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We propose a localized consensus-based method for sampling from non-Gaussian distributions. This method arises from an alternative derivation of consensus-based sampling (CBS). Starting from ensemble-preconditioned Langevin dynamics, we…

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 modern data analysis, random sampling is an efficient and widely-used strategy to overcome the computational difficulties brought by large sample size. In previous studies, researchers conducted random sampling which is according to the…

We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…

Score-based generative models (SGMs) are powerful tools to sample from complex data distributions. Their underlying idea is to (i) run a forward process for time $T_1$ by adding noise to the data, (ii) estimate its score function, and (iii)…

The graphical lasso is a widely used algorithm for fitting undirected Gaussian graphical models. However, for inference on functionals of edge values in the learned graph, standard tools lack formal statistical guarantees, such as control…

Statistical models with constrained probability distributions are abundant in machine learning. Some examples include regression models with norm constraints (e.g., Lasso), probit, many copula models, and latent Dirichlet allocation (LDA).…

The performance of standard stochastic approximation implementations can vary significantly based on the choice of the steplength sequence, and in general, little guidance is provided about good choices. Motivated by this gap, in the first…

Performance-based engineering for natural hazards facilitates the design and appraisal of structures with rigorous evaluation of their uncertain structural behavior under potentially extreme stochastic loads expressed in terms of failure…

Stochastic gradient descent (SGD) is the main algorithm behind a large body of work in machine learning. In many cases, constraints are enforced via projections, leading to projected stochastic gradient algorithms. In recent years, a large…

Gradient descent methods and especially their stochastic variants have become highly popular in the last decade due to their efficiency on big data optimization problems. In this thesis we present the development of data sampling strategies…

Sampling from binary quadratic distributions (BQDs) is a fundamental but challenging problem in discrete optimization and probabilistic inference. Previous work established theoretical guarantees for stochastic localization (SL) in…

We introduce Tiered Sampling, a novel technique for approximate counting sparse motifs in massive graphs whose edges are observed in a stream. Our technique requires only a single pass on the data and uses a memory of fixed size $M$, which…

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…

A stochastic algorithm is proposed, finding the set of generalized means associated to a probability measure on a compact Riemannian manifold M and a continuous cost function on the product of M by itself. Generalized means include p-means…

In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we…

We consider estimating the marginal likelihood in settings with independent and identically distributed (i.i.d.) data. We propose estimating the predictive distributions in a sequential factorization of the marginal likelihood in such…

Split sample methods have recently been put forward as a way to reduce the coverage oscillations that haunt confidence intervals for parameters of lattice distributions, such as the binomial and Poisson distributions. We study split sample…

We propose discrete Langevin proposal (DLP), a simple and scalable gradient-based proposal for sampling complex high-dimensional discrete distributions. In contrast to Gibbs sampling-based methods, DLP is able to update all coordinates in…

Sign-Perturbed Sum (SPS) is a powerful finite-sample system identification algorithm which can construct confidence regions for the true data generating system with exact coverage probabilities, for any finite sample size. SPS was developed…