arXiv research

A clustering algorithm for natural hierarchical clusters with near-linear time complexity.

Efficiently designs distributed controllers for sparse systems with sub-linear sample complexity.

Improved Sinkhorn algorithm for UOT with near-linear complexity.

Unified method for estimating properties of large domain distributions efficiently.

Improved efficient robust regression with near-linear time and subquadratic samples.

New algorithms for approximating multimarginal optimal transport with near-linear time complexity.

New framework for DP-SMO with near-optimal privacy-loss trade-off.

New method for robust linear regression in nearly linear time.

This paper develops a fast algorithm for solving nonlinear PDEs using sparse Cholesky factorization.

Quantum algorithms reduce clustering input size, achieving near-linear approximation.

Local polynomial regression (Fan and Gijbels 1996) is an important class of methods for nonparametric density estimation and regression problems. However, straightforward implementation of local polynomial regression has quadratic time complexity which hinders its applicability in large-scale data analysis. In this pap…

CTT compresses samples to test distributions near-linearly, outperforming existing methods.

New algorithm speeds up Gaussian process optimization.

Computing optimal transport distances such as the earth mover's distance is a fundamental problem in machine learning, statistics, and computer vision. Despite the recent introduction of several algorithms with good empirical performance, it is unknown whether general optimal transport distances can be approximated in …

New algorithm approximates distributions with near-linear time and optimal sample efficiency.

Algorithm finds frequencies, amplitudes, and phases of sinusoids in noisy data.

Compress++ speeds up distribution compression to near-linear time.

Implicit schemes are popular methods for the integration of time dependent PDEs such as hyperbolic and parabolic PDEs. However the necessity to solve corresponding linear systems at each time step constitutes a complexity bottleneck in their application to PDEs with rough coefficients. We present a generalization of ga…

Matrix completion is the problem of recovering a low rank matrix by observing a small fraction of its entries. A series of recent works [KOM12,JNS13,HW14] have proposed fast non-convex optimization based iterative algorithms to solve this problem. However, the sample complexity in all these results is sub-optimal in it…

New algorithm trains neural networks in near-linear time, overcoming slow convergence issues.

A new algorithm estimates mean adaptively to covariance, faster and more flexible than existing methods.

A nonparametric method for time series analysis extracts envelopes, detects peaks, and clusters data.

Finding the diameter of a dataset in multidimensional Euclidean space is a well-established problem, with well-known algorithms. However, most of the algorithms found in the literature do not scale well with large values of data dimension, so the time complexity grows exponentially in most cases, which makes these algo…

Improved sketching for logistic and $\ell_1$ regression with near-linear dimensions.

SAMBA predicts stock returns efficiently using Mamba and graph neural networks.

Lapse improves parameter servers by dynamically allocating parameters, achieving near-linear scaling.

This work generalizes transformer attention to capture higher-order correlations efficiently.

New insights into variable selection with different model assumptions.

Near-logarithmic regret per switch achieved for mixable/exp-concave losses.

CLASSIX is a fast and explainable clustering method that sorts data and merges groups.

WildCat efficiently compresses neural network attention mechanisms.

We consider the problem of Robust PCA in the fully and partially observed settings. Without corruptions, this is the well-known matrix completion problem. From a statistical standpoint this problem has been recently well-studied, and conditions on when recovery is possible (how many observations do we need, how many co…

Proposes a parsimonious graph spectral method for time series data.

Paper proposes FedQ-Advantage for federated Q-learning with near-optimal regret and low communication cost.

SOR-Mamba improves Mamba for robust time series forecasting by minimizing channel order bias.

New algorithm recovers sparse signals from linearly sparse dictionaries efficiently.

We study three fundamental statistical-learning problems: distribution estimation, property estimation, and property testing. We establish the profile maximum likelihood (PML) estimator as the first unified sample-optimal approach to a wide range of learning tasks. In particular, for every alphabet size $k$ and desired…

Direct proof shows adaptive gradient descent converges near-linearly for convex functions.

We show how the discovery of robust scalable numerical solvers for arbitrary bounded linear operators can be automated as a Game Theory problem by reformulating the process of computing with partial information and limited resources as that of playing underlying hierarchies of adversarial information games. When the so…

Clustering consists of grouping together samples giving their similar properties. The problem of modeling simultaneously groups of samples and features is known as Co-Clustering. This paper introduces ROCCO - a Robust Continuous Co-Clustering algorithm. ROCCO is a scalable, hyperparameter-free, easy and ready to use al…

New MCMC method speeds up quantum physics simulations by a factor of 100.

A new model predicts discrete events with flexible, nonparametric baseline and excitation.

We consider the demixing problem of two (or more) high-dimensional vectors from nonlinear observations when the number of such observations is far less than the ambient dimension of the underlying vectors. Specifically, we demonstrate an algorithm that stably estimate the underlying components under general \emph{struc…

New framework models non-conservative stochastic processes without energy conservation constraints.

New method computes affine normal directions efficiently for sparse polynomials.

If learning methods are to scale to the massive sizes of modern datasets, it is essential for the field of machine learning to embrace parallel and distributed computing. Inspired by the recent development of matrix factorization methods with rich theory but poor computational complexity and by the relative ease of map…

AverageTime uses simple averaging to enhance long-term time series forecasting.

Computable Stein discrepancies have been deployed for a variety of applications, ranging from sampler selection in posterior inference to approximate Bayesian inference to goodness-of-fit testing. Existing convergence-determining Stein discrepancies admit strong theoretical guarantees but suffer from a computational co…