Optimal Rates for Spectral Algorithms with Least-Squares Regression over Hilbert Spaces

Chattez avec Graph Search

Posez n’importe quelle question sur les cours, conférences, exercices, recherches, actualités, etc. de l’EPFL ou essayez les exemples de questions ci-dessous.

AVERTISSEMENT : Le chatbot Graph n'est pas programmé pour fournir des réponses explicites ou catégoriques à vos questions. Il transforme plutôt vos questions en demandes API qui sont distribuées aux différents services informatiques officiellement administrés par l'EPFL. Son but est uniquement de collecter et de recommander des références pertinentes à des contenus que vous pouvez explorer pour vous aider à répondre à vos questions.

The theory underlying robust distributed learning algorithms, designed to resist adversarial machines, matches empirical observations when data is homogeneous. Under data heterogeneity however, which is the norm in practical scenarios, established lower bo ...

People are exposed to myriad of airborne pollutants in their homes. Owing to diverse potential sources of air pollution and human activity patterns, accurate assessment of residential exposures is complex. In this study, we explored the relationship betwee ...

Background: A neurocognitive phenotype of post-COVID-19 infection has recently been described that is characterized by a lack of awareness of memory impairment (i.e., anosognosia), altered functional connectivity in the brain's default mode and limbic netw ...

In this paper we fully describe the trajectory of gradient flow over diagonal linear networks in the limit of vanishing initialisation. We show that the limiting flow successively jumps from a saddle of the training loss to another until reaching the minim ...

We present a framework for performing regression when both covariate and response are probability distributions on a compact and convex subset of

\R^d

. Our regression model is based on the theory of optimal transport and links the conditional Fr'echet m ...

Local Hamiltonians of fermionic systems on a lattice can be mapped onto local qubit Hamiltonians. Maintaining the lo-cality of the operators comes at the ex-pense of increasing the Hilbert space with auxiliary degrees of freedom. In order to retrieve the l ...

In this paper, we investigate the impact of stochasticity and large stepsizes on the implicit regularisation of gradient descent (GD) and stochastic gradient descent (SGD) over diagonal linear networks. We prove the convergence of GD and SGD with macroscop ...

Rectified-linear-unit (ReLU) neural networks, which play a prominent role in deep learning, generate continuous and piecewise-linear (CPWL) functions. While they provide a powerful parametric representation, the mapping between the parameter and function s ...

We study the problem of estimating an unknown function from noisy data using shallow ReLU neural networks. The estimators we study minimize the sum of squared data-fitting errors plus a regularization term proportional to the squared Euclidean norm of the ...

Objective: To characterize ambulatory knee moments with respect to medial knee osteoarthritis (OA) severity comprehensively and to assess the possibility of developing a severity index combining knee moment parameters. ...

Neural machine translation (MT) and text generation have recently reached very high levels of quality. However, both areas share a problem: in order to reach these levels, they require massive amounts of data. When this is not present, they lack generaliza ...

Unsupervised Domain Adaptation Regression (DAR) aims to bridge the domain gap between a labeled source dataset and an unlabelled target dataset for regression problems. Recent works mostly focus on learning a deep feature encoder by minimizing the discrepa ...

Correlated errors of experimental data are a common but often neglected problem in physical sciences. Various tools are provided here for thorough propagation of uncertainties in cases of correlated errors. Discussed are techniques especially applicable to ...

Uncertainty quantification is a central challenge in reliable and trustworthy machine learning. Naive measures such as last-layer scores are well-known to yield overconfident estimates in the context of overparametrized neural networks. Several methods, ra ...

Optimal Rates for Spectral Algorithms with Least-Squares Regression over Hilbert Spaces

Chattez avec Graph Search

Robust Distributed Learning: Tight Error Bounds and Breakdown Point under Data Heterogeneity

Adequacy of stationary measurements as proxies for residential personal exposure to gaseous and particle air pollutants

Acute TNF alpha levels predict cognitive impairment 6-9 months after COVID-19 infection

Saddle-to-Saddle Dynamics in Diagonal Linear Networks

Distributional Regression and Autoregression via Optimal Transport

Quantum circuits for solving local fermion-to-qubit map- pings

(S)GD over Diagonal Linear Networks: Implicit Regularisation, Large Stepsizes and Edge of Stability

Stable parameterization of continuous and piecewise-linear functions

Near-Minimax Optimal Estimation With Shallow ReLU Neural Networks

Diverse parameters of ambulatory knee moments differ with medial knee osteoarthritis severity and are combinable into a severity index

Regularization Techniques for Low-Resource Machine Translation

DARE-GRAM : Unsupervised Domain Adaptation Regression by Aligning Inverse Gram Matrices

Reliable uncertainties: Error correlation, rotated error bars, and linear regressions in three-isotope plots and beyond

On double-descent in uncertainty quantification in overparametrized models