Robust test for distributions under Hellinger distance, simpler than optimal tests.
problem Testing and estimating distributions robustly under Hellinger distance.
method Simple robust hypothesis test with optimal sample complexity, robust to Hellinger distance perturbations.
result Empirically demonstrated robustness and power of the test on canonical distributions.
A new robust time series distance metric for k-NN classification.
problem Robustness against arbitrary data contamination in time series classification.
method Proposes a novel distance metric with worst-case O(nlogn) complexity. result Demonstrates competitive classification accuracy in k-NN time series classification.
Paper tackles robust Euclidean distance estimation with sparse outliers.
problem Estimating point positions from corrupted distance measurements.
method Proposes a novel algorithm using Nyström method and robust PCA.
result Achieves accurate recovery with minimal anchors and sparse outliers.
Paper tackles robust optimization under uncertainty using nested distance.
problem Optimizing under distributionally robust uncertainty with nested distance.
method Equivalent recursive and dynamic programming reformulations for tractable optimization.
result Optimal robust policies can be found efficiently using convex optimization.
Optimizes distributions robustly with Sinkhorn distance.
problem Distributionally robust optimization with Wasserstein distance.
method Convex programming dual reformulation, stochastic mirror descent algorithm.
result Demonstrates superior performance in synthetic and real data.
Novel neural network approximates exact distance for robust classification.
problem Adversarial attacks on neural networks in safety-critical systems.
method Signed Distance Classifiers (SDCs) and Unitary-Gradient Neural Network.
result Approximates exact distance from classification boundary for certifiable predictions.
Paper introduces robust market making using Wasserstein distance and entropy regularization.
problem Market making robustness under uncertainty.
method Wasserstein distance, entropy regularization, convex optimization, optimal radius selection.
result The robust market making problem can be reformulated as a convex optimization problem.
A new method detects small holes in noisy data.
problem Detecting small holes in high-density regions from noise.
method Robust Density-Aware Distance (RDAD) filtration, incorporating distance-to-measure concept.
result The RDAD filtration prolongs the persistences of small holes, making them distinguishable from noise.
Study robust distribution estimation with Wasserstein distance, achieving optimal risk.
problem Robust distribution estimation under adversarial corruption.
method Combining partial OT and minimum distance estimation, proving structural properties and deriving a novel dual form.
result Achieves minimax-optimal robust estimation risk in many settings.
This work improves scalability of Wasserstein distances in high dimensions.
problem Scalability issues in computing Wasserstein distances in high dimensions.
method Empirical convergence rates, robustness to data contamination, and computational methods.
result Established fast rates and robust estimation risks for sliced Wasserstein distances.
Study robust hypothesis testing under Hellinger distance, proving lower bounds and providing tests.
problem Testing close variants of specified distributions robustly to Hellinger distance.
method Lower bound on slack factor, testing with Hellinger balls, symmetric chi-squared distance analysis.
result Lower bound on slack factor quantifies robustness under misspecification.
Private minimum Hellinger distance estimators maintain robustness and efficiency while ensuring privacy.
problem Ensuring privacy in robust statistical estimation.
method Derive private minimum Hellinger distance estimators satisfying Hellinger differential privacy.
result Private minimum Hellinger distance estimators retain robustness and efficiency under privacy constraints.
WRAAC uses Wasserstein distance for robust reinforcement learning.
problem Lack of quantified robustness to system dynamics in existing reinforcement learning algorithms.
method Leverages Wasserstein distance to connect state disturbance to transition kernel disturbance, reducing infinite-dimensional optimization to a finite-dimensional problem.
result Designs a novel algorithm, WRAAC, that achieves robust reinforcement learning.
A new robust Wasserstein distance is proposed to handle outliers in probability distributions.
problem Outliers in probability distributions make Wasserstein distances sensitive and impractical.
method Introduces a new outlier-robust Wasserstein distance Wpε. result Achieves strong robust estimation guarantees under the Huber ε-contamination model. We introduce a new metric to evaluate corruption robustness of ML classifiers.
problem Evaluating corruption robustness of machine learning classifiers.
method We propose a test data augmentation method using minimal class separation distance to derive a robustness distance ε and a metric MSCR.
result The MSCR metric allows interpretable comparison of classifier robustness on different datasets.
This work robustifies Wasserstein distance estimation with MoM estimators for outlier-polluted data.
problem Estimating Wasserstein distance between two distributions with outliers.
method Introducing MoM-based robust estimators for Wasserstein distance.
result Consistent MoM-based estimators for Wasserstein distance with convergence rates.
A new robust metric compares distributions more accurately than existing methods.
problem Sensitivity to outliers and sampling discrepancy in Wasserstein distances.
method Introducing k-RPW, a partial p-Wasserstein distance.
result k-RPW converges faster to true distance and is more robust to outliers.
Improved training boosts certified robustness of L-infinity distance nets.
problem Certified robustness of L-infinity distance nets is not as strong as conventional networks.
method Improved training process combining scaled cross-entropy and clipped hinge loss with a decaying mixing coefficient.
result Certified accuracy of L-infinity distance nets improved from 33.30% to 40.06% on CIFAR-10.
Exact generalization guarantees for robust models using Wasserstein distance are established.
problem Capturing data uncertainty and distribution shifts in machine learning models.
method Establishes exact generalization guarantees for robust models based on the Wasserstein distance, covering various cases and transport costs.
result Exact generalization guarantees are provided for a wide range of cases, including deep learning objectives with nonsmooth activations.
Paper proposes a robust hypothesis testing method using Sinkhorn distance.
problem Hypothesis testing for small samples.
method Data-driven approach using Sinkhorn uncertainty sets.
result The method provides a more flexible detector compared to Wasserstein robust test.
Paper proposes a robust metric learning algorithm.
problem Robustness of metric learning against adversarial perturbations is insufficient.
method Proposes a novel Mahalanobis distance metric learning algorithm.
result Certifiable robustness improvement over Euclidean distance.
Paper presents efficient computation of robust Wasserstein distance using Riemannian optimization.
problem Intractability of optimizing Projection Robust Wasserstein (PRW) distance due to non-convexity and non-smoothness.
method Riemannian optimization to efficiently compute PRW/Wasserstein Projection Pursuit (WPP) distance.
result The original formulation of PRW/WPP can be efficiently computed in practice, providing better behavior than its convex relaxation.
Connects robust optimization to conformal prediction for uncertainty sets.
problem Decision-making under uncertainty in sensitive data.
method Defines Mahalanobis distance as a conformity score and generates conformal uncertainty sets.
result Conformal uncertainty sets provide valid and conservative ellipsoidal regions.
Advances robustness of metric learning by adversarial margin in input space.
problem Improving robustness of metric learning algorithms.
method Imposing adversarial margin in input space, minimizing perturbation loss.
result Enlarged adversarial margin improves generalization and robustness.
Paper proposes a method to recover point configurations from noisy distance data.
problem Recovering point configurations from noisy distance data.
method Robust Euclidean Distance Geometry via Dual Basis (RoDEoDB) algorithm.
result Exact recovery guarantees for point configuration and Gram matrix under mild conditions.
This work improves understanding of projection robust optimal transport distances.
problem Understanding the behavior of minimum Wasserstein estimators in high-dimensional and misspecified models.
method Adopting projection robust (PR) optimal transport, establishing statistical properties, proposing IPRW distance, and providing asymptotic guarantees.
result Established fundamental statistical properties and proposed new distances that outperform Wasserstein distances empirically.
Paper tackles robust model training with a new stochastic algorithm.
problem Training robust models against data distribution shift.
method Derives a novel dual formulation and proposes a nested stochastic gradient descent algorithm.
result Establishes polynomial iteration and sample complexities for large-scale DRO problems.
RS-Del provides robustness for sequence classifiers against edit distance attacks.
problem Certifying robustness of discrete sequence classifiers against edit distance attacks.
method Randomized deletion (RS-Del) for discrete sequence classifiers, focusing on edit distance-bounded adversaries.
result Achieved a certified accuracy of 91% at an edit distance radius of 128 bytes on malware detection.
A robust conformal method for set estimation using non-conformity scores.
problem Lack of robustness in standard conformal prediction methods for outliers or heavy tails.
method Robust conformal method based on non-conformity score defined as half-mass radius.
result Empirical conformal regions converge to robust population central set.
Model-based clustering is widely-used in a variety of application areas. However, fundamental concerns remain about robustness. In particular, results can be sensitive to the choice of kernel representing the within-cluster data density. Leveraging on properties of pairwise differences between data points, we propose a…
Develops robust MDPs for unknown disturbances with performance guarantees.
problem Unknown disturbance distribution in MDPs.
method Empirical distribution, sublevel set of distance function, weak convergence, concentration inequality.
result Robust optimal value function converges to true optimal value function with increasing sample sizes.
Robust GW distance improves graph data alignment.
problem Outliers in GW distance lead to inaccurate comparisons.
method Optimistically perturbed marginal constraints within a Kullback-Leibler divergence-based ambiguity set.
result RGW reduces inaccuracies in graph data alignment.
New model improves data augmentation for causal tasks.
problem Optimizing causal models robustly under Wasserstein distances.
method Proposes a new G-Causal Normalizing Flow architecture.
result Empirically outperforms standard generative models.
Paper extends multivariate rank tests for robust subspace detection.
problem Testing distributional similarity in multivariate data.
method Soft and subspace robust multivariate rank tests based on entropy regularized optimal transport.
result Trade-off between detection power and false alarm rate via projections.
Local robustness verification can verify that a neural network is robust wrt. any perturbation to a specific input within a certain distance. We call this distance Robustness Radius. We observe that the robustness radii of correctly classified inputs are much larger than that of misclassified inputs which include adver…
Study robustness of polynomial neural networks using algebraic geometry.
problem Certify robustness radius of polynomial neural networks.
method Metric algebraic geometry, Euclidean distance degree, symbolic elimination, homotopy-continuation methods.
result Found decision boundaries with lower ED degree than generic cubic hypersurfaces.
ClusTR improves clustering-based models' robustness without adversarial training.
problem Improving clustering-based models' robustness.
method Proposes ClusTR, a clustering-based training framework for robust models without adversarial training.
result ClusTR outperforms adversarially-trained models by up to 4% under strong PGD attacks.
Robustly aligns datasets with partial GW distance to handle contamination.
problem Aligning contaminated datasets using Gromov-Wasserstein distances.
method Proposes a partial GW distance estimator to minimize distortion from outliers.
result The partial GW distance estimator is minimax optimal and near-optimal in finite samples.
This paper investigates calculations of robust funding valuation adjustment (FVA) for over the counter (OTC) derivatives under distributional uncertainty using Wasserstein distance as the ambiguity measure. Wrong way funding risk can be characterized via the robust FVA formulation. The simpler dual formulation of the r…
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 robust method for optimal transportation improves statistical inference.
problem Sensitivity to outliers and undefinedness in optimal transportation methods.
method Robust optimal transportation with a tuning parameter λ, leading to robust Wasserstein distance.
result The robust method provides statistical guarantees and improves machine learning applications.
Expands robust profit opportunities to include distributional uncertainty.
problem Distributional uncertainty in financial markets.
method Formulates infinite dimensional primal problems, simplifies to finite dimensional dual problems using Wasserstein distance.
result Distributional uncertainty can enhance robustness of profit opportunities.
Robust learning method combines kernel smoothing and robust optimization.
problem Certifying robustness against distribution shifts in machine learning models.
method Adapting integral operator using supremal convolution for robustness, leveraging optimal transport.
result The method provides theoretical guarantees for certified robustness and competitive performance.
The paper studies robust risk measures with linear penalties under uncertain distributions.
problem Risk measurement under distributional uncertainty.
method Robust distortion risk measures with linear penalty function under distributional constraints.
result Explicit characterization of optimal quantile distribution and value function.
Robust Bayesian inference improves model performance on discrete data.
problem Misspecification of discrete-valued models leads to poor inference and prediction.
method Total Variation Distance (TVD) for discrepancy, efficient estimator and inference method.
result Our approach significantly improves predictive performance on various data.
New method improves PCA robustness using Wasserstein distances.
problem Uncertainty in probability distribution affects PCA robustness.
method Distributionally robust optimization with Wasserstein distances.
result Explicit reformulation leads to efficient smoothing algorithm.
New method robustifies topological data analysis against outliers.
problem Outliers make topological data analysis unstable.
method Proposed a robust distance function (MoM Dist) for persistent homology.
result MoM Dist sublevel filtrations and weighted filtrations are consistent estimators in adversarial settings.
New method learns distances and similarities robustly from noisy data.
problem Scalability and robustness in metric learning for large datasets.
method Robust online Distance-Similarity learning with Rescaled hinge loss.
result Significantly outperforms state-of-the-art methods in noisy data.