The paper studies reward concentration in MDPs, covering asymptotic and non-asymptotic settings.
problem Reward concentration in Markov Decision Processes (MDPs).
method Unified approach to reward concentration in MDPs, including asymptotic and non-asymptotic bounds.
result Rate-equivalent definitions of regret for learning policies.
Study on stochastic approximation with Polyak-Ruppert averaging for linear systems.
problem Understanding the asymptotic and non-asymptotic properties of stochastic approximation procedures.
method Detailed analysis of linear stochastic approximation with Polyak-Ruppert averaging, focusing on asymptotic and non-asymptotic properties.
result Proves CLT and non-asymptotic concentration inequality for averaged iterates, providing refined understanding of linear stochastic approximation.
Paper simplifies concentration inequalities for easier probabilistic analysis.
problem Complexity in probabilistic analysis of random variables.
method Compact notations for concentration inequalities.
result Simplified expressions for typical sizes and tails of random variables.
Prove non-asymptotic bounds for minimal risk in statistical learning
problem Estimating minimal risk in statistical learning
method Using concentration inequalities
result Non-asymptotic bounds for minimal risk
New method tightens sub-Gaussian concentration inequalities.
problem Estimating variance-type parameters of sub-Gaussian distributions.
method Using sub-Gaussian intrinsic moment norm to maximize normalized moments.
result Provides tighter sub-Gaussian concentration inequalities.
The paper reviews and improves concentration inequalities for statistical inference.
problem Analyzing statistical inference in various settings with high-dimensional data.
method Review and improvement of concentration inequalities for different types of random variables and statistical measures.
result Fresh new results and improved bounds with sharper constants.
A new matrix concentration inequality for random products of matrices.
problem Understanding the behavior of random matrix products under bounded independent positive semidefinite matrices.
method Developed a non-asymptotic concentration inequality for the product of matrices.
result The inequality provides a bound on the deviation of the matrix product from its expected value.
The paper provides a finite-sample deviation bound for stable autoregressive processes.
problem Deviation bounds for least squares estimators in Gaussian AR(n) processes.
method Utilizes martingale concentration inequalities and tail-bound for χ² distributed variables.
result Problem-dependent finite-time bound on the deviation probability of AR(n) process parameters.
The paper extends Hoeffding's inequality for Markov chains using a generalized concentrability condition.
problem Applying Hoeffding's inequality to non-ergodic Markov chains.
method Integrates generalized concentrability condition via IPM to extend traditional hypotheses.
result Demonstrates utility in machine learning applications such as empirical risk minimization and bandits.
Paper develops bounds for stochastic approximation with averaging.
problem Establish high-probability bounds for averaged stochastic approximation.
method Develops a general framework for non-asymptotic concentration bounds.
result Derives sharp bounds for averaged iterates and tightens existing results.
The paper proves a non-asymptotic test error approximation for KRR.
problem Understanding the test error of Kernel Ridge Regression.
method Established a non-asymptotic deterministic approximation for test error of KRR.
result The test error of KRR can be approximated by a closed-form estimate derived from the spectrum of the kernel operator.
Study non-asymptotic estimation bounds for LTI models with Gaussian noise.
problem Estimating parameters of LTI models with non-asymptotic error bounds.
method Sharp non-asymptotic lower bounds using Cramér-Rao and van Trees inequalities, concentration results, and differential geometric constructions.
result Sharp and rate-optimal lower bounds for mean square estimation risk.
Study optimizes prediction error for growing-dimensional PFLM models.
problem Optimizing prediction error for growing-dimensional PFLM models.
method Penalized least-squares approach in RKHS with effective dimension consideration.
result Shows exact upper bound for excess prediction risk in non-asymptotic form.
We study the non-asymptotic behavior of a Coulomb gas on a compact Riemannian manifold. This gas is a symmetric n-particle Gibbs measure associated to the two-body interaction energy given by the Green function. We encode such a particle system by using an empirical measure. Our main result is a concentration inequalit…
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.
Improved concentration inequalities for sub-Weibull variables enhance statistical and machine learning applications.
problem Improving concentration inequalities for sub-Weibull random variables.
method Developed new concentration inequalities for sums of independent sub-Weibull random variables, including a new sub-Weibull parameter.
result New concentration inequalities with sharper constants and a mixture of sub-Gaussian and sub-Weibull tails.
This work establishes always-valid risk bounds for online matrix completion.
problem Challenges in establishing always-valid concentration inequalities for online matrix completion.
method Combines non-asymptotic martingale concentration and regularized low-rank matrix regression.
result Establishes always-valid risk bound process for online matrix completion.
This work develops confidence intervals for off-policy evaluation.
problem Estimating expected reward with uncertainty quantification.
method Primal-dual optimization with kernel Bellman loss and martingale concentration inequality.
result Developed practical algorithm for non-asymptotic confidence intervals.
SGD converges to an invariant distribution with sub-Gaussian or sub-exponential properties.
problem Optimizing smooth and strongly convex objectives using SGD.
method Analysis through Markov chains, focusing on convergence and concentration properties.
result SGD iterates and their invariant limit distribution inherit sub-Gaussian or sub-exponential concentration properties.
The paper advances U-statistics in dependent settings, improving spectral estimation and goodness-of-fit tests.
problem Non-asymptotic analysis of U-statistics in dependent Markov chain settings.
method Proved new concentration and exponential inequalities for U-statistics, applied to spectral estimation, online algorithms, and goodness-of-fit tests.
result Established new results for spectral estimation, online algorithms, and goodness-of-fit tests in Markov chain settings.
Paper improves learning efficiency by focusing on effective dimensionality.
problem Dimensionality bottleneck in modern learning tasks.
method Developed tools to reduce dimensional costs using effective dimensionality.
result Uniform concentration bounds involving effective dimensionality, improving over existing results.
We develop a probabilistic framework for sequential random projection.
problem Challenges of sequential decision-making under uncertainty.
method Novel construction of a stopped process and method of mixtures.
result Achieved a non-asymptotic probability bound for random projection.
Study non-asymptotic bounds on correlation in high-dimensional linear systems, revealing invariant subspaces and bottlenecks.
problem Understanding correlation and mixing in high-dimensional linear systems with Gaussian noise.
method Sampling from sub-trajectories, using Talagrand's inequality, and analyzing invariant subspaces.
result Large discrepancy between algebraic and geometric multiplicity leads to bottlenecks between invariant subspaces.
The asymptotic concentration of the Fr{é}chet mean of IID random variables on a Rieman-nian manifold was established with a central limit theorem by Bhattacharya \& Patrangenaru (BP-CLT) [6]. This asymptotic result shows that the Fr{é}chet mean behaves almost as the usual Euclidean case for sufficiently concentrated di…
How many samples are sufficient to guarantee that the eigenvectors and eigenvalues of the sample covariance matrix are close to those of the actual covariance matrix? For a wide family of distributions, including distributions with finite second moment and distributions supported in a centered Euclidean ball, we prove …
Sharp concentration inequalities for sub-Orlicz random variables with phase transition at α=2.
problem Developing concentration inequalities for sub-Orlicz random variables with phase transition.
method New theoretical analysis framework involving variance and min/max functions of Orlicz tails.
result Sharp concentration inequalities with phase transition at α=2 for sub-Orlicz random variables.
The paper improves count data regression models for overdispersed data.
problem Improving regression models for overdispersed count data.
method Double ℓ1-regularized negative binomial regressions. result Oracle inequalities and consistency for Lasso estimators of partial regression coefficients.
We find a deterministic equivalent for random feature regression's test error, independent of feature map dimension.
problem Understanding the generalization performance of random feature ridge regression.
method We derive a deterministic equivalent for the test error of RFRR under a concentration property, showing it can be approximated by a closed-form expression dependent on feature map eigenvalues.
result Our approximation guarantee is non-asymptotic, multiplicative, and independent of the feature map dimension, providing a tight result for the smallest number of features achieving optimal minimax error rate.
The paper analyzes data augmentation for precision matrix estimation in high dimensions.
problem Precision matrix estimation in high-dimensional settings.
method Linear shrinkage estimators and data augmentation methods.
result Concentration bounds for the quadratic error of estimators.
We study the problem of cooperative inference where a group of agents interact over a network and seek to estimate a joint parameter that best explains a set of observations. Agents do not know the network topology or the observations of other agents. We explore a variational interpretation of the Bayesian posterior de…
We develop a new approach to learn the parameters of regression models with hidden variables. In a nutshell, we estimate the gradient of the regression function at a set of random points, and cluster the estimated gradients. The centers of the clusters are used as estimates for the parameters of hidden units. We justif…
Unified framework for studying softmax attention under large prompts.
problem Challenges in theoretical analysis of softmax attention.
method Measure-based framework for finite and infinite prompts.
result Softmax attention converges to linear attention in the large-prompt regime.
In this paper, we propose a general framework for sparse and low-rank tensor estimation from cubic sketchings. A two-stage non-convex implementation is developed based on sparse tensor decomposition and thresholded gradient descent, which ensures exact recovery in the noiseless case and stable recovery in the noisy cas…
Quantum ML predicts data with improved speed and accuracy.
problem Predicting data using maximum likelihood in a quantum setting.
method Quantum states embedding and minimization of quantum relative entropy.
result Unified framework for classical and quantum LLMs with performance guarantees.
Bayesian nonparametric models get better posterior estimates via SPDE methods.
problem Estimating posterior distributions in nonparametric Bayesian models.
method Extending diffusion methods to SPDEs on Hilbert spaces for posterior contraction and Laplace approximation.
result Derivation of posterior contraction rates and finite-sample Bernstein von Mises results.
The study provides error bounds for the generalized Lasso with sub-exponential data.
problem Analyzing the generalized Lasso under sub-exponential data distributions.
method Non-asymptotic analysis using generic chaining-based proof strategy.
result Error bounds for the generalized Lasso can be controlled by two complexity parameters.
We consider a distributed learning setup where a network of agents sequentially access realizations of a set of random variables with unknown distributions. The network objective is to find a parametrized distribution that best describes their joint observations in the sense of the Kullback-Leibler divergence. Apart fr…
Paper proposes a new dynamic pricing method with always-valid online statistical learning.
problem Designing dynamic pricing policies that adapt to online uncertainty and maintain validity.
method Regularized online statistical learning with theoretical guarantees and three major advantages.
result Proposed OORMLP pricing policy secures logarithmic regret in decision horizon.
Study shows RFRR's effectiveness with nearly orthogonal data in overparameterized settings.
problem Understanding the effectiveness of random feature regression with nearly orthogonal data.
method Investigates RFRR with nearly orthogonal deterministic unit-length input data vectors in the overparameterized regime.
result Shows high-probability non-asymptotic concentration results for RFRR's training, cross-validation, and generalization errors.
Algorithm learns linear systems from partial observations with near-optimal rate.
problem Identifying linear dynamical systems from partial observations, especially those with long-term memory.
method Multi-scale low-rank approximation using SVD on Hankel matrices of increasing sizes, combined with Fourier domain concentration bounds.
result Near-optimal rate of $\widetilde O\left(\sqrt\frac{d}{T}
ight)$ in H2 error, with logarithmic dependence on memory length. Study nearest-neighbor radii under dependent sampling, finding they remain informative.
problem Analyzing nearest-neighbor radii under dependent sampling.
method Consider strong mixing dependent observations, establish distribution-free almost sure convergence and sharp non-asymptotic moment bounds.
result Nearest-neighbor geometry remains informative under dependence sampling.
Study the limits of discrete DPPs to continuous DPPs as set size grows.
problem Characterize the behavior of discrete DPPs as they approach continuous DPPs.
method Non-asymptotic characterization of the limit in terms of weak coherency.
result Sufficient conditions for weak coherency are identified.
We provide non-asymptotic bounds for the well-known temporal difference learning algorithm TD(0) with linear function approximators. These include high-probability bounds as well as bounds in expectation. Our analysis suggests that a step-size inversely proportional to the number of iterations cannot guarantee optimal …
Develops a framework for inferring causal relationships in networked data with uncertainty quantification.
problem Extracting reliable inference from complex Hawkes network data with uncertainty.
method Statistical inference framework based on maximum likelihood estimation and concentration inequalities of continuous-time martingales.
result Provides a non-asymptotic confidence set for uncertainty quantification.
DE-PSGLD samples from constrained distributions in a decentralized manner.
problem Sampling from log-concave distributions with constraints.
method Decentralized Proximal Stochastic Gradient Langevin Dynamics with proximal regularization.
result DE-PSGLD converges to a regularized Gibbs distribution and maintains posterior concentration.
ZDP detects drift in large language models without labels, proving key theorems and metrics.
problem Detecting drift in large language models without task labels or output evaluations.
method Zero-Direction Probing (ZDP) framework based on null directions of transformer activations, proving theoretical guarantees.
result Proves the Variance--Leak Theorem, Fisher Null-Conservation, Rank--Leak bound, and logarithmic-regret guarantee.
This review examines bandit problems in AI using statistical methods.
problem Sequential decision-making under uncertainty in AI environments.
method Foundational models, concentration inequalities, minimax regret bounds, frequentist and Bayesian algorithms, K-armed contextual bandits, SCAB, functional data analysis.
result Exploration-exploitation trade-offs and regret analyses in various bandit problems.
Develops a new method for uncertainty quantification in high-dimensional learning.
problem Challenges in uncertainty quantification in high-dimensional regression or learning problems.
method Data-driven approach for UQ that corrects bias terms from training data.
result Non-asymptotic confidence intervals that avoid overestimating uncertainty.