A new PCA method using T-norm outperforms existing methods.
problem Outliers and noise sensitivity in classical PCA.
method PCA based on T-norm maximization.
result The method outperforms PCA-, SPCA, and PCA in numerical experiments.
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A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,051 papers · 148 categories
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48 results for “\(\ell^4\)-norm”
Guarantees recovery of compressible signals from adversarial noise.
problem Recovering compressible signals from noise and adversarial attacks.
method Extends adversarial defense framework to , , and norms.
result Recovery guarantees for various signal recovery methods under different noise types.
New method improves signal estimation by convexifying -norm constraints.
problem Signal estimation with sparsity and smoothness priors.
method Iterative convex conic quadratic relaxations exploiting -norm and smoothness terms.
result Significantly better estimators than -norm approaches and interpretable parameters.
In this paper, we propose -norm regularized models to seek near-optimal sparse portfolios. These sparse solutions reduce the complexity of portfolio implementation and management. Theoretical results are established to guarantee the sparsity of the second-order KKT points of the -norm regularized models…
Paper finds a fast method for a matrix norm proximal operator.
problem Optimizing mixed matrix norms efficiently.
method Closed-form computation using soft-thresholding, iterative algorithm for thresholds.
result Mixed prox can be computed in closed form.
Improved algorithms solve -norm regression problems efficiently.
problem Efficiently solving -norm regression problems for .
method Iterative refinement scheme using smoothed -norms to improve solutions.
result Solves -norm regression to accuracy in iterations.
AdamW optimizes a constrained loss with norm constraint.
problem Understanding the optimization behavior of AdamW with norm constraint.
method Analyzing AdamW as a smoothed version of SignGD and connecting it to Frank-Wolfe optimization.
result AdamW implicitly performs constrained optimization with norm constraint.
New attack reveals adversarial training's inability to handle both and norms.
problem Adversarial training's inability to ensure robustness across and norms.
method Proposed a new attack to expose the weakness of adversarial training.
result Adversarial training fails to achieve robustness in both and norms.
Generalizes inequality for complete manifolds involving homology classes.
problem Volume and simplicial volume inequality for closed manifolds.
method Extends inequality to -norm of homology classes on complete manifolds.
result Inequality involving critical exponent and mass of homology classes.
Proposes new -based methods for low-rank sparse subspace clustering.
problem Clustering high-dimensional data points represented by low-dimensional subspaces.
method Introduces two quasi-norm based regularizations: GMC-LRSSC and -LRSSC. Solves resulting nonconvex optimization problems using alternating direction method of multipliers.
result Demonstrates effectiveness of proposed methods on synthetic and real-world datasets.
The paper studies the minimum ℓ₁-norm interpolator's risk behavior in over-parameterized settings.
problem Understanding the risk behavior of minimum ℓ₁-norm interpolators in high-dimensional settings.
method Exact characterization of the risk behavior through a system of two non-linear equations.
result Observation of a multi-descent phenomenon in the generalization risk of the minimum ℓ₁-norm interpolator.
Advances robust principal component analysis with transformed ℓ1 regularization.
problem Recovering low-rank structures from noisy, partially observed data corrupted by sparse outliers.
method Proposes transformed ℓ1 (TL1) regularization to improve approximations of rank and ℓ0 functional.
result Achieves higher accuracy in estimating low-rank and sparse components compared to classical convex models, especially under non-uniform sampling schemes.
This paper tackles robustness of ensemble stumps and trees under general ℓ_p norm perturbations.
problem The vulnerability of ensemble stumps and trees to small input perturbations under the ℓ_∞ norm.
method Developed dynamic programming algorithms for robustness verification and certified defense under general ℓ_p norm perturbations.
result First certified defense method for ensemble stumps and trees under ℓ_p norm perturbations.
State-of-the-art subspace clustering methods are based on expressing each data point as a linear combination of other data points while regularizing the matrix of coefficients with , or nuclear norms. regularization is guaranteed to give a subspace-preserving affinity (i.e., there are no conne…
CNN layers with large norms are still robust to adversarial attacks.
problem Understanding the relationship between layer norms and adversarial robustness in CNNs.
method Theoretical analysis of and norms, norm decay method, adversarial training frameworks.
result Adversarially robust CNNs can have comparable or larger layer norms than non-adversarially robust ones.
Paper tackles low-rank matrix recovery with column -norm regularization.
problem Low-rank matrix recovery problems with column sparsity constraints.
method Developed alternating majorization-minimization (AMM) methods with extrapolation and hybrid AMM.
result Global convergence analysis and superior performance in matrix completion problems.
This paper assesses Gaussian and Exponential mechanisms for certifying adversarial robustness.
problem Certifying adversarial robustness using randomized smoothing mechanisms.
method Proposes a generic framework to assess the appropriateness of randomized smoothing mechanisms.
result Gaussian mechanism is an appropriate option for certifying both -norm and -norm robustness.
In compressed sensing, in order to recover a sparse or nearly sparse vector from possibly noisy measurements, the most popular approach is -norm minimization. Upper bounds for the - norm of the error between the true and estimated vectors are given in [1] and reviewed in [2], while bounds for the $\ell_…
New algorithm solves -norm constrained multilinear logistic regression for tensor data.
problem Non-convex and nonsmooth -norm constraints in multilinear logistic regression.
method APALM method for globally convergent optimization.
result APALM ensures convergence to a first-order critical point.
The paper proposes a new method for dictionary learning using -norm maximization.
problem Complete dictionary learning problem in signal processing and data analytics.
method The paper investigates -norm maximization approaches for complete dictionary learning, proving global maximizers are close to the true dictionary and developing an efficient algorithm based on the generalized power method.
result The -based approaches are more efficient and robust than conventional methods, with performing best.
Sparse JL with higher sparsity improves feature hashing accuracy.
problem Efficiently reducing high-dimensional feature vectors to lower dimensions.
method Sparse Johnson-Lindenstrauss transform with varying sparsity levels.
result Sparse JL with sparsity greater than 1 provides better norm preservation.
The paper improves neural network robustness against multiple norm types of adversarial attacks.
problem Defending neural networks against adversarial attacks with different norms.
method Combining existing defense mechanisms to train neural networks robust against both and attacks.
result New defense mechanisms offer better protection against both and attacks.
factor analysismath.OC
New method for factor analysis using nuclear and norms.
problem Finding a low-rank plus sparse decomposition from noisy covariance matrix.
method Formulated an optimization problem with nuclear norm, norm, and KL divergence. Used alternating minimization algorithm.
result Algorithm effectively decomposes covariance matrices in synthetic and real datasets.
The paper tackles multi-armed bandits with vector losses, focusing on minimizing the -norm of relative losses.
problem Minimizing the -norm of relative losses in multi-armed bandits with multiple losses.
method Defines relative loss vector, derives lower bounds, and provides matching algorithms for both fixed-confidence best-arm identification and regret minimization.
result Derives problem-dependent sample complexity lower bound and matching algorithms for fixed-confidence best-arm identification.
Paper develops algorithms for sparse linear regression with generalized elastic net penalty.
problem Sparse linear regression with robust penalty for high-dimensional data.
method Iterative Reweighted Framework based on ADMM and PMM with SNN.
result Efficient algorithms provide superior performance in both simulated and real data.
Regularization of minimization for dealing with outliers and noise in Statistics and Signal Recoverymath.OC
We study the robustness properties of norm minimization for the classical linear regression problem with a given design matrix and contamination restricted to the dependent variable. We perform a fine error analysis of the estimator for measurements errors consisting of outliers coupled with noise. We…
Uniformly finite homology is a coarse homology theory, defined via chains that satisfy a uniform boundedness condition. By construction, uniformly finite homology carries a canonical -semi-norm. We show that, for uniformly discrete spaces of bounded geometry, this semi-norm on uniformly finite homology in …
A data filtering method for cluster analysis is proposed, based on minimizing a least squares function with a weighted -norm penalty. To overcome the discontinuity of the objective function, smooth non-convex functions are employed to approximate the -norm. The convergence of the global minimum points o…
Gradient descent-based adversarial training converges to robust classifiers on linearly separable data.
problem Understanding the inductive bias of adversarial training for robustness.
method Gradient descent on binary classification tasks with linearly separable data, focusing on inductive bias and convergence rates.
result Gradient descent-based adversarial training converges to the maximum margin classifier at a faster rate than clean data training.
This work improves robustness guarantees for neural networks using low rank representations.
problem Certified robustness to adversarial perturbations in neural networks.
method Low rank representations to provide improved robustness guarantees.
result Improved robustness guarantees for perturbations using natural low rank representations.
Paper refines cross-lingual word embeddings using Manhattan norm.
problem Sensitivity of norm loss function to outliers in CLWEs.
method Post-processing step using norm to improve CLWEs.
result The refinement substantially outperforms state-of-the-art baselines.
The paper proposes a novel MKL approach for OCC using -norm constraints.
problem Addressing the MKL problem for one-class classification.
method A min-max saddle point Lagrangian optimisation problem is formulated and solved efficiently.
result The proposed method outperforms baselines and other algorithms on various data sets.
Proposes an efficient method for sparse index tracking with -norm constraints.
problem Constructing a sparse portfolio to track a financial index.
method Formulates a new problem using -norm constraints, develops an efficient algorithm based on primal-dual splitting.
result Demonstrates effectiveness through experiments on S&P500 and Russell3000 datasets.
We discuss the problem of adaptive discrete-time signal denoising in the situation where the signal to be recovered admits a "linear oracle" -- an unknown linear estimate that takes the form of convolution of observations with a time-invariant filter. It was shown by Juditsky and Nemirovski (2009) that when the $\ell_2…
Proposes a new method for joint sample and feature selection in multi-view data.
problem Cannot detect latent subsets of samples and remove outliers.
method Weighted Sparse Partial Least Squares (-wsPLS) method for joint sample and feature selection.
result Developed globally convergent algorithm and iterative algorithms for multi-view data fusion.
An elementary proof found for the double bubble problem in a specific norm.
problem Finding the shapes that minimize perimeter for given volumes in a specific norm.
method Direct comparison to a small family of parameterized sets for analysis.
result Existence of minimizing sets for any volume ratio parameter.
Study tightens bounds for interpolating noisy data using minimum l1-norm.
problem Predicting noisy data with minimum l1-norm interpolation.
method Provided matching upper and lower bounds for prediction error.
result Tight consistency up to negligible terms for .
Unified analysis of parameter norms in overparameterized linear models, revealing scaling laws and thresholds.
problem Understanding the scaling of parameter norms in overparameterized linear models.
method Simple dual-ray analysis revealing competition between signal spike and bulk of null coordinates.
result Unified closed-form predictions for parameter norm scaling, including elbow and threshold laws.
Novel framework improves randomized smoothing for various norms.
problem Developing robust defenses against adversarial attacks.
method Proposed a novel framework for devising and analyzing randomized smoothing schemes.
result Significantly improved certified accuracy in ℓ1 on standard datasets.
New method learns complete orthogonal dictionary from samples with theoretical guarantees and efficiency.
problem Learning a complete orthogonal dictionary from sparsely generated signals.
method Maximizes the \(\ell^4\)-norm over the orthogonal group, using a novel algorithm based on matching, stretching, and projection (MSP).
result The MSP algorithm provably converges locally at a superlinear (cubic) rate and is significantly more efficient than existing methods.
We study the column subset selection problem with respect to the entrywise -norm loss. It is known that in the worst case, to obtain a good rank- approximation to a matrix, one needs an arbitrarily large number of columns to obtain a -approximation to the best entrywise -norm low ra…
Algorithm reduces regret in online learning with varying norms.
problem Online convex optimization with changing norms.
method Adaptive online learning algorithm that adjusts to varying norms without tuning.
result Achieves improved regret bounds for full-matrix AdaGrad.
Adversarial training linked to operator norm regularization, proving network sensitivity to attacks.
problem Robustifying neural networks against adversarial attacks.
method Theoretical link established between adversarial training and operator norm regularization.
result Adversarial training is equivalent to data-dependent operator norm regularization.
We simplify Thurston norm computation for 2-bridge link complements.
problem Understanding the complexity of Thurston norm unit balls in 3-manifolds.
method Utilized Floyd and Hatcher's surface description and integral class minimization.
result Thurston norm unit balls of 2-bridge link complements have at most 8 faces.
Semantify-NN verifies neural network robustness against semantic perturbations.
problem Verifying robustness of neural networks against semantic adversarial attacks.
method Inserting semantic perturbation layers (SP-layers) into neural networks to verify robustness.
result Semantify-NN significantly improves robustness verification performance over -norm-based methods.
Improved bounds for discrete probability distribution estimation under the ℓ∞ norm.
problem Estimating discrete probability distributions under the ℓ∞ norm with improved bounds.
method Minimax bounds in expectation and high-probability tail bounds.
result Resolved open questions posed in Kontorovich and Painsky (JMLR, 2025), including a fully empirical tightest risk bound and identifying the worst-case extremal distribution.
We consider the empirical risk minimization problem for linear supervised learning, with regularization by structured sparsity-inducing norms. These are defined as sums of Euclidean norms on certain subsets of variables, extending the usual -norm and the group -norm by allowing the subsets to overlap. T…
New neural network design resists small -norm adversarial perturbations.
problem Vulnerability of neural networks to small -norm adversarial perturbations.
method Designing -dist neurons and constructing -dist nets, proving their 1-Lipschitz property and expressive power.
result Certified robustness of -dist nets with state-of-the-art performance on various datasets.