New flexible confidence sequences for robust statistical inference.
problem Creating robust statistical inference methods that work under mild assumptions.
method Proposed a new class of asymptotic time-uniform confidence sequences.
result Sharp asymptotic time-uniform confidence sequences achieved under mild assumptions.
A new kernel-based CI test improves on existing methods.
problem Testing conditional independence (CI) in a broad range of dependencies.
method Regression-model-agnostic kernel-based CI test using reproducing kernel Hilbert spaces.
result GKCM outperforms state-of-the-art CI tests in simulations.
The paper develops time-uniform inference methods for stochastic approximation parameters.
problem Statistical inference for parameters in stochastic approximation problems.
method Analysis of averaged iterates convergence rates and construction of asymptotic confidence sequences.
result Valid asymptotic confidence sequences for parameters in stochastic approximation problems.
New algorithm FLUTE achieves uniform-PAC convergence in RL with linear approx.
problem RL with linear function approximation lacks uniform-PAC guarantees.
method FLUTE algorithm with minimax value function estimator and multi-level partition scheme.
result Uniform-PAC convergence to optimal policy with high probability.
Estimates time-series drifts from i.i.d. data using a direct Nadaraya-Watson plug-in method.
problem Nonparametric estimation of Schrödinger bridge drifts from single time interval data.
method Direct Nadaraya-Watson plug-in estimator based on kernelized numerator and denominator terms.
result Uniform non-asymptotic bound, CLT under undersmoothing, and adaptive bandwidth selector.
New algorithms achieve uniform-PAC guarantees for RL with bounded eluder dimension.
problem Achieving strong performance guarantees in reinforcement learning.
method Proposes algorithms for nonlinear bandits and model-based episodic RL with a bounded eluder dimension.
result Achieves uniform-PAC sample complexity that matches state-of-the-art regret bounds or sample complexity guarantees.
This paper introduces time-uniform CLT-based confidence intervals for statistical inference.
problem Developing valid statistical inference methods for sequential data.
method Time-uniform central limit theory and strong invariance principles.
result Asymptotic confidence sequences (CSs) that are uniformly valid over time.
Smooth DNNs mitigate the curse of dimensionality in uniform convergence for various regression tasks.
problem The curse of dimensionality in uniform convergence of ReLU networks.
method Analysis of smoothly activated deep neural networks (smooth DNNs), establishing pseudo-dimension bounds and non-asymptotic approximation guarantees.
result Smooth DNNs achieve non-asymptotic uniform convergence rates across multiple statistical contexts, mitigating the curse of dimensionality.
New PAC bound for meta-learning improves generalization guarantees.
problem Provide strong generalization guarantees in meta-learning.
method PAC-Bayes and uniform stability frameworks applied to gradient-based meta-learning.
result Derives a tighter PAC bound for gradient-based meta-learning.
We derive high-probability finite-sample uniform rates of consistency for k-NN regression that are optimal up to logarithmic factors under mild assumptions. We moreover show that k-NN regression adapts to an unknown lower intrinsic dimension automatically. We then apply the k-NN regression rates to establish new …
New algorithms sample convex bodies using Markov chains and restricted Gaussian oracles.
problem Sampling uniformly from convex bodies efficiently.
method Markov chain Monte Carlo with proximal sampler and restricted Gaussian oracle.
result Efficient implementation of RGO for uniform sampling on convex bodies.
A new method for matrix completion with model-free weights.
problem Matrix completion under non-uniform missing structures.
method Constructs weights via convex optimization to adjust for non-uniformity without modeling observation probabilities.
result Recover matrix with stronger theoretical guarantees, especially in heterogeneous missing settings.
New method solves group synchronization with cycle-edge message passing.
problem Solving group synchronization with adversarial or uniform corruption and small noise.
method Cycle-edge message passing procedure using cycle consistency information.
result Exact recovery and linear convergence guarantees under adversarial corruption.
The paper improves the empirical bootstrap method for non-normal estimators.
problem Theoretical properties of empirical bootstrap for non-asymptotically normal estimators.
method Establishing limiting distribution, deriving consistency conditions, proposing alternative methods.
result The empirical bootstrap method can be asymptotically consistent under stability conditions.
New algorithm reduces sample complexity for Top Two method.
problem Fixed-confidence best arm identification for Top Two methods.
method UCB-based Top Two algorithm for non-asymptotic analysis.
result First non-asymptotic upper bound on expected sample complexity.
A new method for efficiently estimating Shapley values in dataset valuation.
problem Quantifying the incremental gain of individual datasets in machine learning tasks.
method Discrete uniform Shapley value approximation.
result Proposes a more efficient method for Shapley value estimation.
Classifies 2-uniform maps on torus with formulas and asymptotic bounds.
problem Classifying 2-uniform maps on torus.
method Classification through arithmetic functions and asymptotic analysis.
result Explicit formulas and asymptotic bounds for 2-uniform maps on torus.
Develops privacy-preserving methods for longitudinal linear regression.
problem Protecting individual information in longitudinal data with privacy-preserving statistics.
method Proposes a user-level private regression estimator and a privatized covariance estimator for longitudinal linear regression under user-level differential privacy.
result Establishes theoretical guarantees for practical user-level differential privacy estimation and inference in longitudinal linear regression.
ECCIT improves conditional independence tests by calibrating for miscalibration.
problem Inaccurate frequentist guarantees in CITs, especially in small samples and misspecified models.
method Empirically Calibrated Conditional Independence Tests (ECCIT) that optimize and correct for miscalibration.
result ECCIT achieves valid FDR with higher power than existing calibration strategies.
A new algorithm speeds up rerandomization for better experiment balance.
problem Achieving optimal covariate balance in randomized experiments.
method Metropolis-Hastings framework with sampling-importance resampling.
result PSRSRR achieves significant speedups while maintaining statistical guarantees.
New method for analyzing elliptic and parabolic equations.
problem Analyzing elliptic and parabolic equations.
method Level set version of partial uniform ellipticity.
result Effective approach to investigate equations.
Let Γ<SL2(Z) be a non-elementary finitely generated subgroup and let Γ(q) be its congruence subgroup of level q for each q∈N. We obtain an asymptotic formula for the matrix coefficients of L2(Γ(q)\SL2(R)) with a {\it uniform} exponential error term…
Develops a method to ensure accurate quantile forecasts across multiple levels.
problem Ensuring accurate quantile forecasts at multiple levels, even under distribution shifts.
method Multi-level quantile tracker (MultiQT) wraps around any forecaster to produce calibrated forecasts.
result Guaranteed calibration of quantile forecasts at multiple levels, even against adversarial shifts.
The paper provides guarantees for high-dimensional DML estimators in observational studies.
problem Estimating treatment effects in observational settings with many covariates.
method Debiased machine learning (DML) with finite-sample guarantees.
result Bounding the deviation of finite-sample distribution from asymptotic Gaussian approximation.
The present paper provides a new generic strategy leading to non-asymptotic theoretical guarantees on the Leave-one-Out procedure applied to a broad class of learning algorithms. This strategy relies on two main ingredients: the new notion of Lq stability, and the strong use of moment inequalities. Lq stability e…
Guarantees uniform convergence for square-root Lipschitz losses.
problem Uniform convergence guarantees for square-root Lipschitz losses.
method Using Rademacher complexity and square root of scalar loss function Lipschitz constant.
result Generalizes previous results and handles non-smooth loss functions.
Study tests uniformity of categorical data against missing-ball alternatives, finding chi-squared test outperforms.
problem Testing uniformity of categorical data against missing-ball alternatives.
method Characterizes minimax risk, uses collisions and chi-squared test, reduces to structured subset of alternatives.
result Minimax test outperforms chi-squared test under least favorable alternative.
Semiparametric method removes bias in functional bilevel gradient estimation.
problem First-order bias in plug-in hypergradient when lower-level problem is nonparametric.
method Semiparametric debiasing theory based on efficient influence function leads to cross-fitted orthogonal hypergradient estimator.
result Asymptotic normality and uniform control over outer parameter established for the estimator.
Develops uniform convergence guarantees for a broad class of risk functionals in supervised learning.
problem Bounding generalization gaps for various risk functionals beyond the expectation.
method Establishes uniform convergence for Hölder risk functionals, providing guarantees for empirical risk minimization.
result First uniform convergence results for estimating the CDF of loss distributions, applicable to various risk functionals.
This paper addresses error bounds and posterior variance for Gaussian process regression.
problem Deriving performance guarantees for Gaussian process regression without prior knowledge.
method Lipschitz continuity and analysis of posterior variance function.
result Uniform error bounds for Gaussian process regression are derived.
A debiasing method improves nonparametric regression's statistical properties.
problem Lack of theoretical guarantees for modern nonparametric regression methods.
method Model-free debiasing method incorporating a correction term.
result Debiased estimator satisfies pointwise and uniform risk convergence, asymptotic normality.
The paper provides Gaussian approximations for decentralized Federated Learning.
problem Lack of asymptotic statistical guarantees for local SGD in Federated Learning.
method Two generalized Gaussian approximation results for local SGD trajectories.
result Valid multiplier bootstrap procedures and Gaussian bootstrap-based tests for detecting adversarial attacks.
New sampling bounds improve uniform coverage verification in machine learning.
problem Conservative bounds in classical coverage analyses at small failure probabilities.
method Variance-based analysis of uniform random sampling on a d-dimensional unit hypercube. result Sample complexity bound with logarithmic dependence on failure probability.
Develops Aleksandrov reflection for hyperbolic flows, proving convergence to umbilic surfaces.
problem Analyzing geometric flows in hyperbolic spaces.
method Aleksandrov reflection framework applied to level-set formulation, with graphical and Lipschitz estimates.
result Solutions converge exponentially fast to an umbilic hypersurface at infinity.
The paper analyzes systemic risk in an insurance model with multiple business lines and heterogeneous claims.
problem Analyzing systemic risk in a multi-dimensional insurance model with heterogeneous claims.
method A multi-dimensional Lévy process-based renewal risk model with pairwise asymptotic independence (PAI).
result Asymptotic formulas for tail probabilities and systemic risk measures are derived.
Near-optimal tests and confidence sequences for non-parametric data.
problem Flexible statistical inference and decision-making with non-parametric data.
method Classic delayed-start normal-mixture sequential probability ratio tests with asymptotic guarantees.
result Asymptotically optimal type-I error and expected rejection time guarantees.
Unified stopping rules ensure accurate policies in contextual learning.
problem Stopping data collection to ensure accurate policies in personalized decision problems.
method Developed unified stopping rules based on GLR statistics for pairwise action comparisons.
result Unified stopping rules achieve target precision with fewer samples than benchmarks.
New method learns nonlinear systems from single finite trajectory samples.
problem Learning stabilizable nonlinear systems from single finite trajectory samples.
method Gradient-based algorithms with noise-sensitive uniform convergence guarantees.
result Efficient learning of general nonlinear systems with high accuracy and small sample complexity.
In this paper, we study the asymptotic behavior of the volume of spheres in metric measure spaces. We first introduce a general setting adapted to the study of asymptotic isoperimetry in a general class of metric measure spaces. We then introduce a notion of "being asymptotically isoperimetric" for a family of finite a…
MPNN improves on UniFL approximation with provable guarantees.
problem Uniform Facility Location (UniFL) optimization problem.
method Graph Neural Network (MPNN) incorporating approximation-algorithmic principles.
result Empirically outperforms standard approximation algorithms.
We study the constrained linear quadratic regulator with unknown dynamics, addressing the tension between safety and exploration in data-driven control techniques. We present a framework which allows for system identification through persistent excitation, while maintaining safety by guaranteeing the satisfaction of st…
New framework improves learning across multiple distributions.
problem Modeling uncertainty in sensitive machine learning applications.
method Inspired by multi-armed bandits, provides distribution-dependent guarantees.
result Enhanced dependence on suboptimality gaps and sample size.
Tests for overfitting in machine learning models.
problem Overfitting in high complexity models.
method Hypothesis test using concentration bounds.
result Valid test for identifying overfitting.
Uniformity and proximity are two different ways for defining small scale structures on a set. Coarse structures are large scale counterparts of uniform structures. In this paper, motivated by the definition of proximity, we develop the concept of asymptotic resemblance as a relation between subsets of a set to define a…
We study the spherical cap packing problem with a probabilistic approach. Such probabilistic considerations result in an asymptotic sharp universal uniform bound on the maximal inner product between any set of unit vectors and a stochastically independent uniformly distributed unit vector. When the set of unit vectors …
Study problem-dependent rates in statistical learning theory, achieving optimal generalization error bounds.
problem Generalization error in statistical learning theory.
method Uniform localized convergence framework.
result Optimal generalization error bounds for various learning problems.
Statistical performance bounds for reinforcement learning (RL) algorithms can be critical for high-stakes applications like healthcare. This paper introduces a new framework for theoretically measuring the performance of such algorithms called Uniform-PAC, which is a strengthening of the classical Probably Approximatel…
This paper sharpens privacy guarantees for high-dimensional PCA under differential privacy.
problem Understanding the exact privacy loss in high-dimensional PCA with differential privacy.
method Analyzes the exponential mechanism in a model-free setting for high-dimensional PCA.
result Sharp utility and privacy characterizations in high dimensions show the difficulty of detecting a target individual's presence.