arXiv research

New methods solve complex optimization problems without strong convexity assumptions.

New combinatorial dimension VCL refines learning curve theory.

Paper improves algorithms for convex-concave minimax optimization problems.

An algorithm learns from multiple models to match an oracle's risk.

Paper sets fundamental limits for distributed covariance estimation with constrained communication.

Paper solves minimax optimization gap with near-optimal algorithms.

New algorithms for private GLM estimation with minimax lower bounds.

Study minimax rates for binary classifier estimation with margin conditions.

In statistical inference problems, we wish to obtain lower bounds on the minimax risk, that is to bound the performance of any possible estimator. A standard technique to obtain risk lower bounds involves the use of Fano's inequality. In an information-theoretic setting, it is known that Fano's inequality typically doe…

Study minimax linear regression under quantile risk, improving existing bounds and providing new results.

Paper finds a lower bound for estimating low-rank matrices in logistic regression.

Develops high-probability minimax quantile bounds for statistical problems.

New algorithm optimally evaluates policies with linear approximations.

New research sets the minimax lower bound for KSD estimation at sqrt(n).

We prove non-asymptotic lower bounds on the expectation of the maximum of $d$ independent Gaussian variables and the expectation of the maximum of $d$ independent symmetric random walks. Both lower bounds recover the optimal leading constant in the limit. A simple application of the lower bound for random walks is an (…

Exact minimax risk derived for linear prediction with sample covariance analysis.

Score attack method provides a lower bound on privacy-constrained minimax risk.

Estimates sparse topic models with improved efficiency and adaptability.

Study on $Q$-function estimation for continuous state-action MDPs, deriving rates and conditions.

Study uses SGD to learn operators in Hilbert spaces with convergence analysis.

Kernel method improves instrumental variable regression rates.

New research shows that binary classification can be done with noisy data, but only if there are clean samples available.

Novel methods for accelerating optimization in complex bilevel and minimax problems.

We study the problem of switching-constrained online convex optimization (OCO), where the player has a limited number of opportunities to change her action. While the discrete analog of this online learning task has been studied extensively, previous work in the continuous setting has neither established the minimax ra…

New method generates private synthetic data with optimal utility for smooth queries.

GP-UCB performs suboptimally under certain conditions, as shown by a new regret lower bound.

Study tackles contamination and heterogeneity in multi-task learning, improving robustness and personalization.

Study finds optimal regret bound for multi-armed bandit problem with expert advice.

Study on statistical estimation over Gaussian MAC, comparing analog and digital schemes.

Dictionary learning is the problem of estimating the collection of atomic elements that provide a sparse representation of measured/collected signals or data. This paper finds fundamental limits on the sample complexity of estimating dictionaries for tensor data by proving a lower bound on the minimax risk. This lower …

Sparse covariance estimation in the vertical-split model achieves exponential improvement over dense estimates.

The paper tackles deep learning from dependent data, achieving optimal performance.

Unified framework for corruption-robust linear bandits with optimal gap-dependent misspecification bounds.

Study minimax regret in sequential probability assignment with and without side information.

Rejection Sampling is a fundamental Monte-Carlo method. It is used to sample from distributions admitting a probability density function which can be evaluated exactly at any given point, albeit at a high computational cost. However, without proper tuning, this technique implies a high rejection rate. Several methods h…

Paper explores generalization of minimax learners, proposing a new metric.

The study establishes minimax bounds for estimating operators from noisy samples.

New minimax optimal learner for robust predictors against adversarial examples.

Develops locally private methods for nonparametric contextual bandits.

Paper explores fair classification with bounded disparity using finite datasets.

New tensor model reduces GLM estimation error and sample complexity.

Transductive learning considers a training set of $m$ labeled samples and a test set of $u$ unlabeled samples, with the goal of best labeling that particular test set. Conversely, inductive learning considers a training set of $m$ labeled samples drawn iid from $P(X,Y)$, with the goal of best labeling any future sample…

We consider a sequential learning problem with Gaussian payoffs and side information: after selecting an action $i$, the learner receives information about the payoff of every action $j$ in the form of Gaussian observations whose mean is the same as the mean payoff, but the variance depends on the pair $(i,j)$ (and may…

Detecting a planted submatrix in random matrices with non-asymptotic methods.

The cost-sensitive classification problem plays a crucial role in mission-critical machine learning applications, and differs with traditional classification by taking the misclassification costs into consideration. Although being studied extensively in the literature, the fundamental limits of this problem are still n…

Spectral algorithms on manifolds using diffusion kernels improve convergence rates.

We study the linear contextual bandit problem with finite action sets. When the problem dimension is $d$, the time horizon is $T$, and there are $n \leq 2^{d/2}$ candidate actions per time period, we (1) show that the minimax expected regret is $Ω(\sqrt{dT (\log T) (\log n)})$ for every algorithm, and (2) introduce a V…

An important class of distance metrics proposed for training generative adversarial networks (GANs) is the integral probability metric (IPM), in which the neural net distance captures the practical GAN training via two neural networks. This paper investigates the minimax estimation problem of the neural net distance ba…