VRPG algorithm optimizes convex constraints with non-asymptotic guarantees.
problem Stochastic convex optimization under convex constraints.
method Natural variance reduced proximal gradient (VRPG) algorithm.
result VRPG achieves local minimax lower bound up to constants and log factor of N N N . Paper provides exponential convergence guarantees for Iterative Markovian Fitting.
problem Addressing the Schrödinger Bridge problem in computational optimal transport and generative modeling.
method Develops non-asymptotic exponential convergence guarantees for Iterative Markovian Fitting.
result First non-asymptotic exponential convergence guarantees for IMF under mild structural assumptions.
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.
Novel framework for uncertainty quantification in metric spaces.
problem Uncertainty quantification in regression models with metric responses.
method Developed algorithms for large datasets, agnostic to predictive models, with asymptotic and non-asymptotic guarantees.
result Asymptotic and non-asymptotic guarantees for special cases, demonstrated in clinical applications.
Normal distributions ensure asymptotic variance reduction in moment matching Monte Carlo.
problem Asymptotic variance reduction in general integration problems.
method Characterization of conditions for asymptotic variance reduction using normal distributions.
result Asymptotic variance reduction is guaranteed for normal distributions in moment matching Monte Carlo.
This paper provides performance guarantees for neural estimation of statistical distances.
problem Developing performance guarantees for neural estimation of statistical distances.
method Non-asymptotic error bounds using function approximation theorems and empirical process theory.
result Established a fundamental tradeoff between approximation and estimation errors in neural estimation of statistical distances.
Study non-asymptotic BPI guarantees for online RL.
problem Identify optimal policy in MDP with high confidence.
method Non-asymptotic sample complexity guarantees for NaS algorithm.
result Sample complexity depends on MDP connectivity and curvature.
New method predicts sets under unknown covariate shift with high confidence.
problem Adapting to unknown covariate shift in prediction sets.
method PredSet-1Step, a flexible distribution-free method.
result Achieves asymptotic probably approximately correct coverage.
New algorithm achieves instance-optimality in decision making.
problem Develop adaptive algorithms for interactive decision making.
method Introduce Allocation-Estimation Coefficient (AEC) and develop A E 2 \mathsf{AE}^2 AE 2 algorithm. result First non-asymptotic instance-optimal performance guarantees.
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.
LPCI provides valid prediction intervals for longitudinal data.
problem Current conformal prediction methods for time series data lack cross-sectional coverage when applied to longitudinal datasets.
method Modeling residual data as a quantile fixed-effects regression problem, constructing prediction intervals with a trained quantile regressor.
result LPCI achieves valid cross-sectional coverage and outperforms existing benchmarks in terms of longitudinal coverage rates.
Paper derives convergence rates and confidence intervals for LSA with Markovian noise.
problem Analyzing convergence rates and constructing confidence intervals for LSA with Markovian noise.
method Derives non-asymptotic Berry-Esseen bounds and multiplier block bootstrap procedure.
result Provides O ( n − 1 / 4 ) \mathcal{O}(n^{-1/4}) O ( n − 1/4 ) convergence rates and guarantees consistent inference. Minimum Description Length prevents overfitting in noisy data.
problem Learning from noisy data with overfitting risk.
method Minimum Description Length learning rule with tempered guarantees.
result Tempered agnostic finite sample learning guarantees and asymptotic behavior characterization.
New quasi-Newton method guarantees global superlinear convergence.
problem Global convergence and superlinear convergence of quasi-Newton methods.
method Hybrid proximal extragradient method with online learning for Hessian approximation.
result First globally convergent quasi-Newton method with explicit superlinear convergence rate.
Bayesian model explains and improves black-box estimators for class distribution.
problem Calibrating probabilistic classifiers and uncertainty quantification for unlabeled data.
method Introduced a Bayesian model approximating the ground-truth generative process, using efficient MCMC sampling.
result The Bayesian model is competitive and sometimes superior to established point estimators.
Improved mean estimation for symmetric distributions with finite-sample guarantees.
problem Estimating the mean of a symmetric distribution from samples.
method Using Fisher information rate for finite-sample guarantees.
result Finite-sample convergence close to subgaussian with variance 1/(n * I_r), where I_r is r-smoothed Fisher information.
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.
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.
Extracting actionable intelligence from distributed, heterogeneous, correlated and high-dimensional data sources requires run-time processing and learning both locally and globally. In the last decade, a large number of meta-learning techniques have been proposed in which local learners make online predictions based on…
Two new algorithms recover ridge lines from point clouds with convergence guarantees.
problem Extracting filamentary structure from point clouds.
method Proposes two novel algorithms with convergence guarantees.
result The algorithms can asymptotically recover the full ridge set.
Unified framework for response-adaptive targeting in multi-treatment experiments
problem Improving ethical and statistical efficiency in multi-treatment clinical trials
method Response-adaptive targeting strategies
result Unified framework for α α α -Rebalancing Targeting Strategies ( α α α RTS) COPP provides reliable intervals for outcomes under a new policy in contextual bandits.
problem Lack of reliable predictive intervals for outcomes under a new policy in contextual bandits.
method Conformal prediction applied to contextual bandits.
result COPP provides finite-sample guarantees without additional assumptions.
The paper develops a method to create non-asymptotic confidence ellipsoids for linear regression without strong noise distribution assumptions.
problem Constructing reliable confidence regions for linear regression with finite sample sizes and general noise distributions.
method The paper introduces the SPS EOA algorithm to create non-asymptotically guaranteed confidence ellipsoids for linear regression problems.
result The sizes of SPS outer ellipsoids are shown to decrease at the optimal rate for linear regression problems.
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.
Study guarantees convergence of mean shift mode estimation.
problem Ensuring reliable mode estimation in KDE using mean shift.
method Utilizes Łojasiewicz inequality to prove convergence rate.
result Extends convergence guarantees to biweight kernel.
kTULA improves sampling from distributions with super-linear log-gradients.
problem Sampling from distributions with super-linearly growing log-gradients in deep learning.
method kTULA: tamed Langevin dynamics algorithm with KL divergence guarantee.
result Improved KL divergence convergence rate of 2- ε ‾ \overlineε ε . 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.
New IRL algorithm identifies optimal reward and policy from expert demonstrations.
problem Understanding reward functions from expert demonstrations with neural networks.
method Two-timescale single-loop IRL algorithm for neural network parameterized rewards.
result First IRL algorithm with non-asymptotic convergence guarantee and global optimality in neural network settings.
Efficient inference for adaptive data with directional stability condition.
problem Efficient inference on scalar targets after adaptive data collection.
method Introduces directional stability, a weaker condition than i.i.d. data, and shows asymptotic normality and efficiency of estimators.
result Estimators remain asymptotically normal and semiparametrically efficient under directional stability.
The paper analyzes k k k -means clustering for missing data, proving statistical guarantees under MCAR.
problem Statistical guarantees for k k k -means clustering with missing data, especially under Missing Completely at Random (MCAR). method Established n \sqrt{n} n -excess risk bound and consistency of cluster centers under general missing mechanisms; derived n \sqrt{n} n -convergence rate and asymptotic normality for MCAR. result Achieving n \sqrt{n} n -rate and converging to true cluster centers requires distinct true cluster centers in every dimension under MCAR. Stochastic approximation proves asymptotic normality for non-smooth problems.
problem Solving non-smooth stochastic approximation problems.
method Stochastic approximation algorithms for solving smooth equations, extended to non-smooth problems.
result Asymptotic normality and optimality in non-smooth stochastic approximation is proven.
An efficient LDP protocol for QMLE with improved practicality and theoretical guarantees.
problem Difficult implementation of existing LDP QMLE for large-scale surveys.
method Developed an alternative LDP protocol without long waiting time, high communication cost, and derivative boundedness assumptions.
result Sufficient conditions for consistency and asymptotic normality of the protocol.
New variational flows improve Monte Carlo and normalization tasks.
problem Intractable global optimum in expressive variational families.
method Constructing asymptotically exact variational flows from involutive MCMC kernels.
result Provable total variation convergence of new variational families.
Corrects local error estimates for UBU integrator in SDEs, improving complexity guarantees.
problem Improper local error estimates in UBU integrator for SDEs.
method Reconciles theory with practice by correcting local error estimates.
result Stronger assumptions needed for O ( d 1 / 4 ε − 1 / 2 ) \mathcal{O}(d^{1/4}ε^{-1/2}) O ( d 1/4 ε − 1/2 ) steps in Wasserstein-2 distance. Paper provides finite-sample guarantees for Wasserstein DRO without dimensionality curse.
problem Tackles empirical success of Wasserstein DRO in operations and ML with performance guarantees.
method Develops non-asymptotic framework for analyzing out-of-sample performance and generalization bound.
result First finite-sample guarantee for generic Wasserstein DRO problems without curse of dimensionality.
We analyze the practices of reservoir computing in the framework of statistical learning theory. In particular, we derive finite sample upper bounds for the generalization error committed by specific families of reservoir computing systems when processing discrete-time inputs under various hypotheses on their dependenc…
Paper proposes a debiased estimator for adaptive linear regression.
problem Non-normal asymptotic behavior of OLS estimator in adaptive linear regression.
method Adaptive linear estimating equations to construct debiased estimator.
result Established asymptotic normality of the debiased estimator.
Theoretical guarantees for STE, a robust subspace recovery method.
problem Recovering a low-dimensional subspace from corrupted data.
method Subspace-constrained Tyler's estimator (STE) with initialization conditions.
result STE can effectively recover the subspace under certain conditions.
Optimizes MCMC chains with neural control variates.
problem Reducing variance in Markov Chain Monte Carlo (MCMC) simulations.
method Uses neural networks as control variates to minimize asymptotic variance.
result Derives optimal convergence rate under various ergodicity assumptions.
Analyzes learning and applying preconditioners in MCMC for efficiency.
problem Improving efficiency of MCMC algorithms.
method Non-asymptotic analysis of schemes that learn preconditioners.
result Established non-asymptotic guarantees for preconditioned ULA.
We study local complexity measures for stochastic convex optimization problems, providing a local minimax theory analogous to that of Hájek and Le Cam for classical statistical problems. We give complementary optimality results, developing fully online methods that adaptively achieve optimal convergence guarantees. Our…
New algorithm for computing Wasserstein barycenters with guarantees.
problem Computing Wasserstein barycenters with varying regularization strengths.
method Damped Sinkhorn iterations followed by exact maximization/minimization steps.
result First non-asymptotic convergence guarantees for approximating Wasserstein barycenters.
Study optimal and instance-dependent guarantees for solving linear equations with Markovian data.
problem Approximately solving linear fixed point equations with Markovian data.
method Non-asymptotic bounds and instance-dependent characterizations for stochastic approximation.
result Instance-optimality of the averaged SA estimator and matching upper and lower bounds.
Study the mass of flat 3-manifolds with boundary using specific methods.
problem Calculate the mass of asymptotically flat 3-manifolds with boundary.
method Use the method of Bray-Kazaras-Khuri-Stern to derive a mass formula.
result Derive sufficient conditions for the positivity of the mass.
New method for semiparametric bandits reduces regret to optimal levels.
problem Complex reward structures in semiparametric bandits.
method Experimental-design approach with sharp regret bound and PAC bound.
result Minimax regret of i l d e O ( d T ) ilde{O}(\sqrt{dT}) i l d e O ( d T ) and logarithmic regret under positive suboptimality gap. 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.
New statistical methods improve TD learning for policy evaluation.
problem Improving statistical inference for reinforcement learning.
method Polyak-Ruppert averaging, refined high-dimensional Berry-Esseen bounds, online plug-in estimator, asymptotic covariance matrix.
result Guaranteed finite-sample coverage of confidence regions and simultaneous confidence intervals.
Improved shuffling technique amplifies privacy guarantees for anonymous data contributions.
problem Enhancing privacy in systems where data is contributed anonymously.
method Developed a new approach to random shuffling that amplifies differential privacy guarantees.
result Achieved asymptotically optimal privacy amplification with nearly optimal dependence in ε.