相关论文: An invariance property of kernel based predictors

The classical kernel ridge regression problem aims to find the best fit for the output $Y$ as a function of the input data $X\in \mathbb{R}^d$, with a fixed choice of regularization term imposed by a given choice of a reproducing kernel…

A linear multiple regression model in function spaces is formulated, under temporal correlated errors. This formulation involves kernel regressors. A generalized least-squared regression parameter estimator is derived. Its asymptotic…

We establish the asymptotic normality of the regression estimator in a fixed-design setting when the errors are given by a field of dependent random variables. The result applies to martingale-difference or strongly mixing random fields. On…

Random Fourier features is one of the most popular techniques for scaling up kernel methods, such as kernel ridge regression. However, despite impressive empirical results, the statistical properties of random Fourier features are still not…

We consider the problem of streaming kernel regression, when the observations arrive sequentially and the goal is to recover the underlying mean function, assumed to belong to an RKHS. The variance of the noise is not assumed to be known.…

Kernel ridge regression (KRR) is a foundational tool in machine learning, with recent work emphasizing its connections to neural networks. However, existing theory primarily addresses the i.i.d. setting, while real-world data often exhibits…

In likelihood-free settings where likelihood evaluations are intractable, approximate Bayesian computation (ABC) addresses the formidable inference task to discover plausible parameters of simulation programs that explain the observations.…

We present a machine learning approach for model-independent new physics searches. The corresponding algorithm is powered by recent large-scale implementations of kernel methods, nonparametric learning algorithms that can approximate any…

We introduce a simulation method for dynamic portfolio valuation and risk management building on machine learning with kernels. We learn the dynamic value process of a portfolio from a finite sample of its cumulative cash flow. The learned…

In recent years, there has been a significant growth in research focusing on minimum $\ell_2$ norm (ridgeless) interpolation least squares estimators. However, the majority of these analyses have been limited to an unrealistic regression…

We introduce a transfer learning framework for regression that leverages heterogeneous source domains to improve predictive performance in a data-scarce target domain. Our approach learns a conditional generative model separately for each…

This work proposed kernel selection approaches for probabilistic classifiers based on features produced by the convolutional encoder of a variational autoencoder. Particularly, the developed methodologies allow the selection of the most…

This paper proves, in very general settings, that convex risk minimization is a procedure to select a unique conditional probability model determined by the classification problem. Unlike most previous work, we give results that are general…

Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…

We tackle the problem of algorithmic fairness, where the goal is to avoid the unfairly influence of sensitive information, in the general context of regression with possible continuous sensitive attributes. We extend the framework of fair…

Feature learning is widely regarded as the key mechanism distinguishing neural networks from fixed-kernel methods, yet its impact on the induced function space remains poorly understood. In this work, we precisely characterize how the…

Kernel methods, being supported by a well-developed theory and coming with efficient algorithms, are among the most popular and successful machine learning techniques. From a mathematical point of view, these methods rest on the concept of…

Reinforcement learning utilizing kernel ridge regression to predict the expected value function represents a powerful method with great representational capacity. This setting is a highly versatile framework amenable to analytical results.…

We present a novel approach to learn a kernel-based regression function. It is based on the useof conical combinations of data-based parameterized kernels and on a new stochastic convex optimization procedure of which we establish…

Applying machine learning to biological sequences - DNA, RNA and protein - has enormous potential to advance human health, environmental sustainability, and fundamental biological understanding. However, many existing machine learning…