In this contribution, genetic programming is combined with continuum regression to produce two novel non-linear continuum regression algorithms. The first is a ‘sequential’ algorithm while the second, adopts a ‘team-based’ strategy. Having discussed continuum regression, the modifications required to extend the algorithm for non-linear modelling are outlined. The results of applying the derived...

We introduce a regression model for data on non-linear manifolds. The model describes the relation between a set of manifold valued observations, such as shapes of anatomical objects, and Euclidean explanatory variables. The approach is based on stochastic development of Euclidean diffusion processes to the manifold. Defining the data distribution as the transition distribution of the mapped st...

Linear regression amounts to estimating a linear model that maps features (e.g., age or gender) to corresponding data (e.g., the answer to a survey or the outcome of a medical exam). It is a ubiquitous tool in experimental sciences. We study a setting in which features are public but the data is private information. While the estimation of the linear model may be useful to participating individ...

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Let (X 1 ; X 2) be an-stable random vector, not necessarily symmetric, with 0 < < 2. The paper investigates the regression E(X 2 jX 1 = x) for all values of. We give conditions for the existence of the conditional moment E(jX 2 j p jX 1 = x) when p , and we obtain an explicit form of the regression E(X 2 jX 1 = x) as a function of x. Although this regression is, in general, not linear, it can b...

The present paper deals with the prediction of three-dimensional fluid flow and heat transfer in rib-roughened ducts of square cross-section. Such flows are of direct relevance to the internal cooling system of modern gas turbine blades. The main objective is to assess how a recently developed variant of a cubic non-linear model (proposed by Craft et al. (1999)), that has been shown to produce ...