arXiv research

Adversarial online nonparametric regression achieves optimal rates with locally adaptive learning.

Study approximates unknown function levels with queries.

In the context of stochastic continuum-armed bandits, we present an algorithm that adapts to the unknown smoothness of the objective function. We exhibit and compute a polynomial cost of adaptation to the H{ö}lder regularity for regret minimization. To do this, we first reconsider the recent lower bound of Locatelli an…

The purpose of these notes is to explain parts of Gromov's survey of Carnot-Carathedory spaces, in the light of subsequent results of M. Rumin. Among the rich material provided by Gromov, most of which pertains to analysis on metric spaces, we choose to concentrate on the H{ö}lder equivalence problem for Carnot manifol…

Efficient algorithms for contextual bandits with smooth regret in continuous action spaces.

We find a local solution to the Ricci flow equation under a negative lower bound for many known curvature conditions. The flow exists for a uniform amount of time, during which the curvature stays bounded below by a controllable negative number. The curvature conditions we consider include 2-non-negative and weakly $\t…

A variant of Gromov's H{ö}lder-equivalence problem, motivated by a pinching problem in Riemannian geometry, is discussed. A partial result is given. The main tool is a general coarea inequality satisfied by packing energies of maps.

This paper selects features in deep neural networks with theoretical guarantees.

Study shows zero-shot super-resolution in neural operators is impossible in many cases.

We study finite energy classes of quasiplurisubharmonic (qpsh) functions in the setting of toric compact K{ä}hler manifolds. We characterize toric qpsh functions and give necessary and sufficient conditions for them to have finite (weighted) energy, both in terms of the associated convex function in R n , and through t…

Let $S$ be a closed oriented surface of genus at least $2$, and denote by $\mathcal{T}(S)$ its Teichm{ü}ller space. For any isotopy class of closed curves $γ$, we compute the first three derivatives of the length function $\ell\_γ:\mathcal{T}(S)\rightarrow\mathbf{R}\_+$ in the shearing coordinates associated to a maxim…

We consider the problem of online nonparametric regression with arbitrary deterministic sequences. Using ideas from the chaining technique, we design an algorithm that achieves a Dudley-type regret bound similar to the one obtained in a non-constructive fashion by Rakhlin and Sridharan (2014). Our regret bound is expre…

In this paper we provide an alternative framework to tackle the first-best Principal-Agent problem under CARA utilities. This framework leads to both a proof of existence and uniqueness of the solution to the Risk-Sharing problem under very general assumptions on the underlying contract space. Our analysis relies on an…

Validates economic scenarios using statistical tests on stochastic processes.

New algorithms for interactive learning match minimax bounds efficiently.

General lower bounds on neural network approximation in L^p norm.

Introduces a space of almost complex structures for complex Lie group bundles.

Extends curve theory to non-smooth data with finite curvature and torsion.

Survey on preserving curvature bounds for non-smooth Ricci flow.

Optimal smooth subspaces approximate large data sets efficiently.

SFM generates smooth functional data without exposing real data.

Entropy data replaces classical charts for smooth manifolds.

Smoothing graphons improve link prediction in Bayesian SBM without increasing computational complexity.

Enhances random forests by smoothing predictions for better performance.

Hierarchical randomized smoothing improves model robustness for complex data.

Paper introduces SLS to improve label smoothing regularization.

Post-estimation smoothing improves prediction accuracy with structural indices.

Smooth bundles with rough data maintain Hodge kernel isomorphism.

A comprehensive methodology is provided for smoothing noisy, irregularly sampled data with non-Gaussian noise using smoothing splines. We demonstrate how the spline order and tension parameter can be chosen a priori from physical reasoning. We also show how to allow for non-Gaussian noise and outliers which are typical…

Smooth dec initial data sets may not extend to smooth spacetimes.

GPCDL uses Gaussian Processes to learn smooth templates from data.

ERM with square loss achieves sublinear error for learnable function classes with smoothed data.

A new clustering algorithm considers data smoothness for better performance.

Diffusion models adapt to data geometry through log-domain smoothing.

We propose a novel method to determine the dissimilarity between subjects for functional data clustering. Spline smoothing or interpolation is common to deal with data of such type. Instead of estimating the best-representing curve for each subject as fixed during clustering, we measure the dissimilarity between subjec…

Diffusion models improve creativity by smoothing the score function, leading to interpolated data.

New bounds for online portfolio selection without smoothness assumptions.

Regularized MFPCA smooths multivariate functional data for clearer patterns.

We prove that the space of smooth initial data and the set of smooth solutions of the Liouville equation are homeomorphic.

Proposes a neural network autoencoder for smoothing and representation learning of functional data.

Smooth compactness theorem for elasticae, except straight segments.

Proposes a spectral method for jointly smooth functions on multiple manifolds.

New neural network smoothness constraints improve model performance.

Enhances deep networks robustness with data mollification and label smoothing.

Solves Ricci flow on Riemann surfaces with measure initial data.

Adaptive data fusion boosts efficiency in multi-task optimization.

Paper introduces a new regularization method for kernel gradient descent learning.

A new federated learning algorithm improves on existing methods by exploiting data smoothness.