Paper solves robust multi-dimensional scaling with accelerated projections.
problem Localize point locations from noisy pairwise distances.
method Alternating projections with tangent space acceleration.
result Linear convergence of reconstructed points to original points.
Study on robust utility maximization with nonconcave utility functions under projective determinacy.
problem Investor's optimal investment strategy under model ambiguity and nonconcave utility.
method Projective functions of the path and sets of priors, upper-semicontinuous utility.
result Existence of optimal investment strategy under PD.
Paper establishes robust no-arbitrage conditions under projective determinacy.
problem Understanding financial models under Knightian uncertainty.
method Adopting a projective framework, treating all model components uniformly in terms of measurability.
result Establishes characterizations of robust no-arbitrage condition under PD.
New algorithm uses random projections for robust, sparse data classification.
problem Improving robustness and sparsity in data classification.
method Randomly projects data into a high-dimensional space, truncates small entries, and applies a cap operation.
result The method enhances classification accuracy with minimal loss, especially in noisy conditions.
Efficiently checks local robustness in neural networks using geometric projections.
problem Ensuring robustness of neural networks against adversarial inputs.
method Systematic search for decision boundaries in convex polyhedral regions using geometric projections.
result Shows geometric projections can efficiently check robustness in neural networks.
While robust parameter estimation has been well studied in parametric density estimation, there has been little investigation into robust density estimation in the nonparametric setting. We present a robust version of the popular kernel density estimator (KDE). As with other estimators, a robust version of the KDE is u…
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.
In this paper, we propose a new fast and robust recursive algorithm for near-separable nonnegative matrix factorization, a particular nonnegative blind source separation problem. This algorithm, which we refer to as the successive nonnegative projection algorithm (SNPA), is closely related to the popular successive pro…
MimicGAN improves robustness of image projections under corruption.
problem Robust projection onto image manifolds is challenging due to corruptions.
method Proposes corruption mimicking to robustly project images.
result Significantly more robust than PGD under various corruptions.
RPE detects anomalies robustly in time-series data.
problem Detecting anomalies in time-series data efficiently and robustly.
method Window-based, robust projection step, closed-form algorithm.
result RPE can identify anomalies in time-stamp level and outperforms existing methods.
New method speeds up PGD for CV robustness evaluation.
problem Computational inefficiency of PGD for robustness evaluation.
method Early termination of PGD based on cycle detection.
result Large speedup factors without sacrificing robustness.
A general duality proof for Wasserstein distributionally robust optimization.
problem Optimizing under uncertainty with Wasserstein distance.
method One-dimensional convex analysis and interchangeability principle.
result General duality result holds for various distributions and costs.
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 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.
This project improves model robustness to affine transformations.
problem Vulnerability of models to affine transformations.
method Evolution strategies for finding worst affine transforms.
result Effective robust models against non-parametric adversarial perturbations.
Adversarial robustness in multi-index models is as easy as standard learning.
problem Adversarial robustness in high-dimensional multi-index models.
method Proves that hidden directions of multi-index models offer a Bayes optimal low-dimensional projection for robustness against ℓ 2 \ell_2 ℓ 2 -bounded adversarial perturbations. result Adversarially robust learning is as easy as standard learning, requiring no additional samples.
Accelerated optimization methods improve robustness and privacy in estimation.
problem Improving robustness and privacy in estimation methods.
method Accelerated gradient methods based on Frank-Wolfe and projected gradient descent, with tailored learning rates and Nesterov's momentum.
result Reduction in iteration complexity, leading to stronger statistical guarantees.
Paper proposes PRWB and RPRWB for Wasserstein barycenters.
problem Numerical challenges in computing Wasserstein barycenters.
method Projection robust Wasserstein barycenter (PRWB) and relaxed PRWB (RPRWB).
result RPRWB improves clustering performance on real text datasets.
Paper improves SPA and its variants' robustness to noise.
problem Robustness of successive projection algorithm (SPA) and its variants to noise.
method Proved and improved error bounds for SPA and variants.
result Significantly improved error bounds for SPA and variants under specific conditions.
FSPA bypasses eigenvalue estimation for quantum PCA, achieving optimal complexity and robustness.
problem Quantum PCA eigenvalue estimation is computationally expensive and prone to errors.
method Filtered Spectral Projection Algorithm (FSPA) that projects onto the dominant spectral subspace directly.
result FSPA achieves optimal complexity and robustness, outperforming classical methods.
The successive projection algorithm (SPA) is a fast algorithm to tackle separable nonnegative matrix factorization (NMF). Given a nonnegative data matrix X X X , SPA identifies an index set K \mathcal{K} K such that there exists a nonnegative matrix H H H with X ≈ X ( : , K ) H X \approx X(:,\mathcal{K})H X ≈ X ( : , K ) H . SPA has been successfully used as a…
Paper tackles robust optimal transport with improved computational complexity and barycenter approximation.
problem Computing robust optimal transport and its barycenter efficiently.
method Sinkhorn-based algorithms for robust optimal transport and iterative Bregman projections for barycenter approximation.
result Improved computational complexity for robust optimal transport and barycenter approximation.
Bayesian approach to portfolio selection reduces pessimism in frequent trading.
problem Tackling the challenge of estimating drift in Merton's portfolio selection model.
method Bayesian distributionally robust control with nonlinear Wasserstein projections.
result Reduced pessimism and improved performance in frequent rebalancing compared to existing methods.
PGD-trained models have a preferential direction in their gradients, which improves robustness.
problem Mathematical lack of clarity in the direction of preferential gradient alignment after adversarial training.
method Proposed a novel definition of preferential direction and evaluated it using a metric based on GANs.
result PGD-trained models have higher alignment with the proposed preferential direction than baseline models.
New method for robustly interpreting ML models using quantile constraints and Wasserstein projections.
problem Assessing robustness of black-box models to input misspecification.
method Quantile-constrained Wasserstein projections for robust interpretability.
result Analytical solution for perturbation problem and smooth perturbations.
PDTS improves robustness in sequential decision-making.
problem Robust active task sampling for efficient and reliable decision-making.
method Characterizes robust active task sampling as a Markov decision process, proposes PDTS method.
result Significantly improves zero-shot and few-shot adaptation robustness.
The successive projection algorithm (SPA) has been known to work well for separable nonnegative matrix factorization (NMF) problems arising in applications, such as topic extraction from documents and endmember detection in hyperspectral images. One of the reasons is in that the algorithm is robust to noise. Gillis and…
Geometric technique determines exactness of SDP robustness certificate.
problem Certifying robustness of neural networks to adversarial examples.
method Geometric projection onto hyperbola, SDP relaxation of ReLU activation.
result SDP certificate is exact for a single hidden layer under mild assumptions.
Paper quantifies distortion risk measures' robustness to distributional uncertainty.
problem Quantifying risk measures' robustness to distributional uncertainty.
method Employing isotonic projections, the paper derives bounds on distortion risk measures' values.
result Sharp bounds on distortion risk measures' values are provided, especially for Value-at-Risk and Range-Value-at-Risk.
Rare data in a large-scale database are called outliers that reveal significant information in the real world. The subspace-based outlier detection is regarded as a feasible approach in very high dimensional space. However, the outliers found in subspaces are only part of the true outliers in high dimensional space, in…
Develops PRPCA for smooth image recovery combining low-rank and smoothness.
problem Image matrix recovery under low-rank and smoothness assumptions.
method Projected Robust PCA (PRPCA) framework combining low-rank and smoothness.
result Explicit statistical guarantees for PRPCA, reducing matrix dimensionality.
s-OTDD compares datasets efficiently without training, robust to class variations.
problem Efficiently compare datasets without training or class variations.
method Moment Transform Projection (MTP) and sliced optimal transport.
result s-OTDD correlates with optimal transport and transfer learning performance.
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.
HD-BWDM improves clustering validation in high-dimensional data.
problem Determining the right number of clusters in high-dimensional data.
method HD-BWDM integrates random projection, PCA, trimmed clustering, and medoid-based distances.
result HD-BWDM remains stable and interpretable under high-dimensional projections and contamination.
A new method solves the projection robust Wasserstein distance problem efficiently.
problem Computing the projection robust Wasserstein distance is challenging due to the curse of dimensionality.
method Riemannian block coordinate descent (RBCD) method to solve the regularized max-min problem over the Stiefel manifold.
result RBCD method significantly improves the complexity of obtaining an ε-stationary point compared to existing methods.
Motivated by vision tasks such as robust face and object recognition, we consider the following general problem: given a collection of low-dimensional linear subspaces in a high-dimensional ambient (image) space, and a query point (image), efficiently determine the nearest subspace to the query in ℓ 1 \ell^1 ℓ 1 distance. In…
Many machine learning systems are vulnerable to small perturbations made to inputs either at test time or at training time. This has received much recent interest on the empirical front due to applications where reliability and security are critical. However, theoretical understanding of algorithms that are robust to a…
We propose a fair principal component analysis method that balances reconstruction error and subgroup fairness.
problem Fairness and robustness in principal component analysis for consequential domains.
method Distributionally robust optimization over the Stiefel manifold with a Riemannian subgradient descent.
result The proposed method achieves better performance on real-world datasets compared to state-of-the-art baselines.
This paper explores robust recovery of a superposition of R R R distinct complex exponential functions from a few random Gaussian projections. We assume that the signal of interest is of 2 N − 1 2N-1 2 N − 1 dimensional and R < < 2 N − 1 R<<2N-1 R << 2 N − 1 . This framework covers a large class of signals arising from real applications in biology, automation,…
SAP corrects model for label noise by identifying and removing noisy samples.
problem Label corruption degrades model performance; acquiring perfect labels is costly.
method SAP uses SVD to identify and project model weights onto a clean activation space.
result SAP improves model generalization by up to 6% on CIFAR dataset with 25% synthetic corruption.
A variety of real-world tasks involve the classification of images into pre-determined categories. Designing image classification algorithms that exhibit robustness to acquisition noise and image distortions, particularly when the available training data are insufficient to learn accurate models, is a significant chall…
Study assesses CNN model robustness to noise in low-cost CT scans.
problem Evaluate CNN model performance on noisy, artifact-prone low-cost CT images.
method Developed and tested a CNN model for head CT triage, varying tube current and projections.
result Model remains robust to reduced tube current and fewer projections, maintaining AUROC close to original.
We address the problem of automatic generation of features for value function approximation. Bellman Error Basis Functions (BEBFs) have been shown to improve the error of policy evaluation with function approximation, with a convergence rate similar to that of value iteration. We propose a simple, fast and robust algor…
RieCUR improves Robust PCA by combining Riemannian optimization and CUR decompositions.
problem Robust Principal Component Analysis (PCA) to recover low-rank and sparse matrices from their sum.
method Riemannian CUR (RieCUR) algorithm that combines Riemannian optimization and robust CUR decompositions.
result RieCUR achieves state-of-the-art performance in Robust PCA with improved robustness to outliers and comparable computational complexity.
Efficiently learns distributions corrupted by both global and local adversarial modifications.
problem Learning distributions with both global and local adversarial corruptions.
method Develops an efficient algorithm to minimize Wasserstein distance with orthogonal projections.
result Achieves optimal risk bounds with error ε k + ρ + i l d e O ( d k n − 1 / ( k ∨ 2 ) ) \sqrt{\varepsilon k} + ρ+ ilde{O}(d\sqrt{k}n^{-1/(k \lor 2)}) ε k + ρ + i l d e O ( d k n − 1/ ( k ∨ 2 ) ) . Concept Factorization (CF) and its variants may produce inaccurate representation and clustering results due to the sensitivity to noise, hard constraint on the reconstruction error and pre-obtained approximate similarities. To improve the representation ability, a novel unsupervised Robust Flexible Auto-weighted Local…
HiPPO framework optimizes memory compression for sequential data.
problem Incremental representation of cumulative history in sequential data.
method Optimal polynomial projections for online function approximation.
result HiPPO-LegS achieves state-of-the-art accuracy on MNIST.
Paper analyzes robust matrix completion with efficient nonconvex method and leave-one-out analysis.
problem Robust matrix completion with sparse noise.
method Alternates between projected gradient step for low-rank and thresholding step for sparse noise.
result Achieves linear convergence for general thresholding functions.