Marie-CHristine Roubaud

Reduced-order filters are proposed for linear and nonlinear systems and their long time behaviour is studied. Using the results of Ocone and Pardoux \cite{ocpa} on the asymptotic stability of the optimal filter with respect to its initial condition, the asymptotic efficiency of these filters is established in various cases.

We focus on the descriptive approach to linear discriminant analysis for matrix-variate data in the binary case. Under a separability assumption on row and column variability, the most discriminant linear combinations of rows and columns are determined by the singular value decomposition of the difference of the class-averages with the Mahalanobis metric in the row and column spaces. This approach provides data representations of data in two-dimensional or three-dimensional plots and singles out discriminant components. An application to electroencephalographic multi-sensor signals illustrates the relevance of the method.

Z. In this work, we propose a modified form of the extended Kalman filter KF for assimilating oceanic data into numerical models. Its development consists essentially of approximating the error covariance matrix by a singular low rank matrix, which amounts in practice to making no correction in those directions for which the error is the most attenuated by the system. This not only reduces the implementation cost but may also improve the filter stability as well. These `directions of correction' evolve with time according to the model evolution, which constitutes the most original feature of this filter and distinguishes it from other sequential assimilation methods based on the projection onto a fixed basis of functions. A method Z. for initializing the filter based on the empirical orthogonal functions EOF is also described. An example of assimilation Z. based on the quasi-geostrophic QG model for a square ocean domain with a certain wind stress forcing pattern is given. Altho...

... Although this is only a simple test case designed to assess the feasibility of the method, the results are very encouraging. ... We shall assume that the linearized system is close enough to the original one for the results in the linear case to be transferable to the non-linear case. ...

In Affymetrix microarrays, detection calls are usually used for preproce ss- ing (control, normalization or filtering). We propose to use this information in th e search for differentially expressed genes. For the sake of simplicity we have limited o urselves to the chi-square test approach, although other tests for categorical var iables can be used. The high simplicity of the

We have identified genes differentially expressed in childhood early B acute lymphoblastic leukemia at diagnosis, according to chemosensitivity. Chemosensitive (M1) and chemoresistant (M3) patients present <5% and >25% of residual leukemic blasts at 21 days of treatment, respectively. The expression profiles of 4205 genes for 32 patients included in the FRALLE93 protocol have been determined using microarray. From differential analysis, CD34, SPI-B and BCR distinguished M1 from M3 patients using microarray and RT-PCR data. Linear discriminant analysis (LDA) and cross-validation show that the combined expression of these three genes classify and predict correctly around 90% and 80% of patients, respectively.

... Although this is only a simple test case designed to assess the feasibility of the method, the results are very encouraging. ... We shall assume that the linearized system is close enough to the original one for the results in the linear case to be transferable to the non-linear case. ...

ABSTRACT A problem of discrete-time piecewise linear filtering with small observation noise is considered. The case in which the observation function is not one-to-one and has two intervals of linearity is studied, in particular when this function is symmetric. Under some detectability assumption, a procedure is presented to detect the intervals of linearity of the observation function. During such time intervals, one can then approximate the optimal filter by the corresponding Kalman-Bucy filter

ABSTRACT La classification de données fortement bruitées et présentant une importante variabilité constitue un enjeu important. Les signaux électrophysiologiques (EEG) de part leur importante variabilité temporelle correspondent à ce type de données. Nous proposons une procédure permettant de discriminer, chez un même sujet, deux classes de signaux cérébraux à partir d'une modélisation par le modèle linéaire mixte gaussien. Ce travail s'inspire de la méthode présentée par Huang et al.(2008). Notre contribution réside d'une part dans une formalisation simplifiée de la modélisation et d'autre part dans l'introduction d'une transformation en ondelettes permettant une réduction de la dimension temporelle sans perte d'information. La procédure présentée est appliquée à la détection d'ondes d'erreurs au cours d'une tâche cognitive, et nous étudions la performance de notre méthode sur six sujets en comparant les résultats obtenus aux résultats d'une analyse factorielle discriminante. The classification of noisy-data with high variability is an important issue. Electrophysiological signals (EEG) with their important temporal variability correspond to this type of data. For one subject, we propose a procedure in order to classify two types of brain signals using a parametric modeling based on the Gaussian Mixed-Effects model. The present work is based on the method presented by Huang et al.(2008). Our contribution is first a simplified formalization of the modeling and second the introduction of a wavelet transform which leads to a reduction of temporal dimension without loss of information. The procedure is applied to the detection of error-negativities during a cognitive task, and we study the performance of our method on six subjects by comparing the results with those obtained with a discriminant analysis.

ABSTRACT L'analyse conjointe de multiples jeux de données de même nature pour en dégager l'information pertinente est un problème complexe. Ce problème est rencontré notamment dans la comparaison des résultats obtenus sur différentes plateformes bio-puces dans la recherche de gènes différentiellement exprimés ou l'inférence de réseaux de régulation géniques. Souvent les analyses sont d'abord effectuées indépendamment sur chacun des jeux de données et les résultats obtenus sont ensuite croisés pour en dégager une information commune. Mais ceci est clairement sous-optimal et il serait souvent préférable d'exploiter simultanément les jeux de données. Le problème inhérent est alors celui de la calibration, c'est à dire le pré-traitement destiné à les rendre comparables. Cette présentation se focalise sur la question primordiale: comment homogénéiser différents jeux de données de même nature pour les rendre comparables? Une méthode basée sur une approche variationnelle est proposée. Des fonctions de "rectification" non-linéaires (une par jeu de données) sont estimées à partir de jeux multiples, par optimisation numérique d'une fonctionnelle. Cette dernière est constituée d'un terme d'attache aux données et d'un terme de régularisation par pénalisation de la dérivée seconde de la fonction de rectification. L'optimisation est effectuée numériquement par un algorithme itératif. L'approche proposée est illustrée sur une simulation, dans laquelle des jeux artificiels sont constitués à partir d'un jeu de données réel d'expression de E. Coli.

ABSTRACT We consider a piecewise linear filtering problem with small observation noise. In two different situations we construct an approximate finite-dimensional filter based on several Kalman-Bucy filters running in parallel and a procedure of tests. In the first case our work generalizes some results of Fleminget al. to more general piecewise linear dynamics.

ABSTRACT An algorithm which is based on several Kalman filters running in parallel is presented. A test procedure for deciding which Kalman filter to follow, which produces a good estimate of the unobserved system process in a nonlinear filtering problem with piecewise linear dynamics and small observation noise is developed. The results generalize those of W.H. Fleming, D. Ji, and E. Pardoux (1988)

Stochastic systems driven by fractional Brownian motions are investigated. At first analogs of the usual representation theorems and Girsanov’s formula are derived. Then the tools are applied to solve some statistical problems of parameter estimation and optimal filtering.

... email: masha.kleptsyna@id.ru TCorresponding author. ... It is well-known that when the noises V and Win (1) are Brownian motions, ie, when h = H = 112, then the optimal filter is theKalman-Bucy filter (see Kalman [8], Kalman and Bucy [9] and, eg [17]). ...