arXiv research

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

In this work, we propose a robust approach to design distributed controllers for unknown-but-sparse linear and time-invariant systems. By leveraging modern techniques in distributed controller synthesis and structured linear inverse problems as applied to system identification, we show that near-optimal distributed con…

Near-optimal algorithms for mean estimation and linear regression with Gaussian covariates and Huber contamination.

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

We consider the fundamental learning problem of estimating properties of distributions over large domains. Using a novel piecewise-polynomial approximation technique, we derive the first unified methodology for constructing sample- and time-efficient estimators for all sufficiently smooth, symmetric and non-symmetric, …

New method for robust linear regression in nearly linear time.

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

New algorithm speeds up Gaussian process optimization.

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

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

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

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 algorithms combat adversarial attacks in stochastic linear bandits.

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

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

Many important applications, including signal reconstruction, parameter estimation, and signal processing in a compressed domain, rely on a low-dimensional representation of the dataset that preserves {\em all} pairwise distances between the data points and leverages the inherent geometric structure that is typically p…

New method achieves near-optimal regret without simulator.

TiDE uses MLP for fast, simple long-term time-series forecasting.

LinMED is a new linear bandit algorithm with near-optimal regret bound.

Analyzes Hessian spectrum for neural networks near optimal learning.

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

New algorithm reduces switching costs in RL beyond linear MDPs.

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

A single policy suffices for near-optimal parallel exploration in RL.

We study the problem of regret minimization for distributed bandits learning, in which $M$ agents work collaboratively to minimize their total regret under the coordination of a central server. Our goal is to design communication protocols with near-optimal regret and little communication cost, which is measured by the…

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…

Grokking occurs in simple binary logistic classification near linear separability and noise.

Efficiently simulates the Heston model with large time steps using a novel method.

New algorithm recovers sparse signals from linearly sparse dictionaries efficiently.

We present an efficient and practical algorithm for the online prediction of discrete-time linear dynamical systems with a symmetric transition matrix. We circumvent the non-convex optimization problem using improper learning: carefully overparameterize the class of LDSs by a polylogarithmic factor, in exchange for con…

We develop efficient algorithms for robust PCA that handle outliers.

We study the behavior of the critical price of an American put option near maturity in the exponential Lévy model when the underlying stock pays dividends at a continuous rate. In particular, we prove that, in situations where the limit of the critical price is equal to the stock price, the rate of convergence to the l…

Develops estimators for near-optimal linear regression under distribution shift.

New algorithms for differentially private optimization in convex and non-convex settings with near-optimal rates.

In this paper, we establish a framework for the analysis of linear parabolic equations on conical surfaces and use them to study the conical Ricci flow. In particular, we prove the long time existence of the conical Ricci flow for general cone angle and show that this solution has the optimal regularity, namely, the ti…

New method speeds up NIR spectroscopy calibration by 400x.

LightOn OPUs accelerate randomized numerical linear algebra, reducing computational costs.

Noise makes learning linear thresholds hard, but algorithms can still learn near-optimal thresholds.

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

Symbolic grounding in causal dynamics achieves near-infinite temporal consistency.

Study cost-driven state representation learning for control from partial observations.

Principal components analysis (PCA) is the optimal linear auto-encoder of data, and it is often used to construct features. Enforcing sparsity on the principal components can promote better generalization, while improving the interpretability of the features. We study the problem of constructing optimal sparse linear a…

We construct the biharmonic heat kernel for a suitable self-adjoint extension of the bi-Laplacian on a manifold with incomplete edge singularities. We employ a microlocal description of the biharmonic heat kernel to establish mapping properties of the corresponding biharmonic heat operator on certain Banach spaces. Thi…

New algorithms for model selection in linear bandits adapt to instance complexity.

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

New approach achieves optimal rates for differentially private stochastic convex optimization with heavy-tailed gradients.

In this paper, we settle the sampling complexity of solving discounted two-player turn-based zero-sum stochastic games up to polylogarithmic factors. Given a stochastic game with discount factor $γ\in(0,1)$ we provide an algorithm that computes an $ε$-optimal strategy with high-probability given $\tilde{O}((1 - γ)^{-3}…

Designs a single policy for collecting data to train near-optimal policies.