Paper analyzes minimax risks of personalized federated learning algorithms.
problem Statistical heterogeneity among clients in federated learning.
method Minimax analysis of FedAvg and local training approaches.
result Threshold for optimality between FedAvg and local training depends on data heterogeneity.
CARROT optimizes LLM routing by choosing the cheapest and most accurate model.
problem Optimizing query routing to the most cost-effective LLM for a given task.
method CARROT uses cost and performance estimates to select the best LLM for each query.
result CARROT is minimax optimal, selecting the best LLM for any query.
ERM and RERM minimize error even with malicious label corruptions.
problem Malicious label corruptions in regression problems.
method Empirical Risk Minimizers (ERM) and Regularized Empirical Risk Minimizers (RERM) under a local Bernstein condition.
result The L2-error rate is bounded by $r_N + AL |\cO|/N$ under the local Bernstein condition. Biclustering structures in data matrices were first formalized in a seminal paper by John Hartigan (1972) where one seeks to cluster cases and variables simultaneously. Such structures are also prevalent in block modeling of networks. In this paper, we develop a unified theory for the estimation and completion of matri…
Study minimax off-policy evaluation in multi-armed bandits with known and unknown behavior policies.
problem Evaluate policies in multi-armed bandits with unknown behavior policies.
method Develop minimax rate-optimal procedures for known and unknown behavior policies, including the Switch estimator and Chebyshev polynomial-based estimator.
result Plug-in estimator achieves optimal competitive ratio up to a logarithmic factor when behavior policy is unknown.
Optimally tackles covariate shift in RKHS-based nonparametric regression.
problem Covariate shift in nonparametric regression over RKHS.
method Two families of covariate shift problems defined using likelihood ratios. Minimax rate-optimal estimators for KRR and reweighted KRR.
result KRR is minimax rate-optimal and strictly sub-optimal compared to naive estimator under covariate shift.
Simplified proof shows SGD optimality for least squares.
problem Optimizing SGD for least squares efficiency.
method Analyzing SGD as a stochastic process, characterizing stationary covariance matrix.
result Statistical minimax optimality of SGD for least squares.
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.
Survey of network analysis limits and optimal methods.
problem Graphon estimation, community detection, and hypothesis testing.
method Review of minimax optimal rates and procedures.
result Optimal algorithms for network analysis.
KL nearest neighbor estimator achieves near-minimax rates for differential entropy.
problem Estimating differential entropy with Hölder smoothness.
method Uniform upper and lower bounds on KL estimator performance.
result KL estimator is near-minimax rate-optimal without knowing smoothness.
New methods improve estimation accuracy in noisy settings.
problem Estimating treatment effects in the presence of treatment noise.
method Developed new structure-agnostic cumulant estimators and practical procedures for higher-order robustness.
result Demonstrated that existing DML estimator is suboptimal for non-Gaussian treatment noise and introduced ACE procedures for improved accuracy.
STAT-SVD method reduces high-dimensional data sparsity, achieving optimal estimation.
problem Sparse tensor singular value decomposition for high-dimensional data.
method STAT-SVD method with double projection & thresholding scheme.
result STAT-SVD provides sharp thresholding criterion and minimax rate-optimal estimation.
New algorithm AG-OG optimizes separable convex-concave problems efficiently.
problem Efficiently solving separable convex-concave minimax optimization problems.
method Leverages Nesterov acceleration and optimistic gradient on component and coupling parts of the problem.
result Achieves optimal convergence rate for various settings including bilinearly coupled problems.
New algorithms for private GLM estimation with minimax lower bounds.
problem Privacy in generalized linear models.
method Differentially private algorithms using projected gradient descent.
result Nearly rate-optimal performance with privacy-constrained minimax lower bounds.
Study optimizes shared singular subspace estimation from noisy matrices.
problem Estimating shared singular subspaces across multiple noisy matrices.
method Low-rank matrix denoising framework with Stack-SVD and novel estimators.
result Stack-SVD achieves minimax rate-optimality for identical shared subspaces, and novel estimators for partial sharing.
This paper studies continuum-armed bandits under Besov smoothness conditions and derives minimax rates.
problem Optimizing an unknown function with limited evaluations.
method Studies continuum-armed bandits under Besov smoothness conditions and derives minimax rates.
result Minimax rates over Besov spaces are identical to those over the smallest Hölder space into which Besov spaces embed.
Study reveals differences in label shift problem difficulty in supervised vs. unsupervised settings.
problem Label shift problem in non-parametric classification.
method Analysis of minimax rates in supervised and unsupervised settings, focusing on class conditional distributions estimation.
result A class proportion estimation approach is minimax rate-optimal in the unsupervised setting.
A new test statistic speeds up MMD while maintaining power.
problem Efficiently testing two distributions without permutations.
method Cross-MMD statistic based on sample-splitting and studentization.
result Cross-MMD has a limiting standard Gaussian distribution under the null.
Neural networks estimate statistical divergences with performance guarantees.
problem Estimating statistical divergences with theoretical performance guarantees.
method Parametrizing empirical variational form by a neural network and optimizing over parameter space.
result Established non-asymptotic absolute error bounds for neural estimators of four f-divergences. Estimates inner products between nonparametric distributions using Fourier basis.
problem Estimating inner products between two nonparametric distributions.
method Proposes estimators for inner products and induced norms, proves mean squared error bounds and minimax lower bounds.
result Proposed estimators are rate-optimal over Fourier ellipsoids.
Paper analyzes how unlabeled data improves SSL and adversarial robustness.
problem Understanding how unlabeled data impacts SSL and adversarial robustness.
method Minimax analysis and adversarial training.
result Reconstruction-based SSL algorithm is rate-optimal under various models and enhances adversarial robustness.
Study sharp convergence rates of empirical UOT for spatio-temporal point processes.
problem Statistical analysis of UOT for spatio-temporal point processes.
method Empirical plug-in estimators for Kantorovich-Rubinstein distance between intensity measures.
result Sharp convergence rates of empirical UOT in terms of intrinsic dimensions of measures.
Improved Mondrian Forests achieve optimal rate for online classification.
problem Consistency and minimax rates for online Mondrian Forests.
method Modified Mondrian Forest algorithm with increasing lifetime parameters and alternative updating rule.
result Achieves minimax rate for Lipschitz regression function estimation.
Adaptive kNN method closes the gap for unbounded support distributions.
problem Inability of standard kNN to achieve minimax optimal rate for unbounded support distributions.
method Adaptive kNN method with varying k for different samples.
result The adaptive kNN method matches the minimax lower bound.
AEW estimator achieves optimal risk in expectation for large enough temperatures.
problem Understanding minimax-rate optimality of AEW estimator in model selection aggregation.
method Analyzing AEW estimator with exponential weights for squared loss under random design.
result AEW achieves excess risk Tlog(M)/(n+1) in expectation for large enough temperatures. Paper tackles adversarial attacks on nonparametric regression models.
problem Vulnerability of machine learning models to adversarial attacks in nonparametric regression.
method Establishes minimax rate and proposes adaptive estimators for robust nonparametric regression under adversarial Lq-risks. result Achieves minimax optimality and provides adaptive estimators for robust nonparametric regression.
Develops a high-dimensional differentially-private EM algorithm with near-optimal statistical guarantees.
problem Designing differentially-private EM algorithms for high-dimensional latent variable models.
method Noisy iterative hard-thresholding, statistical guarantees, near-optimal convergence rates.
result Near-optimal statistical guarantees and minimax rate optimality in high-dimensional settings.
New method clusters matrix-valued data by latent variables.
problem Clustering matrix-valued data with hidden structure.
method Latent variable model with hierarchical clustering.
result Algorithm attains clustering consistency in high dimensions.
Spectrally-truncated KRR outperforms full KRR for large data.
problem Computational intensity of KRR for large datasets.
method Spectrally truncating the kernel matrix to its largest r eigenvalues. result Spectrally-truncated KRR can outperform full KRR for all finite samples above a threshold.
Optimal algorithm for high-dimensional stochastic linear bandits with sparse parameters.
problem High-dimensional stochastic linear bandits with sparse parameters.
method Three-stage arm selection algorithm using thresholded Lasso for estimation.
result Achieves exact minimax optimality in cumulative regret.
New model for pairwise comparisons without stochastic transitivity.
problem Suboptimal performance of models assuming stochastic transitivity in real-world scenarios.
method Proposes a general family of statistical models using a skew-symmetric matrix.
result Achieves minimax-rate optimality and adapts to data sparsity.
Paper investigates optimal transport map estimation in infinite-dimensional spaces.
problem Estimating optimal transport maps in infinite-dimensional spaces is challenging.
method Characterizes γ-smoothness for optimal transport maps and develops a polynomial-rate estimator. result Shows polynomial-order minimax risk for optimal transport map estimation.
The paper analyzes expected improvement policies for minimizing functions in RKHSs and derives regret bounds.
problem Minimizing deterministic functions in RKHSs with Gaussian-process models.
method Analyzes expected improvement policies, uses sequential separation radii, and estimates Gram determinants and Kolmogorov widths.
result Simple regret rates for Matérn and squared-exponential kernels are derived.
Study on efficient estimation of Gaussian mean with limited communication.
problem Estimating Gaussian mean under communication constraints.
method Decomposition into localization and refinement stages, development of communication-efficient and statistically optimal procedures.
result Established minimax rates of convergence and developed optimal procedures.
Adapting Hedge algorithm for semi-adversarial data with root-entropy regularization.
problem Minimizing regret in prediction with expert advice under varying distributions.
method Follow-the-Regularized-Leader (FTRL) with root-entropy regularization.
result Adaptive minimax optimal regret across all levels of constraint sets.
Bayesian histograms achieve optimal distribution estimation with minimal memory usage.
problem Efficiently estimating distributions with minimal memory footprint.
method Bayesian histograms for distribution estimation under Wasserstein distance.
result Bayesian histograms require fewer bins to achieve minimax optimality, reducing memory usage by a polynomial factor.
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 Lq-norms. result NLA minimax rates continuously depend on noise level and match optimal recovery rates as noise decreases.
New method for private linear regression under privacy constraints, achieving optimal rates.
problem Statistical complexity of private linear regression under unknown, ill-conditioned covariates.
method Information-Weighted Regression method
result Optimal convergence rates for both central and local privacy models.
Paper studies transfer learning for nonparametric classification, establishing rates and proposing adaptive classifiers.
problem Transfer learning in nonparametric classification under different distributions.
method Established minimax rates and proposed adaptive classifiers based on weighted K-NN approach.
result Data-driven adaptive classifier achieves near-optimal rates over various parameter spaces.
Matrix completion works well for smooth non-linear structures, even without low-rank assumptions.
problem Matrix completion for smooth non-linear structures.
method Nuclear-norm penalization for matrices lying in a low-dimensional non-linear manifold.
result Nuclear-norm penalization is minimax rate optimal for recovering smooth non-linear matrices with missing data.
New method estimates minimizer and minimum value of a regression function.
problem Estimating minimizer and minimum value of a regression function from noisy data.
method Projected gradient descent with gradient estimated by regularized local polynomial algorithm, followed by a rate optimal nonparametric procedure.
result Achieves minimax optimal rates of convergence for smooth and strongly convex functions.
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 on Q-function estimation for continuous state-action MDPs, deriving rates and conditions.
problem Estimating Q-function in off-policy evaluation for continuous state-action Markov decision processes. method Reformulated as nonparametric instrumental variables (NPIV) problem, derived minimax lower bounds, proposed sieve two-stage least squares estimator.
result First minimax lower bounds for Q-function and its derivatives in sup-norm and L2-norm, same as classical nonparametric regression. The homology groups of a manifold are important topological invariants that provide an algebraic summary of the manifold. These groups contain rich topological information, for instance, about the connected components, holes, tunnels and sometimes the dimension of the manifold. In earlier work, we have considered the s…
New algorithm identifies best arm with optimal budget usage.
problem Identifying the arm with the highest mean reward from multiple options.
method Proposes Almost Tracking, a closed-form algorithm for anytime best arm identification.
result Proven to be rate-optimal and outperforms existing algorithms.
We consider high-dimensional binary classification by sparse logistic regression. We propose a model/feature selection procedure based on penalized maximum likelihood with a complexity penalty on the model size and derive the non-asymptotic bounds for the resulting misclassification excess risk. The bounds can be reduc…
Sobolev quantities (norms, inner products, and distances) of probability density functions are important in the theory of nonparametric statistics, but have rarely been used in practice, partly due to a lack of practical estimators. They also include, as special cases, L2 quantities which are used in many applicatio…
Adaptive transfer learning model for varying mechanisms across domains.
problem Improving inference in a target domain by leveraging related source domains with varying mechanisms.
method Semi-parametric domain-varying coefficient model (DVCM) for structured transfer learning.
result Minimax rate-optimal adaptive transfer learning estimator with provable negative transfer safeguards.