New framework reduces sum-of-squares proof degree, speeding up clustering and robust moment estimation.
problem Sum-of-squares proof optimization and faster algorithms for clustering and robust moment estimation.
method Introducing new variables to reduce the degree of sum-of-squares proofs.
result Significantly faster algorithms for clustering and robust moment estimation with the same statistical guarantees.
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…
Develops a robust GMM estimator for outlier-tolerant inference.
problem Sensitive GMM estimation to outliers in inference problems.
method Robustified GMM estimator with computational efficiency and recovery guarantees.
result First computationally efficient GMM estimator for ε ε ε fraction of adversarial outliers with O ( ε ) O(\sqrtε) O ( ε ) recovery guarantee. Robustly estimates linear regression coefficients with adversarial and noisy data.
problem Estimating robust linear regression coefficients with adversarial and noisy data.
method Adversarial robust weighted Huber regression with polynomial computational complexity.
result Derives an estimation error bound that depends on the stable rank and condition number of the covariance matrix.
Synthesizes robust estimators for domain adaptation.
problem Improving prediction accuracy in target domain with limited data.
method Synthesizes a family of robust least squares estimators using convex optimization.
result Robust strategies can outperform non-robust interpolations.
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.
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.
This paper compares VaR estimation methods under tail misspecification, finding importance sampling underestimates VaR.
problem Tail misspecification in VaR estimation.
method Importance sampling and moment-based VaR bracketing.
result Importance sampling underestimates VaR under heavy-tailed returns, while moment-based methods are robust.
Huber regression assessed for robustness in statistical learning.
problem Understanding Huber regression in nonparametric statistical learning.
method Assessment from statistical learning perspective, focusing on risk consistency, adaptive tuning, and convergence rates.
result Huber regression can be asymptotically mean regression calibrated under ( 1 + ε ) (1+ε) ( 1 + ε ) -moment conditions, justifying its robustness. New method improves estimation of complex models from conditional moment restrictions.
problem Estimation of complex models from conditional moment restrictions.
method Functional Generalized Empirical Likelihood (GEL) with a practical method.
result The method achieves state-of-the-art performance on two problems.
Proposes a robust IV estimator using optimal transport for corrupted or adversarial data.
problem Lack of robustness in traditional IV estimators for corrupted or adversarial data.
method Integrates data-derivative information through optimal transport to address geometric aspects of data.
result Improves robustness against data corruption and adversarial attacks.
Derives moments of PL networks for robust DNNs.
problem Analyzing robustness of DNNs to adversarial attacks.
method Derives exact analytic expressions for moments of PL networks, generalizes variance expression, and constructs sparse and smooth adversarial attacks.
result New variance expressions are tighter and can be efficiently approximated.
Paper develops robust methods for large-scale testing without tuning parameters.
problem Heavy-tailed data in high-dimensional settings.
method Revisits Hodges-Lehmann estimator for robust inference without tuning parameters.
result Develops confidence intervals and controls false discovery proportion.
Study examines robust regression in high dimensions with heavy-tailed data.
problem Analyzing robust regression in high-dimensional settings with heavy-tailed data.
method Sharp asymptotic characterisation of M-estimators and ridge regression in elliptical distributions.
result Ridge regression is optimal and universal for finite second moments but can decay faster without them.
Generative Adversarial Networks improve robust statistics for various distributions.
problem Estimating unknown parameters in adversarially corrupted samples.
method Designing GANs with specific loss functions for robust estimation.
result Extends robust estimation to broader families of distributions.
Improves robust transfer learning with side information.
problem Addressing environmental shift in MDPs with side information.
method Estimate-centered uncertainty sets with side information integration.
result Improved robust policy with reduced sub-optimality gap.
Paper tackles moment estimation under covariate shift with a two-stage algorithm.
problem Estimating moments under covariate shift when source and target distributions differ.
method Proposes a two-stage algorithm: first, an optimal estimator for the source distribution; second, likelihood ratio reweighting for calibration.
result Achieves minimax optimal bound for moment estimation.
New tests for distributional causal effects using improved kernel estimators.
problem Testing for higher-order moments and multidimensional outcomes affected by treatment.
method Improved kernel estimators based on doubly robust mean embeddings.
result New permutation-based tests for distributional causal effects with improved convergence rates.
Paper provides unbiased spectral moment estimates from finite data.
problem Challenges in estimating spectral moments from limited data.
method Dynamic programming approach to estimate spectral moments of kernel integral operator.
result Demonstrates consistency with theoretical spectra and practical utility in neural networks.
The total duration of drawdowns is shown to provide a moment-free, unbiased, efficient and robust estimator of Sharpe ratios both for Gaussian and heavy-tailed price returns. We then use this quantity to infer an analytic expression of the bias of moment-based Sharpe ratio estimators as a function of the return distrib…
We consider the problem of sparsity-constrained M M M -estimation when both explanatory and response variables have heavy tails (bounded 4-th moments), or a fraction of arbitrary corruptions. We focus on the k k k -sparse, high-dimensional regime where the number of variables d d d and the sample size n n n are related through $…
Enhances DP linear regression using public data moments.
problem Limited utility of traditional DP methods in linear regression.
method Transform private data using public second-moment matrix for a better OLSE.
result Improved accuracy and robustness of OLSE in DP linear regression.
We develop a behavioral asset pricing model in which agents trade in a market with information friction. Profit-maximizing agents switch between trading strategies in response to dynamic market conditions. Due to noisy private information about the fundamental value, the agents form different evaluations about heteroge…
Paper introduces a new robust method for estimating Pareto tail index from grouped data.
problem Limited robust methods for estimating Pareto tail index from grouped data.
method Method of Truncated Moments (MTuM)
result Inferential justification and validation of MTuM through simulation study.
New method improves robustness of neural network-based debiasing.
problem Improving robustness of neural network-based debiasing.
method Moment-constrained learning for neural networks.
result Improved performance compared to state-of-the-art benchmarks.
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 ℓ 0 \ell_0 ℓ 0 -norm minimization under second moment constraints, and using ℓ 1 \ell_1 ℓ 1 and ℓ p \ell_p ℓ p minimization techniques. result The proposed method achieves order optimal robust mean estimation and significantly outperforms existing methods.
Double machine learning provides n \sqrt{n} n -consistent estimates of parameters of interest even when high-dimensional or nonparametric nuisance parameters are estimated at an n − 1 / 4 n^{-1/4} n − 1/4 rate. The key is to employ Neyman-orthogonal moment equations which are first-order insensitive to perturbations in the nuisance param…
Expands newsvendor model with moment constraints using Wasserstein distance.
problem Optimizing order quantity under distributional ambiguity.
method Formulates infinite dimensional primal problem, derives finite dimensional dual problem using problem of moments duality.
result Distributional ambiguity affects optimal order quantity and profits/costs.
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.
This paper discusses different classes of loss models in non-life insurance settings. It then overviews the class Tukey transform loss models that have not yet been widely considered in non-life insurance modelling, but offer opportunities to produce flexible skewness and kurtosis features often required in loss modell…
Paper tackles robust deep learning from weakly dependent data with unbounded loss and input.
problem Tackles robust deep learning from weakly dependent data with unbounded loss and input.
method Establishes non-asymptotic bounds for expected excess risk under strong mixing and ψ ψ ψ -weak dependence assumptions. result Derives a relationship between bounds and r r r , and shows convergence rate close to i.i.d. results for r = ∞ r=\infty r = ∞ . Paper develops methods for estimating GLMs and SNR under proportional asymptotics.
problem Estimation of regression coefficients and SNR in high-dimensional GLMs.
method Method-of-Moments type estimators that bypass nuisance function estimation.
result Consistent and asymptotically normal estimators derived for targets of inference.
Unified framework for distribution shift estimation, explanation, and improvement.
problem Estimating, explaining, and improving model performance on target domains with distribution shift.
method Entropic Projection Alignment (EPA) aligns source and target distributions by matching moments and minimizing KL divergence.
result EPA consistently outperforms state-of-the-art baselines while offering computational efficiency.
This paper examines how data affects risk measures in uncertain distributions.
problem How does distributional ambiguity affect risk measures?
method Formulated and derived simpler dual problems for infinite and finite dimensional robust moment problems.
result Developed theory and conducted experiments in inventory control and portfolio management.
Paper presents robust confidence sequences for means with known moment bounds and arbitrary corruption.
problem Tackles robustness to outliers and adversarial corruptions in mean estimation.
method Designs new robust exponential supermartingales to create confidence sequences.
result Achieves optimal width and shows smaller margin of error compared to fixed-time robust methods.
Robust estimation under Huber's ε ε ε -contamination model has become an important topic in statistics and theoretical computer science. Statistically optimal procedures such as Tukey's median and other estimators based on depth functions are impractical because of their computational intractability. In this paper, we est…
This work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models---including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation---which exploits a certain tensor structure in their low-order observable moments (typically…
New method for adaptive estimation and inference in econometric models without knowing smoothness.
problem Adaptive estimation and inference in ill-posed linear inverse problems with unknown smoothness.
method Discrepancy principle-based framework for adaptive hyperparameter selection.
result Achieves optimal rates in weak and strong metrics for linear functionals.
We develop efficient algorithms for estimating low-degree moments of unknown distributions in the presence of adversarial outliers. The guarantees of our algorithms improve in many cases significantly over the best previous ones, obtained in recent works of Diakonikolas et al, Lai et al, and Charikar et al. We also sho…
Paper identifies tensor ranks via prior predictive matching, solving system of equations.
problem Determining the latent dimensions (ranks) in tensor factorization models.
method Prior predictive moment matching to transform moment matching conditions into a log-linear system of equations.
result Identifies which tensor models have identifiable ranks and derives rank estimators.
New robust estimator improves variable selection and coefficient estimation in linear regression with heavy-tailed errors and outliers.
problem Heavy-tailed errors and anomalous predictors in high-dimensional regression.
method Adaptive PENSE estimator for robust variable selection and estimation.
result Adaptive PENSE estimator provides reliable results even under very heavy-tailed errors and aberrant predictors.
New method for estimating covariance with robustness to outliers.
problem Estimating covariance from noisy data with outliers.
method Cross-fitted clipped covariance estimator with computable Bernstein certificates.
result The method balances certified stochastic error and robust hold-out proxy for clipping bias.
Robust statistics traditionally focuses on outliers, or perturbations in total variation distance. However, a dataset could be corrupted in many other ways, such as systematic measurement errors and missing covariates. We generalize the robust statistics approach to consider perturbations under any Wasserstein distance…
We present and analyze a central cutting surface algorithm for general semi-infinite convex optimization problems, and use it to develop a novel algorithm for distributionally robust optimization problems in which the uncertainty set consists of probability distributions with given bounds on their moments. Moments of a…
Developed moment estimators for affine stochastic volatility models.
problem Estimating parameters of affine stochastic volatility models.
method Introduced recursive equations for moments and proposed moment estimators.
result Established a central limit theorem and derived asymptotic covariance matrix.
Efficient policy learning from observational data using weighted classification reductions.
problem Efficient policy evaluation does not necessarily lead to efficient estimation of policy parameters.
method Proposed an estimation approach based on generalized method of moments, efficient for policy parameters.
result Demonstrated empirical efficiency and regret benefits of a proposed method.
Study improves robust nonparametric regression in heavy-tailed noise.
problem Robust nonparametric regression with heavy-tailed noise and unbounded functions.
method Huber regression in reproducing kernel Hilbert spaces (RKHS), probabilistic effective hypothesis space, new comparison theorems.
result Explicit finite-sample error bounds and convergence rates for Huber regression in RKHS under heavy-tailed noise.
Efficiently estimates mean of symmetric distributions without moments.
problem Estimating mean of symmetric distributions without moment assumptions.
method Generalization of filtering technique, Huber-loss-based techniques, SoS proofs.
result Achieves optimal error bounds for various symmetric distributions.