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Compressive sampling has become a widely used approach to construct polynomial chaos surrogates when the number of available simulation samples is limited. Originally, these expensive simulation samples would be obtained at random locations…

Expectation propagation is a general approach to fast approximate inference for graphical models. The existing literature treats models separately when it comes to deriving and coding expectation propagation inference algorithms. This comes…

Deep neural networks (DNNs) and Kolmogorov-Arnold networks (KANs) are popular methods for function approximation due to their flexibility and expressivity. However, they typically require a large number of trainable parameters to produce a…

As networks continue to increase in size, current methods must be capable of handling large numbers of nodes and edges in order to be practically relevant. Instead of working directly with the entire (large) network, analyzing sub-networks…

Universality, namely distributional invariance, is a well-known property for many random structures. For example, it is known to hold for a broad range of variational problems with random input. Much less is known about the algorithmic…

Approximate inference in probability models is a fundamental task in machine learning. Approximate inference provides powerful tools to Bayesian reasoning, decision making, and Bayesian deep learning. The main goal is to estimate the…

Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…

In this work, we analyze an efficient sampling-based algorithm for general-purpose reachability analysis, which remains a notoriously challenging problem with applications ranging from neural network verification to safety analysis of…

We describe a novel approach to statistical learning from particles tracked while moving in a random environment. The problem consists in inferring properties of the environment from recorded snapshots. We consider here the case of a fluid…

Particle filtering is used to compute good nonlinear estimates of complex systems. It samples trajectories from a chosen distribution and computes the estimate as a weighted average. Easy-to-sample distributions often lead to degenerate…

Structural network embedding is a crucial step in enabling effective downstream tasks for complex systems that aims to project a network into a lower-dimensional space while preserving similarities among nodes. We introduce a simple and…

In many problems in data mining and machine learning, data items that need to be clustered or classified are not points in a high-dimensional space, but are distributions (points on a high dimensional simplex). For distributions, natural…

Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, but the result depends on distances, which vary continuously.…

Global polynomial optimization is an important tool across applied mathematics, with many applications in operations research, engineering, and physical sciences. In various settings, the polynomials depend on external parameters that may…

A fundamental notion of distance between train and test distributions from the field of domain adaptation is discrepancy distance. While in general hard to compute, here we provide the first set of provably efficient algorithms for testing…

We consider a distributionally robust formulation of stochastic optimization problems arising in statistical learning, where robustness is with respect to uncertainty in the underlying data distribution. Our formulation builds on…

In comparative studies, such as in causal inference and clinical trials, balancing important covariates is often one of the most important concerns for both efficient and credible comparison. However, chance imbalance still exists in many…

In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form…

Covariate shift, a widely used assumption in tackling {\it distributional shift} (when training and test distributions differ), focuses on scenarios where the distribution of the labels conditioned on the feature vector is the same, but the…

Dropout has been witnessed with great success in training deep neural networks by independently zeroing out the outputs of neurons at random. It has also received a surge of interest for shallow learning, e.g., logistic regression. However,…