This paper serves to compare existing models of function learning (EXAM & POLE) on a complex interpolation task. Previous comparisons of the models have focused primarily on extrapolation behaviors. Participants’ mean responses suggested a simple linear interpolation from nearby points of reference. Both models were able to predict a similar response. Although POLE served as a better predictor ...

Fisher tested the fit of Gaussian linear models using replicated observations. We refine this method by (1) constructing near-replicates using an optimal nonbipartite matching and (2) defining a distance that focuses on predictors important to the model’s predictions. Near-replicates may not exist unless the predictor set is lowdimensional; the test addresses dimensionality by betting that mode...

The usual procedure for developing linear models to predict any kind of target variable is to identify a subset of most important predictors and to estimate weights that provide the best possible solution for a given sample. The resulting “optimally” weighted linear composite is then used when predicting new data. This approach is useful in situations with large and reliable datasets and few pr...

A multiple regression method based on distance analysis and metric scaling is proposed and studied. This method allow us to predict a continuous response variable from several explanatory variables, is compatible with the general linear model and is found to be useful when the predictor variables are both continuous and categorical. Real data examples are given to illustrate the results obtained.

In the present study we used the first rock glacier inventory for the entire French Alps to model spatial permafrost distribution in the region. Climatic and topographic data evaluated at the rock glacier locations were used as predictor variables in a Generalized Linear Model. Model performances are strong, suggesting that, in agreement with several previous studies, this methodology is able t...

Generalized linear models (GLMs) outline a wide class of regression models where the effect of the explanatory variables on the mean of the response variable is modelled throughout the link function. The choice of the link function is typically overlooked in applications and the canonical link is commonly used. The estimation of GLMs with unspecified link function is discussed, where the linear...

The data-transformation approach and generalized linear modeling both require specification of a transformation prior to deriving the linear predictor (LP). By contrast, response modeling methodology (RMM) requires no such specifications. Furthermore, RMM effectively decouples modeling of the LP from modeling its relationship to the response. It may therefore be of interest to compare LPs obtai...

Prediction of time series is an important problem in many areas of science and engineering. Extending the horizon of predictions further to the future is the challenging and difficult task of long-term prediction. In this paper, we investigate the problem of selecting noncontiguous input variables for an autoregressive prediction model in order to improve the prediction ability. We present an a...

In this paper, we present an approach to optimal image scaling called Tree-Based Resolution synthesis (TBRS). TBRS works by first performing a fast local classification of a window around the pixel being interpolated, and then by applying an interpolation filter designed for the selected class. The idea behind TBRS is to use a regression tree as a piecewise linear approximation to the condition...

Three interior point methods are proposed for sufficient horizontal linear complementarity problems (HLCP): a large update path following algorithm, a first order corrector-predictor method, and a second order corrector-predictor method. All algorithms produce sequences of iterates in the wide neighborhood of the central path introduced by Ai and Zhang. The algorithms do not depend on the handi...