modeling distributions, probabilistic graphical models also provide an elegant framework for performing statistical inference;…

We present polynomial time and sample efficient algorithms for learning an unknown depth-2 feedforward neural network with general ReLU activations, under mild non-degeneracy assumptions. In particular, we consider learning an unknown…

This paper studies nonparametric regression with repeated measurements when the response in the target domain is unobservable or costly to collect. We adopt a transfer learning framework that leverages a source domain with observable…

A wide variety of activation functions have been proposed for neural networks. The Rectified Linear Unit (ReLU) is especially popular today. There are many practical reasons that motivate the use of the ReLU. This paper provides new…

Large Language Models (LLMs) have been widely employed in programming language analysis to enhance human productivity. Yet, their reliability can be compromised by various code distribution shifts, leading to inconsistent outputs. While…

Motivated by the fact that full diversity order is achieved using the "best-relay" selection technique, we consider opportunistic amplify-and-forward and decode-and-forward relaying systems. We focus on the outage probability of such a…

This paper proposes a paradigm of uncertainty injection for training deep learning model to solve robust optimization problems. The majority of existing studies on deep learning focus on the model learning capability, while assuming the…

Many problems in navigation and tracking require increasingly accurate characterizations of the evolution of uncertainty in nonlinear systems. Nonlinear uncertainty propagation approaches based on Gaussian mixture density approximations…

This paper introduces a novel method for the automatic detection and handling of nonlinearities in a generic transformation. A nonlinearity index that exploits second order Taylor expansions and polynomial bounding techniques is first…

Learning representations that generalize under distribution shifts is critical for building robust machine learning models. However, despite significant efforts in recent years, algorithmic advances in this direction have been limited. In…

In this study, we develop a probabilistic approach to map the parametric uncertainty to the output state uncertainty in first-order hyperbolic conservation laws. We analyze this problem for nonlinear immiscible two-phase transport in…

Spiking Neural Networks (SNNs) are being explored to emulate the astounding capabilities of human brain that can learn and compute functions robustly and efficiently with noisy spiking activities. A variety of spiking neuron models have…

In probability density function (PDF) methods of turbulent flows, the joint PDF of several flow variables is computed by numerically integrating a system of stochastic differential equations for Lagrangian particles. A set of parallel…

Recent advances in deep learning have shown that uncertainty estimation is becoming increasingly important in applications such as medical imaging, natural language processing, and autonomous systems. However, accurately quantifying…

We extend the ReLU Transition Graph (RTG) framework into a comprehensive graph-theoretic model for understanding deep ReLU networks. In this model, each node represents a linear activation region, and edges connect regions that differ by a…

In this paper, we consider discrete-time non-linear stochastic dynamical systems with additive process noise in which both the initial state and noise distributions are uncertain. Our goal is to quantify how the uncertainty in these…

The means by which cortical neural networks are able to efficiently solve inference problems remains an open question in computational neuroscience. Recently, abstract models of Bayesian computation in neural circuits have been proposed,…

We consider the goal of predicting how complex networks respond to chronic (press) perturbations when characterizations of their network topology and interaction strengths are associated with uncertainty. Our primary result is the…

Explanation methods help understand the reasons for a model's prediction. These methods are increasingly involved in model debugging, performance optimization, and gaining insights into the workings of a model. With such critical…

We introduce a unified and computationally efficient framework for regression on network data, addressing limitations of existing models that require specialized estimation procedures or impose restrictive decay assumptions. Our Network…