The study aimed was to determine the best nonlinear function describing growth stages of Japanese quail breed. To this aim, functions such as exponential, logistic, von Bertalanffy, Brody, and Gompertz were used is in description body weight-age relationship male female quails. Multivariate Adaptive Regression Splines (MARS) data mining algorithm applied individual parameters obtained from dete...

Non-linear regression based on reproducing kernel Hilbert space (RKHS) has recently become very popular in fitting high-dimensional data. The RKHS formulation provides an automatic dimension reduction of the covariates. This is particularly helpful when the number of covariates ($p$) far exceed the number of data points. In this paper, we introduce a Bayesian nonlinear multivariate regression m...

We present self-modeling regression models for flexible nonparametric modeling of multiple outcomes measured longitudinally. Based on penalized regression splines, the models borrow strength across multiple outcomes by specifying a global time profile, thereby yielding a means of dimension reduction and estimates of trend more precise than those based on univariate regressions. The proposed mod...

This work concerns the estimation of multidimensional nonlinear regression models using multilayer perceptrons (MLPs). The main problem with such models is that we need to know the covariance matrix of the noise to get an optimal estimator. However, we show in this paper that if we choose as the cost function the logarithm of the determinant of the empirical error covariance matrix, then we get...

Motivated from problems in canonical correlation analysis, reduced rank regression and sufficient dimension reduction, we introduce a double dimension reduction model where a single index of the multivariate response is linked to the multivariate covariate through a single index of these covariates, hence the name double single index model. Since nonlinear association between two sets of multiv...

We propose a general matrix-valued multiple kernel learning framework for highdimensional nonlinear multivariate regression problems. This framework allows a broad class of mixed norm regularizers, including those that induce sparsity, to be imposed on a dictionary of vector-valued Reproducing Kernel Hilbert Spaces. We develop a highly scalable and eigendecompositionfree algorithm that orchestr...