Carlos Eduardo Pedreira

Local Global Neural Networks: A New Approach for Nonlinear Time Series Modeling

We propose the local-global neural networks model within the context of time series models. This formulation encompasses some already existing nonlinear models and also admits the mixture of experts approach. We emphasize the linear expert case and extensively discuss the theoretical aspects of the model: stationarity conditions, existence, consistency and asymptotic normality of the parameter estimates, and model identifiability. The proposed model consists of a mixture of stationary and nonstationary linear models and is able to describe “intermittent” dynamics; the system spends a large fraction of time in a bounded region, but sporadically develops an instability that grows exponentially for some time and then suddenly collapses. Intermittency is a commonly observed behavior in ecology and epidemiology, fluid dynamics, and other natural systems. A model-building strategy is also considered, and the parameters are estimated by concentrated maximum likelihood. The procedure is illustrated with two real time series.

Optimal schedule for cancer chemotherapy

In this paper we consider the problems of modeling the tumor growth and optimize the chemotherapy treatment. A biologically based model is used with the goal of solving an optimization problem involving discrete delivery of antineoplastic drugs. Our model is formulated via compartmental analysis in order to take into account the cell cycle. The cost functional measures not only the final size of the tumor but also the total amount of drug delivered. We propose an algorithm based on the discrete maximum principle to solve the optimal drug schedule problem. Our numerical results show nice interpretations from the medical point of view.

Local-Global Neural Networks for Interpolation

In this paper a new connectionist model is proposed. The proposed architecture is trained by a scheme based on partition of the function domain, approximating the generator function by a set of very simple supporting functions. This method has an interesting ability concerning interpolation. A synthetic experiment and areal data missing data application are presented.

An Online Learning Approach: A Methodology for Time Varying Applications

In this paper, a new procedure to continuously adjust weights in a multi-layered neural network is proposed. The network is initially trained by using a traditional backpropagation algorithm. After this first step, a non-linear programming technique is used to properly calculate the new weights sets online. This methodology is tailored to be used in time varying (non-stationary) models, eliminating the necessity for retraining. Numerical results for a controlled experiment and for real data are presented.

Redes Neurais Locais-Globais: Uma Aplicao ao Problema de Dados Faltantes

In this paper a new connectionist architecture is proposed. The proposed architecture is trained by a scheme based on partition of the function domain, approximating the generator function by a set of very simple supporting functions. This method has an interesting ability concerning interpolation. A synthetic experiment and a real data missing data application are presented.