Estimates barycenter in geodesic spaces with finite sample bounds.
problem Estimating the barycenter of a distribution in geodesic spaces.
method Finite sample error bounds, Hoeffding- and Bernstein-type concentration inequalities, efficient algorithms.
result Statistical guarantees for efficient barycenter computation.
Unified framework for finite-sample RL algorithms using Lyapunov theory.
problem Finite-sample convergence guarantees of asynchronous RL algorithms.
method Reformulate RL algorithms as Markovian SA, develop Lyapunov analysis.
result Mean-square error bounds and convergence for various RL algorithms.
The paper analyzes GTD algorithms with finite-sample bounds.
problem Convergence rate analysis of GTD family of algorithms.
method Formulated as stochastic gradient algorithms and analyzed using saddle-point error.
result Obtained finite-sample bounds on GTD performance.
Kernel smoothing on unknown manifolds with bounds and asymptotic normality.
problem Data on unknown manifolds without boundaries.
method Finite sample bounds and asymptotic normality for kernel smoothing and its derivatives.
result Established finite sample bounds and asymptotic normality for kernel smoothing.
The paper analyzes off-policy TD-learning using generalized Bellman operators and provides finite-sample bounds.
problem High variance in off-policy TD-learning due to importance sampling.
method Derives finite-sample bounds for off-policy TD-like algorithms using generalized Bellman operators.
result First-known finite-sample guarantees for several off-policy TD algorithms.
Efficiently learns polytrees with known skeleton in polynomial time and sample complexity.
problem Learning polytrees with known skeleton structure.
method Proposes an efficient algorithm for learning d d d -polytrees in polynomial time and sample complexity when the skeleton is known. result Establishes finite-sample guarantees for efficient learning of d d d -polytrees. The study tightens bounds on binomial probabilities and minimums using KL-divergence.
problem Tightening bounds on binomial probabilities and minimums of i.i.d. Binomials.
method Applied Sanov's theorem to derive upper and lower bounds on binomial tail probabilities and minimums, expressed in terms of KL-divergence.
result High probability upper and lower bounds on the minimum of i.i.d. Binomial random variables, finite sample, asymptotically tight.
Paper analyzes PSGLD for adaptive IRL with finite-sample bounds.
problem Estimating cost function of a forward learner using noisy gradients.
method Passive stochastic gradient Langevin dynamics (PSGLD) algorithm.
result Explicit bounds on 2-Wasserstein distance between PSGLD sample measure and stationary measure.
The MDL two-part coding index of resolvability \textit{index of resolvability} index of resolvability provides a finite-sample upper bound on the statistical risk of penalized likelihood estimators over countable models. However, the bound does not apply to unpenalized maximum likelihood estimation or procedures with exceedingly small penalties. In this paper,…
New bounds for SMC show its advantage over MCMC in multimodal distributions.
problem Estimating expectations under multimodal distributions with slow global mixing.
method Proves finite sample complexities for SMC with local mixing times, addressing bias through sequential resampling.
result SMC provides fully polynomial time approximation for multimodal problems.
We improve maximum likelihood for location estimation in finite samples.
problem Estimating a parameter from samples with unknown or varying distribution.
method Use smoothed Fisher information for finite sample size and varying distributions.
result Recover optimal estimation theory for finite n n n and arbitrary f f f . Study bounds variance modulation function for K-spider distributions.
problem Bounding variance modulation function for K-spider distributions.
method Used folded moments and total probabilities of spider legs.
result Gave an interval for the variance modulation function.
New bounds show current methods overestimate system parameter errors.
problem Current bounds overestimate parameter errors in system identification.
method Utilized asymptotic normality and second-order decomposition.
result Obtained finite-sample bounds matching optimal rates up to constants.
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.
The paper introduces a frequency-domain estimator for low-order systems from noisy data.
problem Estimating frequency responses of low-order systems from noisy measurements.
method Uses a quadratic data-fitting term regularized by the nuclear norm of a Loewner matrix, subject to a convex stability constraint.
result Proves a finite-sample error bound and extends it to all frequencies through rational interpolation.
This study analyzes LTS in sparse models with finite sample error bounds.
problem Robust regression in high-dimensional sparse models with limited data.
method Non-asymptotic analysis of LTS error bounds.
result Established finite sample error bounds for LTS in sparse models.
This study examines biases in flow matching samplers using finite-sample estimation.
problem Biases in flow matching samplers when using finite-sample surrogates.
method Finite-sample plug-in estimation and hierarchy of empirical FM models.
result Exact empirical minimizer and smoothed plug-in regime identified for affine conditional flows.
Estimating entropy and mutual information consistently is important for many machine learning applications. The Kozachenko-Leonenko (KL) estimator (Kozachenko & Leonenko, 1987) is a widely used nonparametric estimator for the entropy of multivariate continuous random variables, as well as the basis of the mutual inform…
Paper analyzes online tensorial ICA convergence with stochastic approximation.
problem Online tensorial ICA convergence analysis.
method Stochastic approximation for nonconvex optimization.
result Sharp finite-sample error bound of O ~ ( d / T ) \tilde{O}(\sqrt{d/T}) O ~ ( d / T ) . The paper shows how to learn causal representations with few environments and finite samples.
problem Learning causal representations from limited data and environments.
method Explicit, finite-sample guarantees with a logarithmic number of interventions.
result Consistent recovery of latent causal graph, mixing matrix, and unknown intervention targets.
New bounds for score matching in polynomial exponential families.
problem Understanding the sample complexity of score matching for polynomial exponential families.
method Non-asymptotic sample complexity analysis for score matching.
result First finite sample bounds for score matching in polynomial exponential families.
In Bayesian inference, the posterior distributions are difficult to obtain analytically for complex models such as neural networks. Variational inference usually uses a parametric distribution for approximation, from which we can easily draw samples. Recently discrete approximation by particles has attracted attention …
The study sets lower bounds on MMSE for inferring sensitive features from noisy data.
problem Estimating sensitive features from noisy observations of correlated features.
method Adversarial evaluation framework based on MMSE estimation with theoretical lower bounds.
result Derives closed-form bounds for linear models, showing optimality in noise variance.
New algorithm detects changes in heavy-tailed data streams.
problem Detecting changes in heavy-tailed data streams.
method Clipped Stochastic Gradient Descent (SGD) combined with union bound.
result First algorithm with finite-sample false-positive rate guarantees for heavy-tailed data.
Detect changes in noisy dynamical systems using empirical approximations and finite-sample bounds.
problem Change detection in noisy dynamical systems
method Partition-based empirical approximations and finite-state stationary distribution stability
result Finite-sample bound for empirical stationary density
End-to-end algorithm for controlling bilinear systems with probabilistic noise.
problem Controlling bilinear systems with noisy data.
method Proposes an end-to-end algorithm using statistical learning theory and robust controller design.
result Derived finite sample identification error bounds and structurally suitable for control.
In reinforcement learning (RL) , one of the key components is policy evaluation, which aims to estimate the value function (i.e., expected long-term accumulated reward) of a policy. With a good policy evaluation method, the RL algorithms will estimate the value function more accurately and find a better policy. When th…
Despite the increasing interest in multi-agent reinforcement learning (MARL) in multiple communities, understanding its theoretical foundation has long been recognized as a challenging problem. In this work, we address this problem by providing a finite-sample analysis for decentralized batch MARL with networked agents…
Principal component analysis (PCA) has been a prominent tool for high-dimensional data analysis. Online algorithms that estimate the principal component by processing streaming data are of tremendous practical and theoretical interests. Despite its rich applications, theoretical convergence analysis remains largely ope…
Sparse feature selection improves batch RL efficiency.
problem High-dimensional batch RL with many features.
method Sparse linear function approximation, Lasso, group Lasso, fitted Q-evaluation, fitted Q-iteration.
result Sparse feature selection makes batch RL more sample efficient.
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 methods for estimating causal effects with limited overlap, using Stable Probability Weighting.
problem Estimating causal effects with limited overlap in multivalued treatments.
method Stable Probability Weighting (SPW) and Finite-Sample Stable Probability Weighting (FPW) methods.
result SPW and FPW provide practical solutions for estimating and inferring causal effects with limited overlap.
Unified bounds for iterative algorithms with Gaussian data matrices.
problem Establishing non-asymptotic bounds for iterative algorithms with Gaussian data.
method Explicit coupling between iterates and Gaussian process with deterministic covariance.
result Tight, dimension-free bounds for generalized first-order methods.
Study shows DQN's performance degrades with temporal dependence in data.
problem Temporal dependence in replayed data affects DQN's performance.
method Modelled τ τ τ -mixing data, derived risk bounds, and empirical validation. result Temporal dependence leads to a degradation in DQN's performance rate.
MF-TRPO optimizes MFGs with finite sample guarantees.
problem Computing approximate Nash equilibria in MFGs.
method Extends TRPO to MFGs, providing convergence guarantees.
result Theoretical guarantees on MF-TRPO's convergence.
FQE with deep neural networks achieves asymptotic normality and finite-sample bounds.
problem Theoretical understanding of FQE with general differentiable function approximators.
method Z-estimation theory applied to FQE with deep neural networks.
result FQE estimation error is asymptotically normal with explicit variance.
Researchers study fairness-accuracy tradeoffs in predictive models for multiple groups.
problem Understanding the tradeoff between fairness and accuracy in models serving multiple demographic groups.
method Characterizing the fairness-accuracy (FA) Pareto frontier, approximating it from limited data, and bounding the worst-case gap.
result Derivation of worst-case-optimal estimators and uniform finite-sample bounds for the entire FA frontier.
Develops a method to detect changes in linear systems with temporal correlations.
problem Detect abrupt changes in time series data with temporal correlations.
method Data-dependent threshold for online change point detection in linear dynamical systems.
result Achieves a pre-specified upper bound on the probability of false alarms and provides a finite-sample-based bound for detection probability.
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.
We identify linear models from nonlinear systems with initialization constraints.
problem Identifying linear models from nonlinear systems with initialization constraints.
method Multiple trajectories-based deterministic data acquisition algorithm followed by regularized least squares.
result We provide a finite sample error bound on the learned linearized dynamics.
Optimal sparse recovery with decision stumps achieves strong feature selection guarantees.
problem Sparse recovery of active features from high-dimensional data.
method Analysis of single-depth decision trees (decision stumps) for feature selection in linear regression.
result Tight sample performance guarantees for O ( s log p ) O(s \log p) O ( s log p ) , improving upon previous bounds. 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.
New framework improves EM algorithm convergence under log-Sobolev inequality.
problem Improving convergence of the EM algorithm.
method Extending gradient flow techniques to EM algorithm, using free energy representation.
result Exponential convergence of EM algorithm under log-Sobolev inequality.
We introduce a simulation method for dynamic portfolio valuation and risk management building on machine learning with kernels. We learn the dynamic value process of a portfolio from a finite sample of its cumulative cash flow. The learned value process is given in closed form thanks to a suitable choice of the kernel.…
This work analyzes tree-based methods from a ranking perspective, providing insights and new statistics.
problem Understanding the effectiveness of tree-based methods in finite-sample settings, especially symbolic feature selection.
method Local ranking perspective, finite-sample analysis, oracle bounds, posterior contraction results, concordant divergence statistics.
result New insights and statistics for evaluating symbolic feature mappings.
A neural framework corrects bias in estimating individual treatment effects.
problem Estimating individual treatment effects from observational data.
method An anchored neural architecture and precision-corrected intersection-bound inference.
result Corrected bias and maintained nominal coverage in high-dimensional settings.
We learn linear models from nonlinear systems using multiple trajectories and regularization.
problem Identifying linear models from data when the underlying dynamics are nonlinear.
method Multiple trajectories data acquisition followed by regularized least squares.
result Learn linearized dynamics with arbitrarily small error given enough samples.
Kernelized convex clustering handles non-linear and non-convex data.
problem Lack of effective clustering methods for non-linear and non-convex data.
method Kernelized convex clustering in RKHS.
result Superior performance compared to state-of-the-art techniques.