Improved estimation in a non-Gaussian parametric regression

Parametric Gaussian Process Regression for Big Data

This work introduces the concept of parametric Gaussian processes (PGPs), which is built upon the seemingly self-contradictory idea of making Gaussian processes parametric. Parametric Gaussian processes, by construction, are designed to operate in “big data” regimes where one is interested in quantifying the uncertainty associated with noisy data. The proposed methodology circumvents the welles...

Online Non-Parametric Regression

We establish optimal rates for online regression for arbitrary classes of regression functions in terms of thesequential entropy introduced in [14]. The optimal rates are shown to exhibit a phase transition analogous to thei.i.d./statistical learning case, studied in [16]. In the frequently encountered situation when sequential entropyand i.i.d. empirical entropy match, our resu...

Non-parametric Regression Between Manifolds

This paper discusses non-parametric regression between Riemannian manifolds. This learning problem arises frequently in many application areas ranging from signal processing, computer vision, over robotics to computer graphics. We present a new algorithmic scheme for the solution of this general learning problem based on regularized empirical risk minimization. The regularization functional tak...

Non–parametric volatility estimation

Estimation in a Semi-parametric Two-stage Renewal Regression Model.

We discuss estimation in a two-stage modulated renewal process designed for analysis of paired data on a single individual. We consider a model with proportional hazard intensities. U-process methods are used to show consistency and asymptotic normality of the parameter estimates.