No abstract

In this work we propose a general nonparametric test of causality for weakly dependent time series. More precisely, we study the problem of attribution, i.e., the proper comparison of the relative influence that two or more external dynamics trigger on a given system of interest. We illustrate the possible applications of the proposed methodology in very different fields like physiology and climate science.

Ensembles of artificial neural networks show improved generalization capabilities that outperform those of single networks. However, for aggregation to be effective, the individual networks must be as accurate and diverse as possible. An important problem is, then, how to tune the aggregate members in order to have an optimal compromise between these two conflicting conditions. We present here an extensive evaluation of several algorithms for ensemble construction, including new proposals and comparing them with standard methods in the literature. We also discuss a potential problem with sequential aggregation algorithms: the non-frequent but damaging selection through their heuristics of particularly bad ensemble members. We introduce modified algorithms that cope with this problem by allowing individual weighting of aggregate members. Our algorithms and their weighted modifications are favorably tested against other methods in the literature, producing a sensible improvement in performance on most of the standard statistical databases used as benchmarks.

In this work we propose an objective function to guide the search for a state space reconstruction of a dynamical system from a time series of measurements. These statistics can be evaluated on any reconstructed attractor, thereby allowing a direct comparison among different approaches: (uniform or nonuniform) delay vectors, PCA, Legendre coordinates, etc. It can also be used to select the most appropriate parameters of a reconstruction strategy. In the case of delay coordinates this translates into finding the optimal delay time and embedding dimension from the absolute minimum of the advocated cost function. Its definition is based on theoretical arguments on noise amplification, the complexity of the reconstructed attractor, and a direct measure of local stretch which constitutes an irrelevance measure. The proposed method is demonstrated on synthetic and experimental time series.