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Found 16 papers, 0 papers with code
Statistical inverse learning problems with random observations
To achieve these results, the structure of reproducing kernel Hilbert spaces is leveraged to establish minimax rates in the statistical learning setting.
How many Neurons do we need? A refined Analysis for Shallow Networks trained with Gradient Descent
We analyze the generalization properties of two-layer neural networks in the neural tangent kernel (NTK) regime, trained with gradient descent (GD).
Random feature approximation for general spectral methods
Random feature approximation is arguably one of the most popular techniques to speed up kernel methods in large scale algorithms and provides a theoretical approach to the analysis of deep neural networks.
Learning linear operators: Infinite-dimensional regression as a well-behaved non-compact inverse problem
However, we prove that, in terms of spectral properties and regularisation theory, this inverse problem is equivalent to the known compact inverse problem associated with scalar response regression.
Local SGD in Overparameterized Linear Regression
We consider distributed learning using constant stepsize SGD (DSGD) over several devices, each sending a final model update to a central server.
Data splitting improves statistical performance in overparametrized regimes
While large training datasets generally offer improvement in model performance, the training process becomes computationally expensive and time consuming.
From inexact optimization to learning via gradient concentration
Optimization in machine learning typically deals with the minimization of empirical objectives defined by training data.
Stochastic Gradient Descent Meets Distribution Regression
Stochastic gradient descent (SGD) provides a simple and efficient way to solve a broad range of machine learning problems.
Stochastic Gradient Descent in Hilbert Scales: Smoothness, Preconditioning and Earlier Stopping
Stochastic Gradient Descent (SGD) has become the method of choice for solving a broad range of machine learning problems.
Reproducing kernel Hilbert spaces on manifolds: Sobolev and Diffusion spaces
We study reproducing kernel Hilbert spaces (RKHS) on a Riemannian manifold.
Empirical Risk Minimization in the Interpolating Regime with Application to Neural Network Learning
Moreover, we show that the same phenomenon occurs for DNNs with zero training error and sufficiently large architectures.
Beating SGD Saturation with Tail-Averaging and Minibatching
While stochastic gradient descent (SGD) is one of the major workhorses in machine learning, the learning properties of many practically used variants are poorly understood.
Adaptivity for Regularized Kernel Methods by Lepskii's Principle
We address the problem of {\it adaptivity} in the framework of reproducing kernel Hilbert space (RKHS) regression.
Kernel regression, minimax rates and effective dimensionality: beyond the regular case
These questions have been considered in past literature, but only under specific assumptions about the decay, typically polynomial, of the spectrum of the the kernel mapping covariance operator.
Parallelizing Spectral Algorithms for Kernel Learning
We consider a distributed learning approach in supervised learning for a large class of spectral regularization methods in an RKHS framework.
Optimal Rates For Regularization Of Statistical Inverse Learning Problems
We consider a statistical inverse learning problem, where we observe the image of a function $f$ through a linear operator $A$ at i. i. d.
