We tackle the problem of estimating a location parameter with differential privacy guarantees and sub-Gaussian deviations. Recent work in statistics has focused on the study of estimators that achieve sub-Gaussian type deviations even for heavy tailed data. We revisit some of these estimators through the lens of differ…
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48 results for “sub-Gaussian deviation”
Improved median of means estimator with tighter bounds.
problem Improving the efficiency and reliability of median of means estimator.
method Modification of the median of means estimator with sub-Gaussian deviation bounds.
result Achieves nearly optimal constants under minimal assumptions.
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.
New method improves privacy in linear regression with optimal error bounds.
problem Differentially private linear regression with suboptimal error bounds.
method One-pass mini-batch stochastic gradient descent (DP-AMBSSGD) with adaptive clipping.
result Nearly optimal error bounds in terms of key parameters like dimensionality, number of points, and noise standard deviation.
We propose robust sparse reduced rank regression for analyzing large and complex high-dimensional data with heavy-tailed random noise. The proposed method is based on a convex relaxation of a rank- and sparsity-constrained non-convex optimization problem, which is then solved using the alternating direction method of m…
Estimation of the covariance matrix has attracted a lot of attention of the statistical research community over the years, partially due to important applications such as Principal Component Analysis. However, frequently used empirical covariance estimator (and its modifications) is very sensitive to outliers in the da…
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 tackles best arm identification in contaminated bandits with optimal error guarantees and sample complexity.
problem Best arm identification in stochastic bandits with adversarial reward contamination.
method Proposes two algorithms: a gap-based algorithm and a successive elimination-based algorithm for sub-Gaussian bandits.
result Asymptotically optimal sample complexity for both algorithms.
Improved robust regression for heavy-tailed and contaminated data.
problem Linear regression with heavy-tailed and adversarially contaminated covariates and responses.
method Applying a filtering algorithm to covariates and then using Huber regression, least trimmed squares, or least absolute deviation estimators on the remaining data.
result Near-optimal error rates achieved for the Huber regression estimator.
Heavy-tailed distributions are widely used in robust mixture modelling due to possessing thick tails. As a computationally tractable subclass of the stable distributions, sub-Gaussian -stable distribution received much interest in the literature. Here, we introduce a type of expectation maximization algorithm that e…
Sharp sub-Gaussian upper bounds for subsolutions of Trudinger's equation on Riemannian manifoldsmath.AP
Sharp sub-Gaussian bounds for subsolutions of Trudinger's equation on Riemannian manifolds.
problem Bounding weak subsolutions of Trudinger's equation on Riemannian manifolds.
method Proving sub-Gaussian upper bounds for weak subsolutions.
result The upper bounds are sharp for specific classes of manifolds, including \(\mathbb{R}^{n}\).
Random linear mappings are widely used in modern signal processing, compressed sensing and machine learning. These mappings may be used to embed the data into a significantly lower dimension while at the same time preserving useful information. This is done by approximately preserving the distances between data points,…
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.
UCB algorithm adapted for large-scale, non-sub-Gaussian problems.
problem Selecting the best alternative from a large set of options with non-sub-Gaussian performance distributions.
method Adapted UCB algorithm for non-sub-Gaussian settings, focusing on sample size and meta-UCB selection.
result UCB algorithms can achieve sample optimality in large-scale, non-sub-Gaussian problems.
Proves new concentration inequalities for sub-gaussian and sub-exponential variables.
problem Understanding functions of independent random variables better.
method Sub-gaussian and sub-exponential conditions, Rademacher complexities, Lipschitz function classes.
result Extension of Rademacher complexities to unbounded sub-exponential distributions.
Mean embeddings provide an extremely flexible and powerful tool in machine learning and statistics to represent probability distributions and define a semi-metric (MMD, maximum mean discrepancy; also called N-distance or energy distance), with numerous successful applications. The representation is constructed as the e…
Study improves self-normalized bounds for vector-valued processes beyond sub-Gaussianity.
problem Limited understanding of self-normalized concentration for vector-valued processes outside sub-Gaussian frameworks.
method Developed concentration inequalities for self-normalized processes with light tails (e.g., Bennett, Bernstein bounds) for vector-valued data.
result Provided new insights and bounds for self-normalized processes with non-sub-Gaussian distributions.
Algorithmic Gaussianization through Sketching: Converting Data into Sub-gaussian Random Designscs.LG
New algorithm converts data into sub-gaussian designs efficiently.
problem Efficiently converting large datasets into sub-gaussian random designs for robust performance.
method Algorithmic Gaussianization through sketching and averaging, using LESS embeddings.
result Efficient data sketches nearly indistinguishable from sub-gaussian designs.
Quantum algorithm estimates mean with sub-Gaussian error.
problem Estimating mean of quantum-computed random variables.
method Quantum mean estimation algorithm with sub-Gaussian error rate.
result Achieves nearly-optimal quadratic speedup over classical methods.
Sharp comparison for sub-Gaussian random variables in convex order.
problem Comparing sub-Gaussian random variables in convex order.
method Proving dominance using moment generating functions and convex functions.
result Sharp comparison established between specific sub-Gaussian random variables.
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.
Thompson Sampling bounds for contextual bandits with sub-Gaussian rewards.
problem Improving the performance of Thompson Sampling in contextual bandits with sub-Gaussian rewards.
method Proved comprehensive bounds on Thompson Sampling expected cumulative regret based on mutual information and lifted information ratio for sub-Gaussian rewards.
result Explicit regret bounds for various contextual bandit scenarios.
Low-Rank Thinningstat.ML
New method reduces summary points for datasets while maintaining quality.
problem Thinning datasets to reduce summary points while maintaining quality.
method Low-rank analysis of sub-Gaussian thinning.
result Guarantees high-quality compression for any distribution and kernel.
Estimates sub-Gaussian parameter with consistent and optimal rates.
problem Estimating sub-Gaussian parameter from random variables.
method Constrained maximization of empirical weighted cumulant generating function.
result Root-n rate estimator is consistent and optimal under certain conditions.
Proposes a new model for clustering with heavier tails.
problem Clustering with heavy-tailed data.
method Finite mixture of skewed sub-Gaussian stable distributions, maximum likelihood estimation, EM algorithm.
result The proposed model can robustly handle heavy-tailed data.
New study shows mean estimation algorithms can't beat sub-Gaussian rate in general.
problem Improving mean estimation beyond worst-case scenarios.
method Constructing counterexamples and introducing neighborhood optimality.
result No reasonable estimator can achieve better than sub-Gaussian error rate for any distribution.
New winsorized mean improves robustness to up to 50% contamination.
problem Improving robustness of mean estimation in the presence of outliers.
method Outlyingness-induced winsorized mean approach.
result Achieves up to 50% contamination robustness with sub-Gaussian performance.
Nonparametric Thompson Sampling achieves optimal regret for risk-averse bandits with sub-Gaussian rewards.
problem Optimizing risk-averse bandit problems with sub-Gaussian rewards.
method Anchor-free nonparametric Thompson Sampling algorithm .
result Achieves regret matching the instance-dependent lower bound to leading order in .
The paper proves a regret bound for a sub-Gaussian mixture on unbounded data.
problem Tackles the challenge of achieving regret bounds for sub-Gaussian mixtures on unbounded data.
method Uses path-wise (deterministic) regret bounds and a cumulative variance process to derive the bound.
result Shows that on a specific event, the regret is eventually bounded by ln(ln V_T).
We study the problem of estimating the mean of a random vector given a sample of independent, identically distributed points. We introduce a new estimator that achieves a purely sub-Gaussian performance under the only condition that the second moment of exists. The estimator is based on a novel concept of a…
Two new algorithms improve robust PCA and Schatten packing.
problem Robustly estimating the top eigenvector of corrupted sub-Gaussian data.
method Two iterative filtering and nearly-linear time algorithms.
result First polynomial-time algorithms for non-trivial covariance estimation.
Paper analyzes SGMs for learning sub-Gaussian distributions without dimensionality constraints.
problem Learning sub-Gaussian distributions in high dimensions with SGMs.
method Introduced complexity notion and proved approximation and generalization rates.
result SGMs can approximate target sub-Gaussian distributions in total variation with dimension-independent rate.
SVGD algorithm converges at rate 1/sqrt(log log n) for sub-Gaussian distributions.
problem Approximating a probability distribution with particles.
method Stein variational gradient descent (SVGD) with finite particles and sub-Gaussian target distribution.
result SVGD achieves a convergence rate of 1/sqrt(log log n) for sub-Gaussian distributions.
Paper improves SLCB regret bound for bounded noise.
problem Stochastic linear contextual bandits with bounded noise.
method Set-membership estimation (SME) and optimism in the face of uncertainty (OFU).
result Improved regret bound of .
Andreas Maurer in the paper "A vector-contraction inequality for Rademacher complexities" extended the contraction inequality for Rademacher averages to Lipschitz functions with vector-valued domains; He did it replacing the Rademacher variables in the bounding expression by arbitrary idd symmetric and sub-gaussian var…
Flexible model captures varying scales in data clusters.
problem Real-world data often exhibits varying scales or intensities, violating the homogeneity assumption of classical Gaussian mixture models.
method Individual-heterogeneous sub-Gaussian mixture model with an efficient spectral method for exact recovery.
result The method provably achieves exact recovery of true cluster labels under mild separation conditions.
Study shows how over-parameterized classifiers can still perform well on noisy data.
problem Understanding how maximum margin classifiers perform in over-parameterized settings with noisy data.
method Analyzes maximum margin classifiers on sub-Gaussian mixtures, providing risk bounds.
result Characterizes conditions for 'benign overfitting' in linear classification problems.
Efficiently estimates common mean in high-dimensional data with noisy subset.
problem Estimating common mean in high-dimensional data with noisy subset.
method Iterative refinement strategy with rejection sampling and dimension-reduction.
result Achieves near-optimal error of .
One-bit clustering method for two-component sub-Gaussian mixture models
problem Clustering in sub-Gaussian mixture models
method One-bit clustering using dithered quantization
result Decaying misclassification rate with exponential signal-to-noise ratio
A new Markov subsampling strategy based on Huber criterion improves data processing from noisy full data.
problem High noise level in data leads to poor performance of subsampling procedures.
method Design a Markov subsampling strategy based on Huber criterion to construct an informative subset from noisy full data.
result The estimator based on HMS is statistically consistent with a sub-Gaussian deviation bound.
New characterization limits sampling with inexact scores.
problem Limiting sampling with inexact scores for unbiased results.
method Characterized types of inexact score oracle access.
result Weaker error assumptions rule out tractability of unbiased sampling.
Inspired by the Reward-Biased Maximum Likelihood Estimate method of adaptive control, we propose RBMLE -- a novel family of learning algorithms for stochastic multi-armed bandits (SMABs). For a broad range of SMABs including both the parametric Exponential Family as well as the non-parametric sub-Gaussian/Exponential f…
The paper develops algorithms to minimize misallocation and identify the arm with the highest variance.
problem Minimizing misallocation and identifying the arm with the highest variance from a set of arms.
method Developed novel online algorithms UCB-VV for misallocation minimization and SHVV for fixed budget best arm identification.
result The algorithms achieve optimal performance in terms of misallocation and error probability.
Paper analyzes neural network models for sub-Gaussian distributions, proving approximation and generalization abilities.
problem Estimating unknown distributions from i.i.d. observations using neural network models.
method Score-based neural network generative models (SGMs) with specific network architectures and stopping strategies.
result SGMs can approximate scores with high accuracy and achieve nearly optimal convergence rates under mild assumptions.
This paper extends the standard chaining technique to prove excess risk upper bounds for empirical risk minimization with random design settings even if the magnitude of the noise and the estimates is unbounded. The bound applies to many loss functions besides the squared loss, and scales only with the sub-Gaussian or …
We improve bounds for stochastic processes, especially those with heavy tails.
problem Bounding the concentration of sub- processes with heavy tails.
method Variational approach to concentration, focusing on sub-Gaussian and other tail conditions.
result First dimension-free self-normalized empirical Bernstein inequality.
New estimator accurately estimates mean of real-valued distributions without variance knowledge.
problem Estimating the mean of real-valued distributions without prior variance knowledge.
method Introduces a novel estimator that converges sub-Gaussian and works across distributions with bounded variance.
result The estimator achieves accuracy of σ·(1+o(1))√(2log(1/δ)/n) with parameters n, δ, and σ².
The paper strengthens the classical result of MLE convergence to a Gaussian distribution.
problem The classical result of MLE convergence to a Gaussian distribution.
method Sub-Gaussian concentration and entropic normality of the normalized MLE.
result Entropic central limit theorem for a smoothed version of the estimator.