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Traditional learning approaches for classification implicitly assume that each mistake has the same cost. In many real-world problems though, the utility of a decision depends on the underlying context $x$ and decision $y$. However,…

Predicting the behaviors of Hamiltonian systems has been drawing increasing attention in scientific machine learning. However, the vast majority of the literature was focused on predicting separable Hamiltonian systems with their kinematic…

We present and implement two algorithms for analytic asymptotic evaluation of the marginal likelihood of data given a Bayesian network with hidden nodes. As shown by previous work, this evaluation is particularly hard for latent Bayesian…

Non-convex optimization plays a central role in many statistics and machine learning problems. Despite the landscape irregularities for general non-convex functions, some recent work showed that for many learning problems with random data…

We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…

In this article we consider sampling from log concave distributions in Hamiltonian setting, without assuming that the objective gradient is globally Lipschitz. We propose two algorithms based on monotone polygonal (tamed) Euler schemes, to…

We present a simple noise-robust margin-based active learning algorithm to find homogeneous (passing the origin) linear separators and analyze its error convergence when labels are corrupted by noise. We show that when the imposed noise…

We investigate the problem of learning a Single Index Model (SIM)- a popular model for studying the ability of neural networks to learn features - from anisotropic Gaussian inputs by training a neuron using vanilla Stochastic Gradient…

This work investigates robust monotonic convergent iterative learning control (ILC) for uncertain linear systems in both time and frequency domains, and the ILC algorithm optimizing the convergence speed in terms of $l_{2}$ norm of error…

In this paper, we propose a general mathematical framework to represent many multi-agent signalling systems in recent works. Our goal is to apply previous results in monotonicity to this class of systems and study their asymptotic behavior.…

We study the fundamental problem of learning a marginally stable unknown nonlinear dynamical system. We describe an algorithm for this problem, based on the technique of spectral filtering, which learns a mapping from past observations to…

Despite remarkable empirical success, the training dynamics of generative adversarial networks (GAN), which involves solving a minimax game using stochastic gradients, is still poorly understood. In this work, we analyze last-iterate…

We propose SLIM (Stochastic Learning and Inference in overidentified Models), a scalable stochastic approximation framework for nonlinear GMM. SLIM forms iterative updates from independent mini-batches of moments and their derivatives,…

We study a tandem of agents who make decisions about an underlying binary hypothesis, where the distribution of the agent observations under each hypothesis comes from an uncertainty class. We investigate both decentralized detection rules,…

Here and in a follow-on paper, we consider a simple control problem in which the underlying dynamics depend on a parameter $a$ that is unknown and must be learned. In this paper, we assume that $a$ is bounded, i.e., that $|a| \le…

We give the first fully polynomial-time algorithm for learning halfspaces with respect to the uniform distribution on the hypercube in the presence of contamination, where an adversary may corrupt some fraction of examples and labels…

In high-stakes AI applications, even a single action can cause irreparable damage. However, nearly all of sequential decision-making theory assumes that all errors are recoverable (e.g., by bounding rewards). Standard bandit algorithms that…

Nonlinear self-interference cancellation (SIC) is essential for full-duplex communication systems, which can offer twice the spectral efficiency of traditional half-duplex systems. The challenge of nonlinear SIC is similar to the classic…

Inspired by the problem of improving classification accuracy on rare or hard subsets of a population, there has been recent interest in models of learning where the goal is to generalize to a collection of distributions, each representing a…

Evidential occupancy grid maps (OGMs) are a popular representation of the environment of automated vehicles. Inverse sensor models (ISMs) are used to compute OGMs from sensor data such as lidar point clouds. Geometric ISMs show a limited…