Spatial adaptation in heteroscedastic regression: Propagation approach

A general approach to heteroscedastic linear regression

Our article presents a general treatment of the linear regression model, in which the error distribution is modelled nonparametrically and the error variances may be heteroscedastic, thus eliminating the need to transform the dependent variable in many data sets. The mean and variance components of the model may be either parametric or nonparametric, with parsimony achieved through variable sel...

Active Heteroscedastic Regression

An active learner is given a model class Θ, a large sample of unlabeled data drawn from an underlying distribution and access to a labeling oracle that can provide a label for any of the unlabeled instances. The goal of the learner is to find a model θ ∈ Θ that fits the data to a given accuracy while making as few label queries to the oracle as possible. In this work, we consider a theoretical ...

Variational Heteroscedastic Gaussian Process Regression

Standard Gaussian processes (GPs) model observations’ noise as constant throughout input space. This is often a too restrictive assumption, but one that is needed for GP inference to be tractable. In this work we present a non-standard variational approximation that allows accurate inference in heteroscedastic GPs (i.e., under inputdependent noise conditions). Computational cost is roughly twic...

Variance Function Estimation in Heteroscedastic Regression Models

Efficient Quantile Regression for Heteroscedastic Models

Quantile regression provides estimates of a range of conditional quantiles. This stands in contrast to traditional regression techniques, which focus on a single conditional mean function. Lee et al. (2012) proposed efficient quantile regression by rounding the sharp corner of the loss. The main modification generally involves an asymmetric l2 adjustment of the loss function around zero. We ext...