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Found 33 papers, 8 papers with code
Conditioning of Banach Space Valued Gaussian Random Variables: An Approximation Approach Based on Martingales
In this paper we investigate the conditional distributions of two Banach space valued, jointly Gaussian random variables.
Mind the spikes: Benign overfitting of kernels and neural networks in fixed dimension
In this paper, we show that the smoothness of the estimators, and not the dimension, is the key: benign overfitting is possible if and only if the estimator's derivatives are large enough.
Physics-Informed Gaussian Process Regression Generalizes Linear PDE Solvers
Crucially, this probabilistic viewpoint allows to (1) quantify the inherent discretization error; (2) propagate uncertainty about the model parameters to the solution; and (3) condition on noisy measurements.
Utilizing Expert Features for Contrastive Learning of Time-Series Representations
We therefore devise ExpCLR, a novel contrastive learning approach built on an objective that utilizes expert features to encourage both properties for the learned representation.
A Framework and Benchmark for Deep Batch Active Learning for Regression
We provide open-source code that includes efficient implementations of all kernels, kernel transformations, and selection methods, and can be used for reproducing our results.
SOSP: Efficiently Capturing Global Correlations by Second-Order Structured Pruning
We validate SOSP-H by comparing it to our second method SOSP-I that uses a well-established Hessian approximation, and to numerous state-of-the-art methods.
Fast and Sample-Efficient Interatomic Neural Network Potentials for Molecules and Materials Based on Gaussian Moments
Artificial neural networks (NNs) are one of the most frequently used machine learning approaches to construct interatomic potentials and enable efficient large-scale atomistic simulations with almost ab initio accuracy.
Which Minimizer Does My Neural Network Converge To?
The loss surface of an overparameterized neural network (NN) possesses many global minima of zero training error.
Training Two-Layer ReLU Networks with Gradient Descent is Inconsistent
We prove that two-layer (Leaky)ReLU networks initialized by e. g. the widely used method proposed by He et al. (2015) and trained using gradient descent on a least-squares loss are not universally consistent.
Reproducing Kernel Hilbert Spaces Cannot Contain all Continuous Functions on a Compact Metric Space
Given an uncountable, compact metric space, we show that there exists no reproducing kernel Hilbert space that contains the space of all continuous functions on this compact space.
Wide Neural Networks are Interpolating Kernel Methods: Impact of Initialization on Generalization
The recently developed link between strongly overparametrized neural networks (NNs) and kernel methods has opened a new way to understand puzzling features of NNs, such as their convergence and generalization behaviors.
Best-scored Random Forest Classification
We propose an algorithm named best-scored random forest for binary classification problems.
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.
A Sober Look at Neural Network Initializations
Initializing the weights and the biases is a key part of the training process of a neural network.
Optimal Learning with Anisotropic Gaussian SVMs
This paper investigates the nonparametric regression problem using SVMs with anisotropic Gaussian RBF kernels.
Strictly proper kernel scores and characteristic kernels on compact spaces
Strictly proper kernel scores are well-known tool in probabilistic forecasting, while characteristic kernels have been extensively investigated in the machine learning literature.
Adaptive Clustering Using Kernel Density Estimators
We derive and analyze a generic, recursive algorithm for estimating all splits in a finite cluster tree as well as the corresponding clusters.
Learning Rates for Kernel-Based Expectile Regression
Conditional expectiles are becoming an increasingly important tool in finance as well as in other areas of applications.
Sobolev Norm Learning Rates for Regularized Least-Squares Algorithm
In this paper we extend these rates to norms stronger than the $L_2$-norm without requiring the regression function to be contained in the hypothesis space.
liquidSVM: A Fast and Versatile SVM package
liquidSVM is a package written in C++ that provides SVM-type solvers for various classification and regression tasks.
Learning with Hierarchical Gaussian Kernels
We investigate iterated compositions of weighted sums of Gaussian kernels and provide an interpretation of the construction that shows some similarities with the architectures of deep neural networks.
Spatial Decompositions for Large Scale SVMs
Our contributions are two fold: On the theoretical side we establish an oracle inequality for the overall learning method using the hinge loss, and show that the resulting rates match those known for SVMs solving the complete optimization problem with Gaussian kernels.
Kernel Density Estimation for Dynamical Systems
We study the density estimation problem with observations generated by certain dynamical systems that admit a unique underlying invariant Lebesgue density.
Learning theory estimates with observations from general stationary stochastic processes
We show that when the stochastic processes satisfy a generalized Bernstein-type inequality, a unified treatment on analyzing the learning schemes with various mixing processes can be conducted and a sharp oracle inequality for generic regularized empirical risk minimization schemes can be established.
Representation of Quasi-Monotone Functionals by Families of Separating Hyperplanes
We characterize when the level sets of a continuous quasi-monotone functional defined on a suitable convex subset of a normed space can be uniquely represented by a family of bounded continuous functionals.
Towards an Axiomatic Approach to Hierarchical Clustering of Measures
We propose some axioms for hierarchical clustering of probability measures and investigate their ramifications.
Optimal Learning Rates for Localized SVMs
In addition, their motivation was always based on computational requirements.
An SVM-like Approach for Expectile Regression
Expectile regression is a nice tool for investigating conditional distributions beyond the conditional mean.
Fully adaptive density-based clustering
The clusters of a distribution are often defined by the connected components of a density level set.
Optimal learning rates for least squares SVMs using Gaussian kernels
We prove a new oracle inequality for support vector machines with Gaussian RBF kernels solving the regularized least squares regression problem.
Universal Kernels on Non-Standard Input Spaces
We apply this technique for the following special cases: universal kernels on the set of probability measures, universal kernels based on Fourier transforms, and universal kernels for signal processing.
Fast Learning from Non-i.i.d. Observations
We prove an oracle inequality for generic regularized empirical risk minimization algorithms learning from $\a$-mixing processes.
Sparsity of SVMs that use the epsilon-insensitive loss
In this paper lower and upper bounds for the number of support vectors are derived for support vector machines (SVMs) based on the epsilon-insensitive loss function.
