We prove non-asymptotic lower bounds on the expectation of the maximum of independent Gaussian variables and the expectation of the maximum of 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 (…
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48 results for “Non-Asymptotic Bounds”
Recent works have derived non-asymptotic upper bounds for convergence of underdamped Langevin MCMC. We revisit these bound and consider introducing scaling terms in the underlying underdamped Langevin equation. In particular, we provide conditions under which an appropriate scaling allows to improve the error bounds in…
Non asymptotic estimation lower bounds for LTI state space models with Cramér-Rao and van Treesmath.ST
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.
Off-policy estimation of linear functionals: Non-asymptotic theory for semi-parametric efficiencymath.ST
The paper analyzes methods for estimating linear functionals from observational data, proving upper bounds and showing optimal procedures.
problem Estimating linear functionals from observational data in causal inference and bandit literature.
method Two-stage procedures that first estimate treatment effect function, then use it to estimate the linear functional.
result Proves non-asymptotic upper bounds on mean-squared error for two-stage procedures and shows instance-dependent optimality.
This paper improves non-asymptotic bounds for denoising diffusions, focusing on the Ornstein-Uhlenbeck process.
problem Improving non-asymptotic bounds for denoising diffusions, especially for the Ornstein-Uhlenbeck process.
method Explicit non-asymptotic bounds on forward diffusion error in total variation, considering multi-modal data distributions.
result The Ornstein-Uhlenbeck process cannot be significantly improved in terms of reducing terminal time for multi-modal data distributions.
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.
New oracles improve stochastic optimization with noisy or biased measurements.
problem Optimizing functions with noisy or biased measurements.
method Introduced biased gradient oracles for stochastic optimization, analyzed RSG and SGD algorithms with these oracles.
result Derived non-asymptotic bounds for convergence rates of algorithms with biased gradient oracles.
The paper provides a non-asymptotic error bound for linear system identification under nonlinear policies.
problem System identification for linear systems with nonlinear and/or time-varying policies under i.i.d. random excitation noises.
method Least square estimation with non-asymptotic error bound for bounded state and action trajectories.
result The error bound is consistent with linear policies and generalizes existing guarantees.
Detecting a planted submatrix in random matrices with non-asymptotic methods.
problem Detecting a planted submatrix in random matrices with non-zero entries.
method Established minimax lower bounds and derived optimal tests for distinguishing the null and alternative hypotheses.
result Non-asymptotic upper and lower bounds match for any configuration of matrix dimensions.
Simple bounds for covariance and Gram matrices across various settings.
problem Capturing the behavior of smaller eigenvalues in covariance and Gram matrices.
method General-purpose theorem converting uniform bounds into relative bounds.
result Sharper control of eigenvalues across the spectrum.
Non-asymptotic tail bounds for Kostlan-Shub-Smale field on sphere
problem Estimating rank-R symmetric signal tensor from Gaussian observation
method Profile maximum likelihood estimator
result Finite-(k,d) error bound recovers asymptotically optimal rate
Optimizes shortfall risk using gradient-based methods.
problem Optimizing utility-based shortfall risk measures.
method Gradient-based stochastic optimization, non-asymptotic bounds derivation.
result Non-asymptotic convergence rate for optimizing UBSR.
DALMC provides non-asymptotic error bounds for generative models.
problem Efficiently generating samples from complex data distributions.
method Analysis of diffusion paths and Langevin Monte Carlo.
result Theoretical guarantees for a class of generative models.
Estimates and optimizes UBSR risk in recursive settings.
problem Estimating and optimizing UBSR risk in a recursive setting with one-at-a-time samples.
method Casts UBSR as a root finding problem, uses stochastic approximation and gradient descent.
result Derives non-asymptotic bounds on estimation and optimization errors.
Non-asymptotic Optimal Prediction Error for Growing-dimensional Partially Functional Linear Modelsmath.ST
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.
Study non-asymptotic bounds for robust estimators under misspecified models.
problem Evaluate performance of robust estimators under adversarial conditions.
method Propose a general approach to adversarial risk analysis, including investigations on generalization and approximation errors.
result Establish non-asymptotic upper bounds for adversarial excess risk under Lipschitz loss functions.
Study shows robust method for estimating density ratios even with heavy contamination.
problem Estimating density ratios in the presence of heavy contamination.
method Weighted density ratio estimation (DRE) with doubly strong robustness.
result Weighted DRE achieves sparse consistency under heavy contamination.
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 .
This paper establishes that optimistic algorithms attain gap-dependent and non-asymptotic logarithmic regret for episodic MDPs. In contrast to prior work, our bounds do not suffer a dependence on diameter-like quantities or ergodicity, and smoothly interpolate between the gap dependent logarithmic-regret, and the $\wid…
New bounds on efficiency for conformalized regression methods.
problem Efficiency of conformal prediction in regression models.
method Non-asymptotic bounds on prediction set length for conformalized quantile and median regression.
result Identifies phase transitions in convergence rates across different regimes of miscoverage level.
Study non-asymptotic Langevin Monte Carlo for Gibbs distributions.
problem Sampling from Gibbs distributions with dissipative potentials.
method Langevin-type algorithms based on Liptser--Shiryaev theory and Poincaré inequalities.
result Upper bound on 2-Wasserstein distance for accurate approximation.
Non-asymptotic analysis of the performance of the penalized least trimmed squares in sparse modelsstat.ML
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.
The paper honors Lai's contributions to multi-armed bandits and establishes new regret bounds.
problem Improving regret bounds in multi-armed bandit problems.
method Establishes non-asymptotic regret bounds for upper confidence bound indices.
result New regret bounds match Lai-Robbins lower bound.
This paper establishes non-asymptotic learning bounds for the DR covariate shift adaptation.
problem Distribution shift between training and test domains in machine learning.
method Doubly-robust (DR) estimator combining density ratio estimation and pilot regression model.
result First non-asymptotic learning bounds for DR covariate shift adaptation.
Conditional diffusion models improve data generation with non-asymptotic convergence bounds.
problem Lack of non-asymptotic properties in conditional diffusion models.
method Integrates a pre-trained model into the diffusion model framework to capture conditional distributions.
result Established upper error bounds for the convergence between original and generated conditional distributions.
The paper gives bounds for how long it takes for gossip protocols to spread information in networks.
problem Understanding the diffusion time in asynchronous gossip protocols.
method Provides non-asymptotic bounds for the number of messages needed for consensus in asynchronous gossip protocols.
result Explicit formula and approximation for the number of messages needed for consensus in different types of graphs.
Restoration-Degradation Beyond Linear Diffusions: A Non-Asymptotic Analysis For DDIM-Type Samplerscs.LG
Develops new bounds for deterministic samplers in diffusion models.
problem Analyzing deterministic samplers in diffusion generative models.
method Operational interpretation of deterministic sampling; restoration and degradation steps.
result First polynomial convergence bounds for DDIM-type samplers.
New algorithm achieves near optimal sample complexity for 1-identification problem.
problem Determining if an arm's mean reward is at least a known threshold with high probability.
method Design of Sequential-Exploration-Exploitation (SEE) algorithm with non-asymptotic analysis.
result Achieves near optimality in sample complexity, matching upper and lower bounds up to a polynomial logarithmic factor.
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
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 convergence rates and guarantees consistent inference.
Sharp bounds derived for test error of finite-rank kernel ridge regression.
problem Loose bounds on test error for finite-rank kernels in machine learning.
method Sharp non-asymptotic upper and lower bounds for KRR test error.
result Tighter bounds on finite-rank KRR test error, valid for any regularization parameters.
A new strategy for identifying the best arm in Gaussian bandits with improved exploration.
problem Best-arm identification for Gaussian bandits with bounded means and unit variance.
method Exploration-Biased Sampling, a non-asymptotic approach with improved exploration behavior.
result Improved exploration behavior makes the strategy more stable and interpretable.
In this paper, we are concerned with a non-asymptotic analysis of sampling algorithms used in nonconvex optimization. In particular, we obtain non-asymptotic estimates in Wasserstein-1 and Wasserstein-2 distances for a popular class of algorithms called Stochastic Gradient Langevin Dynamics (SGLD). In addition, the afo…
The paper improves confidence set construction for statistical inference.
problem Constructing reliable confidence sets in statistical inference.
method Establishes a finite-sample bound using effective dimension and generalized self-concordance.
result Developed a confidence set adapted to optimization landscapes.
New sampling algorithms for complex distributions without log-concavity.
problem Efficient sampling from complex, high-dimensional distributions.
method Randomized splitting Langevin Monte Carlo (RSLMC) algorithm.
result Uniform-in-time error bounds for RSLMC and RLMC algorithms.
New algorithm reduces neural net error in contextual bandits.
problem Neural contextual bandits with general activation functions.
method Proposed an efficient algorithm with sublinear regret bound.
result Demonstrated provably sublinear regret bound in finite regime.
This paper analyzes error bounds for biased SMC samplers in conditional sampling.
problem Analyzing error bounds for biased SMC samplers in conditional sampling.
method Develops a non-asymptotic error analysis for SMC samplers with biased mutation kernels.
result Derives the first non-asymptotic error bound for conditional sampling with score-based diffusion models.
New algorithm achieves instance-optimality in decision making.
problem Develop adaptive algorithms for interactive decision making.
method Introduce Allocation-Estimation Coefficient (AEC) and develop algorithm.
result First non-asymptotic instance-optimal performance guarantees.
The paper develops approximations for Pearson's chi-square statistic and applies them to confidence intervals.
problem Finding confidence intervals for strictly convex functions of discrete distribution weights.
method Non-asymptotic local normal approximation for multinomial probabilities, deriving bounds and coupling inequalities.
result Developed methods to find confidence intervals for negative entropy of discrete distributions.
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.
kTULA: A Langevin sampling algorithm with improved KL bounds under super-linear log-gradientsmath.ST
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-.
The paper analyzes Karcher means on restricted PSD matrices with statistical guarantees.
problem Statistical analysis of non-linear manifolds in machine learning.
method Intrinsic mean model on restricted PSD matrices, Karcher mean analysis, extrinsic signal-plus-noise model.
result Non-asymptotic statistical analysis of Karcher means with deterministic error bounds.
Study optimal stopping for diffusion processes using data-driven methods.
problem Optimal stopping for diffusion processes under unknown conditions.
method Data-driven approach, deriving upper and lower bounds on simple and cumulative regret.
result Verified minimax optimality and improved convergence rates.
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 compares dropout and l2 regularization in linear models.
problem Understanding the statistical behavior of dropout and l2 regularization in linear models.
method Derives non-asymptotic bounds for gradient descent iterates with dropout and compares them to l2 regularization.
result Indicates a more subtle relationship between dropout and l2 regularization, highlighting interactions between dynamics and randomness.
New methods improve temporal difference learning for policy evaluation in Markov decision processes.
problem Improving temporal difference learning for policy evaluation in Markov decision processes.
method Introduced variance-reduced forms of stochastic approximation to achieve non-asymptotic, instance-dependent optimality.
result Temporal difference learning is strictly suboptimal, but variance-reduced forms achieve optimality up to logarithmic factors.
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 and logarithmic regret under positive suboptimality gap.
Discrete time analogues of ergodic stochastic differential equations (SDEs) are one of the most popular and flexible tools for sampling high-dimensional probability measures. Non-asymptotic analysis in the Wasserstein distance of sampling algorithms based on Euler discretisations of SDEs has been recently develop…