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Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…

Machine Learning · Statistics 2025-11-26 Jonas Latz , Aretha L. Teckentrup , Simon Urbainczyk

In this paper we introduce a novel online time series forecasting model we refer to as the pM-GP filter. We show that our model is equivalent to Gaussian process regression, with the advantage that both online forecasting and online…

Machine Learning · Statistics 2015-10-13 Yves-Laurent Kom Samo , Stephen J. Roberts

Gaussian Process (GP) regression models typically assume that residuals are Gaussian and have the same variance for all observations. However, applications with input-dependent noise (heteroscedastic residuals) frequently arise in practice,…

Machine Learning · Statistics 2012-12-27 Chunyi Wang , Radford M. Neal

We study pathwise invariances of centred random fields that can be controlled through the covariance. A result involving composition operators is obtained in second-order settings, and we show that various path properties including…

Statistics Theory · Mathematics 2013-08-07 David Ginsbourger , Olivier Roustant , Nicolas Durrande

I propose kernel ridge regression estimators for nonparametric dose response curves and semiparametric treatment effects in the setting where an analyst has access to a selected sample rather than a random sample; only for select…

Econometrics · Economics 2022-08-24 Rahul Singh

Gaussian Process (GP) models are a powerful tool in probabilistic machine learning with a solid theoretical foundation. Thanks to current advances, modeling complex data with GPs is becoming increasingly feasible, which makes them an…

Machine Learning · Computer Science 2025-03-04 Sarem Seitz

A method to reconstruct fields, source strengths and physical parameters based on Gaussian process regression is presented for the case where data are known to fulfill a given linear differential equation with localized sources. The…

Data Analysis, Statistics and Probability · Physics 2019-09-10 Christopher G. Albert

We consider kernel estimation of marginal densities and regression functions of stationary processes. It is shown that for a wide class of time series, with proper centering and scaling, the maximum deviations of kernel density and…

Statistics Theory · Mathematics 2010-10-21 Weidong Liu , Wei Biao Wu

This paper proposes a novel kernel-based optimization scheme to handle tasks in the analysis, e.g., signal spectral estimation and single-channel source separation of 1D non-stationary oscillatory data. The key insight of our optimization…

Machine Learning · Statistics 2022-12-12 Jieren Xu , Yitong Li , Haizhao Yang , David Dunson , Ingrid Daubechies

We characterize the sample size required for accurate graphical model selection from non-stationary samples. The observed data is modeled as a vector-valued zero-mean Gaussian random process whose samples are uncorrelated but have different…

Machine Learning · Computer Science 2019-06-28 Nguyen Q. Tran , Oleksii Abramenko , Alexander Jung

Gaussian Processes (GPs) are a class of kernel methods that have shown to be very useful in geoscience applications. They are widely used because they are simple, flexible and provide very accurate estimates for nonlinear problems,…

Machine Learning · Statistics 2020-12-10 Juan Emmanuel Johnson , Valero Laparra , Gustau Camps-Valls

In this paper, we are interested in nonparametric kernel estimation of a generalized regression function, including conditional cumulative distribution and conditional quantile functions, based on an incomplete sample $(X_t, Y_t,…

Statistics Theory · Mathematics 2021-10-19 Mohamed Chaouch , Naâmane Laïb

We develop a novel approach towards causal inference. Rather than structural equations over a causal graph, we learn stochastic differential equations (SDEs) whose stationary densities model a system's behavior under interventions. These…

Machine Learning · Computer Science 2024-03-19 Lars Lorch , Andreas Krause , Bernhard Schölkopf

We propose multivariate nonstationary Gaussian processes for jointly modeling multiple clinical variables, where the key parameters, length-scales, standard deviations and the correlations between the observed output, are all time…

Methodology · Statistics 2019-10-15 Rui Meng , Braden Soper , Herbert Lee , Vincent X. Liu , John D. Greene , Priyadip Ray

The Gaussian process (GP) is a nonparametric prior distribution over functions indexed by time, space, or other high-dimensional index set. The GP is a flexible model yet its limitation is given by its very nature: it can only model…

Machine Learning · Statistics 2019-07-15 Gonzalo Rios , Felipe Tobar

Gaussian process (GP) regression provides a flexible, nonparametric framework for probabilistic modeling, yet remains computationally demanding in large-scale applications. For one-dimensional data, state space (SS) models achieve…

Machine Learning · Statistics 2025-11-07 Liang Ding , Rui Tuo , Lu Zhou

The declining response rates in probability surveys along with the widespread availability of unstructured data has led to growing research into non-probability samples. Existing robust approaches are not well-developed for non-Gaussian…

Methodology · Statistics 2022-03-29 Ali Rafei , Michael R. Elliott , Carol A. C. Flannagan

Gaussian process regression networks (GPRN) are powerful Bayesian models for multi-output regression, but their inference is intractable. To address this issue, existing methods use a fully factorized structure (or a mixture of such…

Machine Learning · Computer Science 2020-05-19 Shibo Li , Wei Xing , Mike Kirby , Shandian Zhe

Stationarity is a key assumption in many statistical models for random processes. With recent developments in the field of graph signal processing, the conventional notion of wide-sense stationarity has been extended to random processes…

Signal Processing · Electrical Eng. & Systems 2019-09-10 Arman Hasanzadeh , Xi Liu , Nick Duffield , Krishna R. Narayanan

Granger causal inference is a contentious but widespread method used in fields ranging from economics to neuroscience. The original definition addresses the notion of causality in time series by establishing functional dependence…

Methodology · Statistics 2023-09-19 Noah D. Gade , Jordan Rodu