This paper introduces an influence diagram (ID) model that permits continuous decision variables with multiple continuous parents. The marginalization operation for a continuous decision variable first develops a piecewise linear decision rule as a continuous function of the next continuous parent in the deletion sequence. Least squares regression is used to convert this rule to a piecewise lin...

We propose a novel algorithm for unsupervised extraction of piecewise planar models from depth-data. Among other applications, such models are a good way of enabling autonomous agents (robots, cars, drones, etc.) to effectively perceive their surroundings and to navigate in three dimensions. We propose to do this by fitting the data with a piecewise-linear Gaussian mixture regression model whos...

Many methods can fit models with higher prediction accuracy, on average, than least squares linear regression. But the models, including linear regression, are typically impossible to interpret or visualize. We describe a tree-structured method that fits a simple but non-trivial model to each partition of the variable space. This ensures that each piece of the fitted regression function can be ...

Many methods can fit models with higher prediction accuracy, on average, than least squares linear regression. But the models, including linear regression, are typically impossible to interpret or visualize. We describe a tree-structured method that fits a simple but non-trivial model to each partition of the variable space. This ensures that each piece of the fitted regression function can be ...

The model of adaptive hinging hyperplanes (AHH) is proposed in this paper for black-box modeling. It is based on Multivariate Adaptive Regression Splines (MARS) and Generalized Hinging Hyperplanes (GHH) and shares attractive properties of the two. By making a modification to the basis function of MARS, AHH shows linear property in each subarea. It is proved that AHH model is identical to a spec...

Asymptotically minimax nonparametric estimation of a regression function observed in white Gaussian noise over a bounded interval is considered, with respect to a L 2-loss function. The unknown function f is assumed to be m times diierentiable except for an unknown, though nite, number of jumps, with piecewise mth derivative bounded in L 2-norm. An estimator is constructed, attaining the same o...

This technical note extends recent results on the computational complexity of globally minimizing the error of piecewise-affine models to the related problem of minimizing the error of switching linear regression models. In particular, we show that, on the one hand the problem is NP-hard, but on the other hand, it admits a polynomial-time algorithm with respect to the number of data for any fix...

In this paper a new method of detection of homogeneous zones and singularity parts of a 1D signal is proposed. The entropy function is used to transform signal in piecewise linear one. The multiple regression permits to detect lines and project them in the Hough parameters space in order to easily recognise homogeneous zone and abrupt changes of the signal. Two application examples are analysed...

the problem of finding the minimum cost multi-commodity flow in an undirected and completenetwork is studied when the link costs are piecewise linear and convex. the arc-path model and overflowmodel are presented to formulate the problem. the results suggest that the new overflow model outperformsthe classical arc-path model for this problem. the classical revised simplex, frank and wolf and a ...