English
Related papers

Related papers: Robust Gaussian Process Regression with Huber Like…

200 papers

Heteroscedastic regression considering the varying noises among observations has many applications in the fields like machine learning and statistics. Here we focus on the heteroscedastic Gaussian process (HGP) regression which integrates…

Machine Learning · Statistics 2020-01-22 Haitao Liu , Yew-Soon Ong , Jianfei Cai

Bayesian inference and Gaussian processes are widely used in applications ranging from robotics and control to biological systems. Many of these applications are safety-critical and require a characterization of the uncertainty associated…

Machine Learning · Computer Science 2018-10-26 Luca Cardelli , Marta Kwiatkowska , Luca Laurenti , Andrea Patane

Learning in Gaussian Process models occurs through the adaptation of hyperparameters of the mean and the covariance function. The classical approach entails maximizing the marginal likelihood yielding fixed point estimates (an approach…

Machine Learning · Statistics 2020-04-07 Vidhi Lalchand , Carl Edward Rasmussen

This paper focuses on efficient computational approaches to compute approximate solutions of a linear inverse problem that is contaminated with mixed Poisson--Gaussian noise, and when there are additional outliers in the measured data. The…

Numerical Analysis · Mathematics 2018-01-22 Marie Kubínová , James G. Nagy

We develop a computational procedure to estimate the covariance hyperparameters for semiparametric Gaussian process regression models with additive noise. Namely, the presented method can be used to efficiently estimate the variance of the…

Machine Learning · Computer Science 2022-06-22 Siavash Ameli , Shawn C. Shadden

The Gaussian process (GP) regression can be severely biased when the data are contaminated by outliers. This paper presents a new robust GP regression algorithm that iteratively trims the most extreme data points. While the new algorithm…

Machine Learning · Computer Science 2021-06-15 Zhao-Zhou Li , Lu Li , Zhengyi Shao

In this article, we investigate posterior convergence in nonparametric regression models where the unknown regression function is modeled by some appropriate stochastic process. In this regard, we consider two setups. The first setup is…

Statistics Theory · Mathematics 2020-05-04 Debashis Chatterjee , Sourabh Bhattacharya

Forecasting multivariate time series is a computationally intensive task challenged by extreme or redundant samples. Recent resampling methods aim to increase training efficiency by reweighting samples based on their running losses.…

Machine Learning · Computer Science 2024-06-21 Jiang You , Arben Cela , René Natowicz , Jacob Ouanounou , Patrick Siarry

Gaussian graphical model is one of the powerful tools to analyze conditional independence between two variables for multivariate Gaussian-distributed observations. When the dimension of data is moderate or high, penalized likelihood methods…

Methodology · Statistics 2025-01-24 Takahiro Onizuka , Shintaro Hashimoto

In Bayesian nonparametric models, Gaussian processes provide a popular prior choice for regression function estimation. Existing literature on the theoretical investigation of the resulting posterior distribution almost exclusively assume a…

Statistics Theory · Mathematics 2015-03-06 Debdeep Pati , Anirban Bhattacharya , Guang Cheng

The kernel function and its hyperparameters are the central model selection choice in a Gaussian proces (Rasmussen and Williams, 2006). Typically, the hyperparameters of the kernel are chosen by maximising the marginal likelihood, an…

Machine Learning · Statistics 2022-11-07 Vidhi Lalchand , Wessel P. Bruinsma , David R. Burt , Carl E. Rasmussen

Robust regression has attracted a great amount of attention in the literature recently, particularly for taking asymmetricity into account simultaneously and for high-dimensional analysis. However, the majority of research on the topics…

Methodology · Statistics 2023-07-25 Sanna Soomro , Keming Yu , Yan Yu

Big data can easily be contaminated by outliers or contain variables with heavy-tailed distributions, which makes many conventional methods inadequate. To address this challenge, we propose the adaptive Huber regression for robust…

Statistics Theory · Mathematics 2018-10-11 Qiang Sun , Wenxin Zhou , Jianqing Fan

It has historically been a challenge to perform Bayesian inference in a design-based survey context. The present paper develops a Bayesian model for sampling inference in the presence of inverse-probability weights. We use a hierarchical…

Methodology · Statistics 2020-06-24 Yajuan Si , Natesh S. Pillai , Andrew Gelman

We consider a robust estimation of linear regression coefficients. In this note, we focus on the case where the covariates are sampled from an $L$-subGaussian distribution with unknown covariance, the noises are sampled from a distribution…

Statistics Theory · Mathematics 2024-05-27 Takeyuki Sasai , Hironori Fujisawa

We present a novel extension of multi-output Gaussian processes for handling heterogeneous outputs. We assume that each output has its own likelihood function and use a vector-valued Gaussian process prior to jointly model the parameters in…

Machine Learning · Statistics 2019-01-04 Pablo Moreno-Muñoz , Antonio Artés-Rodríguez , Mauricio A. Álvarez

We study Gaussian sparse estimation tasks in Huber's contamination model with a focus on mean estimation, PCA, and linear regression. For each of these tasks, we give the first sample and computationally efficient robust estimators with…

Machine Learning · Computer Science 2024-03-18 Ilias Diakonikolas , Daniel M. Kane , Sushrut Karmalkar , Ankit Pensia , Thanasis Pittas

In a Bayesian learning setting, the posterior distribution of a predictive model arises from a trade-off between its prior distribution and the conditional likelihood of observed data. Such distribution functions usually rely on additional…

Machine Learning · Statistics 2011-11-01 Andrea Schirru , Simone Pampuri , Giuseppe De Nicolao , Sean McLoone

Spike-and-slab and horseshoe regression are arguably the most popular Bayesian variable selection approaches for linear regression models. However, their performance can deteriorate if outliers and heteroskedasticity are present in the…

Methodology · Statistics 2022-10-20 Alberto Cabezas , Marco Battiston , Christopher Nemeth

A method to perform unfolding with Gaussian processes (GPs) is presented. Using Bayesian regression, we define an estimator for the underlying truth distribution as the mode of the posterior. We show that in the case where the bin contents…

Data Analysis, Statistics and Probability · Physics 2018-11-07 Adam Bozson , Glen Cowan , Francesco Spanò