Distributed Kernel Regression: An Algorithm for Training Collaboratively

This paper addresses the problem of distributed learning under communication constraints, motivated by distributed signal processing in wireless sensor networks and data mining with distributed databases. After formalizing a general model for distributed learning, an algorithm for collaboratively training regularized kernel least-squares regression estimators is derived. Noting that the algorithm can be viewed as an application of successive orthogonal projection algorithms, its convergence properties are investigated and the statistical behavior of the estimator is discussed in a simplified theoretical setting.Comment: To be presented at the 2006 IEEE Information Theory Workshop, Punta del Este, Uruguay, March 13-17, 200

The analog data assimilation

In light of growing interest in data-driven methods for oceanic, atmospheric, and climate sciences, this work focuses on the field of data assimilation and presents the analog data assimilation (AnDA). The proposed framework produces a reconstruction of the system dynamics in a fully data-driven manner where no explicit knowledge of the dynamical model is required. Instead, a representative catalog of trajectories of the system is assumed to be available. Based on this catalog, the analog data assimilation combines the nonparametric sampling of the dynamics using analog forecasting methods with ensemble-based assimilation techniques. This study explores different analog forecasting strategies and derives both ensemble Kalman and particle filtering versions of the proposed analog data assimilation approach. Numerical experiments are examined for two chaotic dynamical systems: the Lorenz-63 and Lorenz-96 systems. The performance of the analog data assimilation is discussed with respect to classical model-driven assimilation. A Matlab toolbox and Python library of the AnDA are provided to help further research building upon the present findings.Fil: Lguensat, Redouane. Université Bretagne Loire; FranciaFil: Tandeo, Pierre. Université Bretagne Loire; FranciaFil: Ailliot, Pierre. University of Western Brittany. Laboratoire de Mathématiques de Bretagne Atlantique; FranciaFil: Pulido, Manuel Arturo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Modelado e Innovación Tecnológica. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas Naturales y Agrimensura. Instituto de Modelado e Innovación Tecnológica; ArgentinaFil: Fablet, Ronan. Université Bretagne Loire; Franci