arXiv research

Generalized Huber's theorem for specific manifold curvature types.

The paper extends Huber's theorem to higher dimensions with specific geometric constraints.

We show that for compact orientable hyperbolic orbisurfaces, the Laplace spectrum determines the length spectrum as well as the number of singular points of a given order. The converse also holds, giving a full generalization of Huber's theorem to the setting of compact orientable hyperbolic orbisurfaces.

The paper extends Huber's theorem to higher dimensions using n-Laplace equations.

New theorems in 2D and 4D for metrics with curvature or singularity.

New proof shows special surfaces have finite type.

Paper uses Gromov-Hausdorff convergence to re-examine surface classification.

Paper proposes a robust framework for detecting multiple periodic components in time series.

Paper proposes an algorithm for robust estimation using Huber's criterion.

Huber regression assessed for robustness in statistical learning.

Study on Hausdorff dimension of singular CR Yamabe problem.

Deep Huber QRNs predict Huber quantiles for house prices.

The Huber loss is a robust loss function used for a wide range of regression tasks. To utilize the Huber loss, a parameter that controls the transitions from a quadratic function to an absolute value function needs to be selected. We believe the standard probabilistic interpretation that relates the Huber loss to the H…

The paper proves new inequalities on the unit ball in higher dimensions.

The paper proposes new cross-correlators using Price's Theorem and piecewise-linear decomposition.

Proposes a new Huber loss combining absolute and quadratic properties.

Paper introduces a new robust loss function for RL.

A new Markov subsampling strategy based on Huber criterion improves data processing from noisy full data.

The paper counts geodesic loops on surfaces without conjugate points.

The paper derives estimates for linear potentials and applies them to improve Hausdorff dimensions of singular sets in conformal geometry.

Study improves robust nonparametric regression in heavy-tailed noise.

Super learner with Huber loss improves cost prediction and causal effect estimation in healthcare expenditure data.

The paper applies potential theory to conformal geometry, proving theorems and dimension estimates.

The paper introduces a new FOR framework using Huber and ε-insensitive losses.

This paper examines how noise affects deep neural networks and improves their performance.

Counting periodic geodesics of bounded length and commutator structure on hyperbolic surfaces.

We show that if two closed hyperbolic surfaces (not necessarily orientable or even connected) have the same Laplace spectrum, then for every length they have the same number of orientation-preserving geodesics and the same number of orientation-reversing geodesics. Restricted to orientable surfaces, this result reduces…

Study improves $H$-consistency bounds for regression analysis.

Improved robust regression with clean covariates achieves better rates than Huber's model.

Proposes a new loss function for robust learning.

This paper solves hedging in incomplete markets using neural networks.

New proof shows faster convergence rate for robust estimation with Lasso in adversarially contaminated outputs.

A robust Gaussian process model using Huber likelihood for outlier resistance.

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…

In this paper, we generalize Huber's criterion to multichannel sparse recovery problem of complex-valued measurements where the objective is to find good recovery of jointly sparse unknown signal vectors from the given multiple measurement vectors which are different linear combinations of the same known elementary vec…

New method recovers sparse signals from nonlinear observations with robust error bounds.

Supervised learning is an active research area, with numerous applications in diverse fields such as data analytics, computer vision, speech and audio processing, and image understanding. In most cases, the loss functions used in machine learning assume symmetric noise models, and seek to estimate the unknown function …

New method uses robust estimators for Newton's method in empirical risk minimization.

RHPSVM improves SVM performance with robust loss function.

Study minimax rates for density estimation under Huber contamination and Besov IPM losses.

Robust estimators for Gaussian sparse tasks with optimal error under contamination.

Near-optimal algorithms for mean estimation and linear regression with Gaussian covariates and Huber contamination.

The normal map given by Birkhoff orthogonality yields extensions of principal, Gaussian and mean curvatures to surfaces immersed in three-dimensional spaces whose geometry is given by an arbitrary norm and which are also called Minkowski spaces. We obtain characterizations of the Minkowski Gaussian curvature in terms o…

Paper presents robust confidence sequences for means with known moment bounds and arbitrary corruption.

Study improves error bounds for sparse regression with heavy-tailed covariates.

A new method quantizes conditional probability measures using deep learning.

New RESK distributions improve robust clustering of skewed data.

Improved robust regression for heavy-tailed and contaminated data.