Study robust mean estimation under coordinate-level corruptions using Hamming distance.
problem Robust mean estimation under realistic coordinate-level corruptions.
method Introduce a novel Hamming distance-based measure and present information-theoretic analysis.
result Data cleaning-inspired approaches can match information theoretic bounds for robust mean estimation.
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.
New method estimates robust mean in high dimensions with minimized outliers.
problem Estimating the mean in high dimensions when a fraction of data is corrupted.
method Formulating the problem as ℓ0-norm minimization under second moment constraints, and using ℓ1 and ℓp minimization techniques. result The proposed method achieves order optimal robust mean estimation and significantly outperforms existing methods.
Develops a computationally tractable differentially private mean estimator called the balloon mean.
problem Robust mean estimation in the presence of outliers and heavy-tailed distributions.
method Iterative clipping procedure over Mahalanobis balls.
result Balloon mean is robust to outliers and outperforms existing estimators in contaminated settings.
New algorithms robustly estimate mean with near-optimal error rates.
problem Outlier robust mean estimation in high-dimensional data.
method Stability condition and iterative filtering algorithms.
result Optimal error rates with subgaussian rates for robust mean estimation.
Robustly estimates mean with quantized data and corruption.
problem Mean estimation under quantization and adversarial corruption.
method Constructs multivariate robust estimators in two settings.
result Optimal estimators up to logarithmic factors.
Paper proposes robust gossip algorithms for mean and trimmed mean estimation.
problem Vulnerability of mean-based gossip algorithms to malicious nodes.
method Developed extsc{GoRank} for rank estimation and extsc{GoTrim} for trimmed mean estimation.
result Established convergence rates for rank and trimmed mean estimation.
Paper introduces MoM-KDE for robust density estimation robust to anomalous data.
problem Density estimation robustness to anomalous data.
method Combines Kernel Density Estimation and Median-of-Means principle.
result Achieves competitive results with lower computational complexity compared to other robust estimators.
Gradient descent solves robust mean estimation in high dimensions.
problem High-dimensional robust mean estimation in the presence of adversarial outliers.
method Gradient descent with a structural lemma showing near-optimal solutions.
result Gradient descent can solve the robust mean estimation problem directly.
New measure of robustness for estimators, with tight bounds for Gaussian mean estimation.
problem Developing robust statistical estimators for datasets with noise or outliers.
method Introducing empirical sensitivity as a new robustness measure and proving lower bounds for Gaussian mean estimation.
result Empirical sensitivity bounds for optimal estimators are tight, showing obstructions on mean and variance.
New robust estimators achieve subgaussian bounds using VC-dimension.
problem Robust estimation of sparse and corrupted data.
method Use of VC-dimension to measure statistical complexity.
result First robust estimators for sparse estimation with subgaussian rate.
Robustly estimates mean in incomplete data with corrupted examples.
problem Estimating mean in data with missing values and outliers.
method Algorithms for robust estimation with optimal error guarantees in nearly-linear time.
result Information-theoretically optimal error guarantees for mean estimation.
Efficiently estimates sparse mean from heavy-tailed data.
problem Robustly estimating sparse mean from heavy-tailed distributions.
method Stability-based approach adapted for heavy-tailed data.
result Optimal sample complexity with logarithmic dependence on dimension.
PRIME algorithm estimates mean while ensuring privacy and robustness.
problem Privacy and robustness in shared data analysis.
method Introduces PRIME, the first efficient algorithm for both privacy and robustness.
result Achieves both privacy and robustness for a wide range of distributions.
New algorithm reduces runtime for robust sparse mean estimation.
problem Efficiently estimating mean from corrupted data with sparse constraints.
method Subquadratic time algorithm using poly(k, log d, 1/ε) samples.
result First subquadratic time algorithm for robust sparse mean estimation.
Study examines mean estimation in high dimensions with small data.
problem Efficiently estimating mean in high-dimensional data with limited data size.
method Extensive experimentation of various mean estimation techniques.
result Developed robust methods for mean estimation with low data size.
Efficiently estimates mean in contaminated Gaussian data with near-optimal sample complexity.
problem Robust mean estimation in the presence of mean-shift contamination.
method First computationally efficient algorithm with near-optimal sample complexity and polynomial-time running.
result Approximates the target mean to any desired accuracy with constant fraction of outliers tolerated.
Learning in the presence of outliers is a fundamental problem in statistics. Until recently, all known efficient unsupervised learning algorithms were very sensitive to outliers in high dimensions. In particular, even for the task of robust mean estimation under natural distributional assumptions, no efficient algorith…
K-bMOM robustly clusters data with outliers, improving on Lloyd-type methods.
problem Outliers in datasets disrupt traditional clustering algorithms.
method Lloyd-type iterations with robust median-of-means estimates.
result K-bMOM outperforms existing robust K-means methods.
Study robust estimation under varying corruption probabilities in data.
problem Robust estimation in scenarios with heterogeneous corruption rates.
method Developed estimators for mean and regression under various corruption patterns.
result Optimal estimators can discard corrupted samples beyond a specific threshold.
Robust CG methods avoid data corruption and solve structured statistical estimation problems.
problem Data corruption and heavy-tailed data in structured statistical estimation.
method Robustification of Conditional Gradient (CG) type methods using Huber's corruption model and robust mean gradient estimation.
result Robust CG methods converge linearly with correct sample complexity, even for high-dimensional problems.
Unified approach for robust and heavy-tailed mean estimation in high dimensions.
problem Estimating mean in high dimensions with adversarial corruption or heavy-tailed distributions.
method Unified meta-problem and duality theorem leading to Filter algorithm and QUE scheme.
result Unified and efficient algorithms for both robust and heavy-tailed mean estimation.
Paper improves statistical efficiency of median-of-means estimator for Byzantine robust distributed inference.
problem Byzantine robustness in distributed learning systems.
method Variance reduced median-of-means (VRMOM) estimator for Byzantine robust distributed inference.
result Achieves a fast convergence rate with only a constant number of rounds of communications.
Polynomial-time private algorithm for robust estimation of mean and covariance in the presence of outliers.
problem Estimating mean and covariance in the presence of adversarial outliers.
method Stabilizing convex relaxations using a new estimate-dependent noise injection mechanism.
result First efficient private robust estimation algorithm for covariance without condition-number assumptions.
Privacy improves robustness in statistical estimation.
problem Sparse mean estimation under privacy constraints.
method Sum-of-Squares method and exponential-time mechanisms.
result Private algorithms matching optimal tradeoffs are not known, but achieved via Sum-of-Squares.
We introduce a criterion, resilience, which allows properties of a dataset (such as its mean or best low rank approximation) to be robustly computed, even in the presence of a large fraction of arbitrary additional data. Resilience is a weaker condition than most other properties considered so far in the literature, an…
Robust estimators for Gaussian sparse tasks with optimal error under contamination.
problem Robust mean estimation, PCA, and linear regression in the presence of Huber contamination.
method Novel multidimensional filtering method for sparse regime.
result Optimal error guarantees within constant factors for Gaussian robust k-sparse mean estimation. New methods solve sparse estimation robustly, even with outliers.
problem Sparse estimation in high-dimensional data with outliers.
method Non-convex optimization formulations for robust sparse mean estimation and PCA.
result Any approximate stationary point yields near-optimal solutions.
We study two problems in high-dimensional robust statistics: \emph{robust mean estimation} and \emph{outlier detection}. In robust mean estimation the goal is to estimate the mean μ of a distribution on Rd given n independent samples, an ε-fraction of which have been corrupted by a malicious…
Paper shows robust estimators converge to true risk minimizers at optimal rates.
problem Understanding asymptotic properties of robust risk minimizers.
method Investigates robust analogues of empirical risk minimization, focusing on median of means estimator.
result Robust minimizers converge to true minimizers at optimal rates and have similar asymptotic variance.
Survey of robust statistical methods for efficient computation.
problem Efficient robust statistical methods for various forms of data contamination and heavy-tailed distributions.
method Survey and technical connections between robustness forms, showing efficient algorithms.
result Same algorithmic ideas lead to efficient estimators for robustness in different settings.
New algorithms improve privacy in statistical estimation by making them robust.
problem Improving privacy in statistical estimation methods.
method Black-box reduction from privacy to robustness, using Sum-of-Squares method.
result Design of polynomial-time private estimators with optimal tradeoffs among sample complexity, accuracy, and privacy.
This work proves MultiKrum is robust in mean estimation with adversaries.
problem Mean estimation in the presence of Byzantine adversaries.
method Introducing κ* and constructing upper and lower bounds on MultiKrum's robustness coefficient.
result MultiKrum is the first provably robust aggregation rule, with robustness coefficient bounds.
We propose a method for nonparametric density estimation that exhibits robustness to contamination of the training sample. This method achieves robustness by combining a traditional kernel density estimator (KDE) with ideas from classical M-estimation. We interpret the KDE based on a radial, positive semi-definite ke…
Develops a computationally tractable high-dimensional differential privacy estimator.
problem Differential privacy in high dimensions is computationally intractable.
method Combines high-dimensional robust statistics with differential privacy techniques.
result A computationally tractable algorithm with dimension-independent privacy loss.
Paper solves outlier robust mean estimation near breakdown point.
problem Estimating mean in presence of adversarial outliers.
method Sum-of-Squares approach to optimize error rate efficiently.
result Achieves optimal error rate for all ε ∈ [0, 1/2).
An algorithm estimates the mean of a process from noisy, online sensor data.
problem Estimating the mean of a process from noisy, online sensor data with some sensors behaving maliciously.
method An efficient online algorithm that produces estimates as data comes in, achieving nearly competitive error bounds.
result The algorithm can compute a good approximation to the true mean with error bounds of O(δlog(T)). Robust diffusion adaptive estimation algorithms based on the maximum correntropy criterion (MCC), including adaptation to combination MCC and combination to adaptation MCC, are developed to deal with the distributed estimation over network in impulsive (long-tailed) noise environments. The cost functions used in distri…
In this paper, we develop connections between two seemingly disparate, but central, models in robust statistics: Huber's epsilon-contamination model and the heavy-tailed noise model. We provide conditions under which this connection provides near-statistically-optimal estimators. Building on this connection, we provide…
Study improves portfolio risk estimation methods using robust covariance and CVaR constraints.
problem Improving portfolio risk estimation in the presence of financial data noise and extreme market conditions.
method Exploration of robust covariance estimators, application of CVaR constraints, use of K-means clustering in optimization.
result Robust covariance estimators can outperform market-weighted benchmarks, especially during bull markets.
Heavy-tailed outliers are more resilient to robust estimation than adversarial ones.
problem Developing robust estimators for data with outliers.
method Analyzing the relationship between adversarial and heavy-tailed outlier models.
result Optimal estimators for heavy-tailed outliers are also optimal for adversarial settings, but not vice versa.
Paper proposes a robust method for federated ICA with geometric median aggregation.
problem Federated ICA with permutation ambiguity in client estimations.
method Geometric median aggregation with k-means clustering to resolve permutation ambiguity.
result The method provably remains effective in highly heterogeneous scenarios.
Robust estimation methods find global minima efficiently via quasi-gradients.
problem Efficiently solving robust estimation problems with non-convex optimization.
method Identifying generalized quasi-gradients to guarantee low-regret algorithms.
result Generalized quasi-gradients ensure efficient approximation of global minima.
Proves subgaussian distributions are SoS-certifiably subgaussian, enabling efficient algorithms for various statistical tasks.
problem Efficiently learning from subgaussian distributions in high dimensions.
method Universal constant C and polynomial sum of squares (SoS) approach. result Proves subgaussian distributions are SoS-certifiably subgaussian.
New algorithm learns Bayesian networks robustly in nearly-linear time.
problem Learning Bayesian networks with adversarially corrupted samples.
method Developed a nearly-linear time algorithm connecting robust learning to robust mean estimation.
result First nearly-linear time algorithm with comparable error guarantees.
Proposes CCME framework for estimating heterogeneous treatment effects.
problem Estimating heterogeneous treatment effects in complex distributions.
method Embeds conditional distributions into RKHS, develops meta-estimators for CCME.
result Establishes finite-sample convergence rates and double robustness for CCME estimators.
CPME embeds counterfactual outcomes in RKHS for flexible policy evaluation.
problem Estimating counterfactual policy outcomes for decision-making.
method Counterfactual Policy Mean Embedding (CPME) framework in RKHS, plug-in and doubly robust estimators, kernel test statistic.
result Doubly robust estimator improves convergence rates and asymptotic normality.
Proposes a Doubly Robust mean-CVaR portfolio method to improve investment risk management.
problem Portfolio optimization challenges in unstable financial markets.
method Doubly Robust approach to mean-CVaR portfolio optimization.
result The proposed method outperforms traditional mean-variance optimization.