Local asymptotic minimax risk bounds in a locally asymptotically mixture of normal family of distributions have been investigated under asymmetric loss functions and the asymptotic distribution of the optimal estimator that attains the bound has been obtained.
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48 results for “asymptotic minimax”
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 (…
New estimator achieves minimax optimal risk in transfer learning.
problem Nonparametric regression with transfer learning.
method Confidence thresholding estimator and data-driven adaptive algorithm.
result Adaptive algorithm achieves minimax risk up to a logarithmic factor.
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 .
We propose the kl-UCB ++ algorithm for regret minimization in stochastic bandit models with exponential families of distributions. We prove that it is simultaneously asymptotically optimal (in the sense of Lai and Robbins' lower bound) and minimax optimal. This is the first algorithm proved to enjoy these two propertie…
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.
GNA optimally identifies the best arm with small gaps.
problem Best arm identification in fixed-budget settings.
method Generalized Neyman Allocation (GNA) for asymptotically locally minimax optimal BAI.
result GNA's worst-case bounds match the lower and upper bounds in the small-gap regime.
E algorithm optimizes batched linear bandits with minimal regret and batches.
problem Optimizing batched linear bandits for minimal regret.
method Explore-Estimate-Eliminate-Exploit framework with optimal exploration rate.
result Achieves minimax and asymptotic optimality in regret and batch complexity.
Proposes online debiasing estimators for adaptive linear regression.
problem Adaptive data collection leads to non-normal asymptotic behavior in simple methods.
method Online debiasing estimators that correct distributional anomalies.
result Asymptotic normality and minimax lower bound for proposed estimators.
Optimal algorithm for identifying best-arm with minimal regret.
problem Identifying the best arm in two treatments with limited budget.
method Neyman allocation based on outcome standard deviations.
result Neyman allocation is minimax optimal for simple regret.
Double Machine Learning estimators are asymptotically inadmissible under structure-agnostic models.
problem Minimax estimators may be inadmissible under structure-agnostic models.
method Exhibit second-order (U-statistic) estimators that asymptotically dominate DML estimators.
result Double Machine Learning estimators are asymptotically inadmissible under structure-agnostic models.
Improved analysis shows Maillard sampling achieves optimal regret bounds.
problem Optimal regret bounds for K-armed bandit problem.
method Improved analysis of Maillard sampling (MS) to achieve asymptotical optimality and minimax regret bound.
result MS achieves both asymptotical optimality and minimax regret bound of √(KT log T).
New findings show many popular bandit algorithms are unstable, contradicting minimax optimality.
problem Challenges in statistical inference from bandit algorithms due to adaptive, non-i.i.d. nature.
method Analysis of stability properties of optimism-based bandit algorithms.
result Widely used minimax-optimal UCB-style algorithms are unstable.
We develop a new theoretical framework, the \emph{envelope complexity}, to analyze the minimax regret with logarithmic loss functions and derive a Bayesian predictor that adaptively achieves the minimax regret over high-dimensional -balls within a factor of two. The prior is newly derived for achieving the mini…
Paper analyzes kNN estimator for KL divergence, proving its optimality.
problem Estimating KL divergence from identical samples.
method kNN estimator based on nearest neighbor distances.
result kNN method is asymptotically rate optimal for KL divergence estimation.
Efficient estimator for two-sample functionals improves on oracle performance.
problem Estimating two-sample integral functionals efficiently.
method Weighted nearest neighbour estimator, central limit theorem.
result The estimator can outperform the oracle in certain cases.
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.
The paper studies inference in hypergraph β-models with multiple layers.
problem Estimating and testing in hypergraph β-models with degree heterogeneity.
method Maximum likelihood estimation and likelihood ratio test for hypergraph β-models with multiple layers.
result The ML estimate and LR test are optimally powerful under the null hypothesis.
Community detection is a central problem of network data analysis. Given a network, the goal of community detection is to partition the network nodes into a small number of clusters, which could often help reveal interesting structures. The present paper studies community detection in Degree-Corrected Block Models (DCB…
Study on estimating invertible functions with minimax analysis.
problem Minimizing risk of estimating invertible functions on a plane.
method Introduce two types of -risks, derive lower and upper rates for minimax values, develop an asymptotically almost everywhere invertible estimator.
result Invertibility does not reduce the complexity of the estimation problem in terms of the rate.
Study shows plug-in model-based reinforcement learning is minimax optimal.
problem Finding optimal policies in MDPs with limited generative model access.
method Developed and analyzed a plug-in approach to model-based reinforcement learning.
result Plug-in approach yields minimax optimal policies with sublinear sample complexity.
Develops a new test for comparing two groups' densities, showing minimax optimality.
problem Comparing probability densities between two groups.
method Probabilistic tensor product smoothing spline framework for joint density modeling; penalized likelihood ratio test for interaction testing.
result Proposed test is minimax optimal and outperforms conventional approaches.
MOTS improves Thompson sampling to match minimax bounds for bandit problems.
problem Achieving optimal regret bounds for Thompson sampling in multi-armed bandit problems.
method Proposes MOTS, a variant of Thompson sampling that clips arm sampling.
result Proves MOTS achieves minimax optimal regret bounds .
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.
Study optimizes best-arm identification with minimax and Bayes strategies.
problem Efficiently identifying the best arm in fixed-budget scenarios.
method Adaptive procedure with two stages: pilot phase and minimax game.
result Single strategy is asymptotically minimax and Bayes optimal.
This work establishes distribution-free upper and lower bounds on the minimax label complexity of active learning with general hypothesis classes, under various noise models. The results reveal a number of surprising facts. In particular, under the noise model of Tsybakov (2004), the minimax label complexity of active …
Develops GLRT for defending against adversarial attacks in hypothesis testing.
problem Adversarial attacks on machine learning models causing misclassification.
method Generalized likelihood ratio test applied to composite hypothesis testing problem.
result GLRT approach yields competitive robustness-accuracy tradeoff under various attacks.
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.
This work optimizes signal estimation for sparse MRA with collision-free signals.
problem Recovering an unknown signal from repeated observations under cyclic isometries with high noise.
method Investigates minimax optimality for collision-free signals in the MRA model.
result The minimax optimal rate of estimation is \( \sigma^2/\sqrt{n} \) for sparse MRA.
Sharp bounds for high-probability estimation of discrete distributions.
problem Estimating discrete distributions with high probability under -divergence.
method Sharp upper and lower bounds for the classical Laplace estimator, and characterization of minimax high-probability risk for any estimator.
result Sharp bounds for high-probability estimation of discrete distributions can be achieved through a simple smoothing strategy.
Asymptotically optimal algorithm for contextual linear bandits.
problem Contextual linear bandits with suboptimal algorithms.
method Decoupling context distribution and exploration policy, incremental primal-dual approach, confidence intervals.
result Asymptotic optimality and scalability of the algorithm.
We consider a sequential learning problem with Gaussian payoffs and side information: after selecting an action , the learner receives information about the payoff of every action in the form of Gaussian observations whose mean is the same as the mean payoff, but the variance depends on the pair (and may…
Paper reconciles minimax rates and optimal recovery rates for noisy observations.
problem Estimating a function from noisy observations.
method Develops NLA minimax rates for Besov classes in -norms.
result NLA minimax rates continuously depend on noise level and match optimal recovery rates as noise decreases.
We study high-dimensional asymptotic performance limits of binary supervised classification problems where the class conditional densities are Gaussian with unknown means and covariances and the number of signal dimensions scales faster than the number of labeled training samples. We show that the Bayes error, namely t…
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.
Optimal strategy identified for minimizing regret in fixed-budget best arm selection.
problem Minimizing expected simple regret in fixed-budget best arm selection.
method Two-Stage (TS)-Hirano-Imbens-Ridder (HIR) strategy using HIR estimator.
result TS-HIR strategy is asymptotically minimax optimal.
Optimal algorithm for linear bandits on ellipsoids with minimax regret bound.
problem Linear stochastic bandits on ellipsoids.
method Novel sequential procedure to estimate norm of parameters, followed by an explore-and-commit strategy.
result Regret bound matches minimax lower bound with multiplicative constant.
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.
Subspace Perspective on Canonical Correlation Analysis: Dimension Reduction and Minimax Ratesmath.ST
Canonical correlation analysis (CCA) is a fundamental statistical tool for exploring the correlation structure between two sets of random variables. In this paper, motivated by recent success of applying CCA to learn low dimensional representations of high dimensional objects, we propose to quantify the estimation loss…
On Estimating Divergencestat.ML
We give a comprehensive theoretical characterization of a nonparametric estimator for the divergence between two continuous distributions. We first bound the rate of convergence of our estimator, showing that it is -consistent provided the densities are sufficiently smooth. In this smooth regime, we t…
We study sparse principal components analysis in the high-dimensional setting, where (the number of variables) can be much larger than (the number of observations). We prove optimal, non-asymptotic lower and upper bounds on the minimax estimation error for the leading eigenvector when it belongs to an …
This study improves estimation of the first principal component in multivariate functional data.
problem Estimating the first principal component of multivariate random processes.
method Defined covariance functions and operators, introduced LASSO optimization, and established minimax lower bounds.
result The method provides an optimal variance in the minimax sense for estimating eigenelements.
MOPI optimizes flexible set-valued mappings to achieve superior shape adaptivity in conformal prediction.
problem Challenges in achieving valid conditional coverage in conformal prediction.
method Minimax Optimization Predictive Inference (MOPI) framework that optimizes over a flexible class of set-valued mappings.
result MOPI achieves superior shape adaptivity and maintains a principled connection to mean squared coverage error.
This work optimizes identifying good arms in nonparametric multi-armed bandits.
problem Efficiently identifying arms with high means in nonparametric settings.
method Combining reward-maximizing sampling with a nonparametric sequential test for anytime-valid labeling.
result Achieves minimax optimal stopping times for identifying arms above a threshold.
Optimal algorithm reduces regret in adversarial bandit problem with multiple plays.
problem Minimizing regret in adversarial bandit problem with multiple plays.
method Introducing a new expert advice algorithm for multiple-play setting, achieving minimax optimal regret bounds.
result Minimizes regret asymptotically to the best switching strategy with optimal bounds.
A permutation-based SW test achieves minimax-optimal power for two-sample testing.
problem Nonparametric two-sample testing using the sliced Wasserstein distance.
method Proposes a permutation-based SW test and analyzes its performance.
result Achieves minimax separation rate over multinomial and bounded-support alternatives.
Finite-Time Regret of Thompson Sampling Algorithms for Exponential Family Multi-Armed Banditsstat.ML
New Thompson sampling algorithm reduces regret for exponential family bandits.
problem Minimizing regret in multi-armed bandit problems with exponential family rewards.
method Proposes ExpTS and ExpTS algorithms using novel sampling distributions.
result Minimizes both finite-time and asymptotic regret for exponential family rewards.
Stochastic Approximation with Decision-Dependent Distributions: Asymptotic Normality and Optimalitymath.OC
Stochastic algo learns from evolving data, achieving optimal performance.
problem Performative prediction and multiplayer extensions.
method Stochastic approximation with decision-dependent distributions.
result Asymptotic normality and optimality of the algorithm's performance.