arXiv research

New method improves subspace iteration for eigenvectors in machine learning.

OptEx accelerates first-order optimization with parallelized iterations.

New algorithms solve robust MDPs efficiently, significantly faster than existing methods.

This dissertation advances scalable Gaussian processes using iterative methods and pathwise conditioning.

Extends JKO scheme for iterative algorithms with unknown parameters.

Enhances LMC for log-concave sampling, reducing computational cost.

Innovative neural networks reduce memory usage for efficient, accurate segmentation.

Study compares methods for computing hypergradients in machine learning problems.

Distributed gradient descent (DGD) is an efficient way of implementing gradient descent (GD), especially for large data sets, by dividing the computation tasks into smaller subtasks and assigning to different computing servers (CSs) to be executed in parallel. In standard parallel execution, per-iteration waiting time …

We study iteration maps of recurrence relations arising from mutation periodic quivers of arbitrary period. Combining tools from cluster algebra theory and (pre)symplectic geometry, we show that these cluster iteration maps can be reduced to symplectic maps on a lower dimensional submanifold, provided the matrix repres…

Optimal ridge regularization computed iteratively from generative parameters.

Faster WIND accelerates iterative BOND for LLM alignment.

Implicit models can match or exceed explicit models with more test-time compute.

Study examines parallel computing strategies for faster imputation of missing data.

Warm starts improve Gaussian process regression by up to 16x.

Traditional learning methods for training Markov random fields require doing inference over all variables to compute the likelihood gradient. The iteration complexity for those methods therefore scales with the size of the graphical models. In this paper, we propose \emph{block belief propagation learning} (BBPL), whic…

New algorithm for computing Wasserstein barycenters with guarantees.

Due to the surprisingly good representation power of complex distributions, neural network (NN) classifiers are widely used in many tasks which include natural language processing, computer vision and cyber security. In recent works, people noticed the existence of adversarial examples. These adversarial examples break…

New method solves constrained stochastic optimization problems efficiently.

New method speeds up distributed linear regression.

Banach's fixed point theorem for contraction maps has been widely used to analyze the convergence of iterative methods in non-convex problems. It is a common experience, however, that iterative maps fail to be globally contracting under the natural metric in their domain, making the applicability of Banach's theorem li…

New framework for probabilistic linear solvers reduces manual effort.

Improved ADMM for convex distributed learning with differential privacy.

New method reduces variance in random coordinate descent for Langevin Monte Carlo.

We present an iterative Markov chainMonte Carlo algorithm for computingreference priors and minimax risk forgeneral parametric families. Ourapproach uses MCMC techniques based onthe Blahut-Arimoto algorithm forcomputing channel capacity ininformation theory. We give astatistical analysis of the algorithm,bounding the n…

Study wSAA for contextual decisions, improving uncertainty quantification under computational constraints.

Motivated principally by the low-rank matrix completion problem, we present an extension of the Frank-Wolfe method that is designed to induce near-optimal solutions on low-dimensional faces of the feasible region. This is accomplished by a new approach to generating ``in-face" directions at each iteration, as well as t…

New sampler reduces MCMC complexity for Bayesian variable selection.

We propose a novel method to accelerate Lloyd's algorithm for K-Means clustering. Unlike previous acceleration approaches that reduce computational cost per iterations or improve initialization, our approach is focused on reducing the number of iterations required for convergence. This is achieved by treating the assig…

Polyak step size GD reaches final radius of convergence after log iterations.

LASER compresses recursive model activations by exploiting their low-dimensional structure.

Alternating direction method of multiplier (ADMM) is a popular method used to design distributed versions of a machine learning algorithm, whereby local computations are performed on local data with the output exchanged among neighbors in an iterative fashion. During this iterative process the leakage of data privacy a…

Value iteration is a fixed point iteration technique utilized to obtain the optimal value function and policy in a discounted reward Markov Decision Process (MDP). Here, a contraction operator is constructed and applied repeatedly to arrive at the optimal solution. Value iteration is a first order method and therefore …

FPI methods compute barycenters of Gaussian sets for various dissimilarity measures.

Ball k-means reduces point-centroid distance computations for faster k-means clustering.

Basic elements of integral calculus over algebras of iterated differential forms, are presented. In particular, defining complexes for modules of integral forms are described and the corresponding berezinians and complexes of integral forms are computed. Various applications and the integral calculus over the algebra $…

SNAP improves robust computation by emphasizing trustworthy items and downweighting outliers.

This paper accelerates TV regularization algorithms by unrolling proximal gradient descent.

We introduce a novel class of rotation invariants of two dimensional curves based on iterated integrals. The invariants we present are in some sense complete and we describe an algorithm to calculate them, giving explicit computations up to order six. We present an application to online (stroke-trajectory based) charac…

Paper solves DRO for continuous distributions with iterative algorithms.

The cost of computing the spectrum of Laplacian matrices hinders the application of spectral clustering to large data sets. While approximations recover computational tractability, they can potentially affect clustering performance. This paper proposes a practical approach to learn spectral clustering based on adaptive…

A new algorithm reduces communication in distributed SVD by $p$ factors.

We introduce a novel numerical approach for a class of stochastic dynamic programs which arise as discretizations of backward stochastic differential equations or semi-linear partial differential equations. Solving such dynamic programs numerically requires the approximation of nested conditional expectations, i.e., it…

This paper investigates asymptotic behaviors of gradient descent algorithms (particularly accelerated gradient descent and stochastic gradient descent) in the context of stochastic optimization arising in statistics and machine learning where objective functions are estimated from available data. We show that these alg…

Graph neural network executes value iteration for flexible environments.

New method approximates CV efficiently for large-scale problems.

OMWU shows last iterate convergence in convex-concave games.

The paper approximates financial derivatives using neural networks and iterated integrals.