A kernel extension to handle missing data

An extension for univariate kernels that deals with missing values is proposed. These extended kernels are shown to be valid Mercer kernels and can adapt to many types of variables, such as categorical or continuous. The proposed kernels are tested against standard RBF kernels in a variety of benchmark problems showing different amounts of missing values and variable types. Our experimental results are very satisfactory, because they usually yield slight to much better improvements over those achieved with standard methods.Postprint (author’s final draft

Mining Multivariate Time Series Models with Soft-Computing Techniques: A Coarse-Grained Parallel Computing Approach

This paper presents experimental results of a parallel implementation of a soft-computing algorithm for model discovery in multivariate time series, possibly with missing values. It uses a hybrid neural network with two different types of neurons trained with a non-traditional procedure. Models describing the multivariate time dependencies are encoded as binary strings representing neural networks, and evolved using genetic algorithms. The present paper studies its properties from an experimental point of view (using homogeneous and heterogeneous clusters) focussing on: i) the influence of missing values, ii) the factors controlling the parallel computation, and iii) the effectiveness of the time series prediction results. Results confirm that i) the algorithm possesses high tolerance to missing data, ii) Athon-based homogeneous clusters have higher throughput than Xeon-based homogeneous clusters, iii) an increase of the number of slaves reduces the processing time until communication overhead dominates (as expected), and iv) running the algorithm in parallel does not affect the RMS error (as expected). Even though much of this behaviour could be qualitatively expected, appropriate tradeoffs between error and time were actually discovered, thereby enabling more effective, systematic, future uses of the system.Ce rapport pr\ue9sente les r\ue9sultats de recherches exp\ue9rimentales sur la mise en oeuvre parall\ue8le d'un algorithme de calcul souple en vue de d\ue9couvrir des mod\ue8les dans les s\ue9ries chronologiques multivari\ue9es, \ue9ventuellement avec des valeurs manquantes. L'algorithme utilise un r\ue9seau neuronal hybride avec deux diff\ue9rents types de neurones programm\ue9s d'apr\ue8s une proc\ue9dure non traditionnelle. Les mod\ue8les d\ue9crivant les d\ue9pendances chronologiques multivari\ue9es sont cod\ue9s en cha\ueenes binaires repr\ue9sentant des r\ue9seaux neuronaux, et ont \ue9volu\ue9 \ue0 l'aide d'algorithmes g\ue9n\ue9tiques. Le pr\ue9sent document \ue9tudie les propri\ue9t\ue9s de ces mod\ue8les, du point de vue exp\ue9rimental (\ue0 l'aide de grappes homog\ue8nes et h\ue9t\ue9rog\ue8nes), et met l'accent sur i) l'influence des valeurs manquantes, ii) les facteurs qui contr\uf4lent le calcul parall\ue8le et iii) l'efficacit\ue9 des r\ue9sultats de la pr\ue9diction des s\ue9ries chronologiques. Les r\ue9sultats confirment que i) l'algorithme pr\ue9sente une tol\ue9rance \ue9lev\ue9e aux donn\ue9es manquantes, ii) les grappes homog\ue8nes Athon offrent une meilleure production que les grappes homog\ue8nes Xeon, iii) une augmentation du nombre d'esclaves r\ue9duit le temps de traitement jusqu'\ue0 ce que le temps inactif de communication domine (comme pr\ue9vu) et iv) l'ex\ue9cution de l'algorithme en parall\ue8le n'a pas d'effet sur l'erreur quadratique moyenne (comme pr\ue9vu). M\ueame s'il est possible de pr\ue9dire de mani\ue8re qualitative ce comportement, on a d\ue9couvert des compensations appropri\ue9es entre l'erreur et le temps, ce qui permettra d'utiliser plus efficacement et syst\ue9matiquement le syst\ue8me dans l'avenir.NRC publication: Ye