Related papers: Kernel Three Pass Regression Filter

We consider the kernel partial least squares algorithm for non-parametric regression with stationary dependent data. Probabilistic convergence rates of the kernel partial least squares estimator to the true regression function are…

The current landscape in time-series forecasting is dominated by Transformer-based models. Their high parameter count and corresponding demand in computational resources pose a challenge to real-world deployment, especially for commercial…

This paper discusses predictive inference and feature selection for generalized linear models with scarce but high-dimensional data. We argue that in many cases one can benefit from a decision theoretically justified two-stage approach:…

Kernel Adaptive Filtering (KAF) are mathematically principled methods which search for a function in a Reproducing Kernel Hilbert Space. While they work well for tasks such as time series prediction and system identification they are…

Transformer-based models are at the forefront in long time-series forecasting (LTSF). While in many cases, these models are able to achieve state of the art results, they suffer from a bias toward low-frequencies in the data and high…

We introduce a class of semiparametric time series models by assuming a quasi-likelihood approach driven by a latent factor process. More specifically, given the latent process, we only specify the conditional mean and variance of the time…

The paper considers linear regression problems where the number of predictor variables is possibly larger than the sample size. The basic motivation of the study is to combine the points of view of model selection and functional regression…

We introduce an algorithm which, in the context of nonlinear regression on vector-valued explanatory variables, chooses those combinations of vector components that provide best prediction. The algorithm devotes particular attention to…

Semiparametric forecasting and filtering are introduced as a method of addressing model errors arising from unresolved physical phenomena. While traditional parametric models are able to learn high-dimensional systems from small data sets,…

This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…

This research focuses on the estimation of a non-parametric regression function designed for data with simultaneous time and space dependencies. In such a context, we study the Trend Filtering, a nonparametric estimator introduced by…

We consider a high-dimensional linear regression problem. Unlike many papers on the topic, we do not require sparsity of the regression coefficients; instead, our main structural assumption is a decay of eigenvalues of the covariance matrix…

We consider the problem of multivariate regression in a setting where the relevant predictors could be shared among different responses. We propose an algorithm which decomposes the coefficient matrix into the product of a long matrix and a…

While numerous forecasters have been proposed using different network architectures, the Transformer-based models have state-of-the-art performance in time series forecasting. However, forecasters based on Transformers are still suffering…

Random Fourier features (RFF) represent one of the most popular and wide-spread techniques in machine learning to scale up kernel algorithms. Despite the numerous successful applications of RFFs, unfortunately, quite little is understood…

Variable selection is central to high-dimensional data analysis, and various algorithms have been developed. Ideally, a variable selection algorithm shall be flexible, scalable, and with theoretical guarantee, yet most existing algorithms…

We give an algorithm for prediction on a quantum computer which is based on a linear regression model with least squares optimisation. Opposed to related previous contributions suffering from the problem of reading out the optimal…

The paper presents a novel deep learning approach, which extracts latent information from trained Deep Neural Networks (DNNs) and derives concise representations that are analyzed in an effective, unified way for prediction purposes. It is…

In the context of time series forecasting, it is a common practice to evaluate multiple methods and choose one of these methods or an ensemble for producing the best forecasts. However, choosing among different ensembles over multiple…

We consider the problem of predicting values of a random process or field satisfying a linear model $y(x)=\theta^\top f(x) + \varepsilon(x)$, where errors $\varepsilon(x)$ are correlated. This is a common problem in kriging, where the case…