Fast hyperbolic wavelet regression meets ANOVA

Functional ANOVA Models for Generalized Regression

Functional ANOVA models are considered in the context of generalized regression, which includes logistic regression, probit regression and Poisson regression as special cases. The multivariate predictor function is modeled as a speci ed sum of a constant term, main e ects and interaction terms. Maximum likelihood estimates are used, where the maximizations are taken over suitably chosen approxi...

Topic 3: ANOVA, Regression, and Forecasting

Hyperbolic Wavelet Approximation

We study the multivariate approximation by certain partial sums (hyperbolic wavelet sums) of wavelet bases formed by tensor products of univariate wavelets. We characterize spaces of functions which have a prescribed approximation error by hyperbolic wavelet sums in terms of a K -functional and interpolation spaces. The results parallel those for hyperbolic trigonometric cross approximation of ...

Tensor Regression Meets Gaussian Processes

Low-rank tensor regression, a new model class that learns high-order correlation from data, has recently received considerable attention. At the same time, Gaussian processes (GP) are well-studied machine learning models for structure learning. In this paper, we demonstrate interesting connections between the two, especially for multi-way data analysis. We show that low-rank tensor regression i...

Penalized wavelet monotone regression

In this paper we focus on nonparametric estimation of a constrained regression function using penalized wavelet regression techniques. This results into a convex optimization problem under linear constraints. Necessary and sufficient conditions for existence of a unique solution are discussed. The estimator is easily obtained via the dual formulation of the optimization problem. In particular w...