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19 results on '"Tuleau-Malot, Christine"'

1. Random Forests for Big Data

Author

Genuer, Robin, Poggi, Jean-Michel, Tuleau-Malot, Christine, and Villa-Vialaneix, Nathalie

Subjects
Statistics - Machine Learning, Computer Science - Learning, Mathematics - Statistics Theory
Abstract

Big Data is one of the major challenges of statistical science and has numerous consequences from algorithmic and theoretical viewpoints. Big Data always involve massive data but they also often include online data and data heterogeneity. Recently some statistical methods have been adapted to process Big Data, like linear regression models, clustering methods and bootstrapping schemes. Based on decision trees combined with aggregation and bootstrap ideas, random forests were introduced by Breiman in 2001. They are a powerful nonparametric statistical method allowing to consider in a single and versatile framework regression problems, as well as two-class and multi-class classification problems. Focusing on classification problems, this paper proposes a selective review of available proposals that deal with scaling random forests to Big Data problems. These proposals rely on parallel environments or on online adaptations of random forests. We also describe how related quantities -- such as out-of-bag error and variable importance -- are addressed in these methods. Then, we formulate various remarks for random forests in the Big Data context. Finally, we experiment five variants on two massive datasets (15 and 120 millions of observations), a simulated one as well as real world data. One variant relies on subsampling while three others are related to parallel implementations of random forests and involve either various adaptations of bootstrap to Big Data or to "divide-and-conquer" approaches. The fifth variant relates on online learning of random forests. These numerical experiments lead to highlight the relative performance of the different variants, as well as some of their limitations.

Published
2015

2. A model of Poissonian interactions and detection of dependence

Author

Sansonnet, Laure and Tuleau-Malot, Christine

Subjects
Mathematics - Statistics Theory
Abstract

This paper proposes a model of interactions between two point processes, ruled by a reproduction function h, which is considered as the intensity of a Poisson process. In particular, we focus on the context of neurosciences to detect possible interactions in the cerebral activity associated with two neurons. To provide a mathematical answer to this specific problem of neurobiologists, we address so the question of testing the nullity of the intensity h. We construct a multiple testing procedure obtained by the aggregation of single tests based on a wavelet thresholding method. This test has good theoretical properties: it is possible to guarantee the level but also the power under some assumptions and its uniform separation rate over weak Besov bodies is adaptive minimax. Then, some simulations are provided, showing the good practical behavior of our testing procedure., Comment: 27 pages

Published
2013
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3. Variable selection through CART

Author

Sauvé, Marie and Tuleau-Malot, Christine

Subjects
Mathematics - Statistics Theory, Statistics - Applications, 62G05, 62G07, 62G20
Abstract

This paper deals with variable selection in the regression and binary classification frameworks. It proposes an automatic and exhaustive procedure which relies on the use of the CART algorithm and on model selection via penalization. This work, of theoretical nature, aims at determining adequate penalties, i.e. penalties which allow to get oracle type inequalities justifying the performance of the proposed procedure. Since the exhaustive procedure can not be executed when the number of variables is too big, a more practical procedure is also proposed and still theoretically validated. A simulation study completes the theoretical results., Comment: 33 pages

Published
2011

4. Adaptive density estimation: a curse of support?

Author

Reynaud-Bouret, Patricia, Rivoirard, Vincent, and Tuleau-Malot, Christine

Subjects
Mathematics - Statistics Theory, 62G05, 62G07, 62G20
Abstract

This paper deals with the classical problem of density estimation on the real line. Most of the existing papers devoted to minimax properties assume that the support of the underlying density is bounded and known. But this assumption may be very difficult to handle in practice. In this work, we show that, exactly as a curse of dimensionality exists when the data lie in $\R^d$, there exists a curse of support as well when the support of the density is infinite. As for the dimensionality problem where the rates of convergence deteriorate when the dimension grows, the minimax rates of convergence may deteriorate as well when the support becomes infinite. This problem is not purely theoretical since the simulations show that the support-dependent methods are really affected in practice by the size of the density support, or by the weight of the density tail. We propose a method based on a biorthogonal wavelet thresholding rule that is adaptive with respect to the nature of the support and the regularity of the signal, but that is also robust in practice to this curse of support. The threshold, that is proposed here, is very accurately calibrated so that the gap between optimal theoretical and practical tuning parameters is almost filled., Comment: 34 pages 9 figures

Published
2009

9. Reconstructing the functional connectivity of multiple spike trains sing Hawkes models

Author

Lambert, Régis, Tuleau-Malot, Christine, Bessaih, Thomas, Rivoirard, Vincent, Bouret, Yann, Leresche, Nathalie, Reynaud-Bouret, Patricia, Neuroscience Paris Seine (NPS), Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut de Biologie Paris Seine (IBPS), Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Jean Alexandre Dieudonné (JAD), Université Nice Sophia Antipolis (... - 2019) (UNS), Université Côte d'Azur (UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Réseaux de neurones et rythmes physiopathologiques = Neuronal Networks and Physiopathological Rhythms (NPS-09), Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut de Biologie Paris Seine (IBPS), CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Université Paris Dauphine-PSL-Centre National de la Recherche Scientifique (CNRS), Laboratoire de physique de la matière condensée (LPMC), Centre National de la Recherche Scientifique (CNRS)-Université Nice Sophia Antipolis (... - 2019) (UNS), Université Côte d'Azur (UCA)-Université Côte d'Azur (UCA), UCAJEDI'Investissements d'Avenir' managed by the National Research Agency (ANR-15-IDEX-01), CNRS PEPS BMI 2012-2013, Interdisciplinaryaxis MTC-NSC of the University of Nice Sophia-Antipolis.ANR 2011 BS01 010 01, Neurosciences Paris Seine (NPS), Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut de Biologie Paris Seine (IBPS), Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut de Biologie Paris Seine (IBPS), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), and Leresche, Nathalie

Subjects
lasso penalization, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], connectivity, [SDV.NEU.NB]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC]/Neurobiology, [SDV.NEU.NB] Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC]/Neurobiology, least-square estimation, spike train analysis, [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], Hawkes processes, neuron correlation
Abstract

Background: Statistical models that predict neuron spike occurrence from the earlier spiking activity of the whole recorded network are promising tools to reconstruct functional connectivity graphs. Some of the previously used methods were in the general statistical framework of the multivariate Hawkes processes but they often required huge amount of data, prior knowledge about the recorded network, and may generate non stationary models that could not be directly used in simulation. New Method: Here, we present a method, based on least-square estimators and LASSO penalty criteria, optimizing Hawkes models that can be used for simulation. Results: Challenging our method to multiple Integrate and Fire models of neuron networks demonstrated that it eciently detects both excitatory and inhibitory connections. The few errors that occasionally occurred with complex networks including common inputs, weak and chained connections, could easily be discarded based on objective criteria. Conclusions: The present method is robust, stable, applicable with an experimentally realistic amount of data, and does not require any prior knowledge of the studied network. Therefore, it can be used on a personal computer as a turn-key procedure to infer connectivity graphs and generate simulation models from simultaneous spike train recordings

Published
2017

11. Random forests and big data

Author

Genuer, Robin, Poggi, Jean-Michel, Tuleau-Malot, Christine, Villa-Vialaneix, Nathalie, Statistics In System biology and Translational Medicine (SISTM), Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)- Bordeaux population health (BPH), Université de Bordeaux (UB)-Institut de Santé Publique, d'Épidémiologie et de Développement (ISPED)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université de Bordeaux (UB)-Institut de Santé Publique, d'Épidémiologie et de Développement (ISPED)-Institut National de la Santé et de la Recherche Médicale (INSERM), Institut de Santé Publique, d'Epidémiologie et de Développement (ISPED), Université Bordeaux Segalen - Bordeaux 2, Laboratoire de Mathématiques d'Orsay (LM-Orsay), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Unité de Mathématiques et Informatique Appliquées de Toulouse (MIAT INRA), Institut National de la Recherche Agronomique (INRA), Société Française de Statistique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Epidémiologie et Biostatistique [Bordeaux], Université Bordeaux Segalen - Bordeaux 2-Institut de Santé Publique, d'Épidémiologie et de Développement (ISPED)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Bordeaux Segalen - Bordeaux 2-Institut de Santé Publique, d'Épidémiologie et de Développement (ISPED)-Institut National de la Santé et de la Recherche Médicale (INSERM), Laboratoire Jean Alexandre Dieudonné (JAD), Université Nice Sophia Antipolis (... - 2019) (UNS), Université Côte d'Azur (UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Vialaneix, Nathalie, Institut National de Recherche en Informatique et en Automatique (Inria), Institut National de la Santé et de la Recherche Médicale (Inserm)-Université de Bordeaux, Epidémiologie et Biostatistique [Bordeaux], Université Bordeaux Segalen - Bordeaux 2-Institut de Santé Publique, d'Épidémiologie et de Développement (ISPED)-Institut National de la Santé et de la Recherche Médicale (INSERM), Université Paris-Sud - Paris 11 (UP11), Université Paris Descartes - Paris 5 (UPD5), COMUE Université Côte d'Azur (2015 - 2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015 - 2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), and Société Française de Statistique (SFdS). FRA.

Subjects
Big Data, forêts aléatoires, big data, data stream, random forest, flux de données, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Statistiques (Mathématiques), Random forests, [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], Data streams
Abstract

Big Data is one of the major challenges of statistical science and has numerous consequences from algorithmic and theoretical viewpoints. Big Data always involves massive data but it also often includes data streams and data heterogeneity. Recently some statistical methods have been adapted to process Big Data, like linear regression models, clustering methods and bootstrapping schemes. Based on decision trees combined with aggregation and bootstrap ideas, random forests, introduced by Breiman in 2001, are a powerful nonparametric statistical method allowing to consider in a single and versatile framework regression problems as well as two-class or multi-class classification problems. This paper reviews available proposals about random forests in parallel environments as well as about online random forests. Then, we formulate various remarks and sketch some alternative directions for random forests in the Big Data context., Le Big Data est un des grands défis que doit relever la statistique et a de nombreuses conséquences sur les plans théorique et algorithmique. Le Big Data implique toujours le caractère massif des donn ées mais comprend bien souvent aussi des données en flux (en ligne) et implique le traitement de données hétérogènes. Récemment certaines méthodes statistiques ont été adapt ées pour traiter le Big Data, par exemple les modèles de r égression linéaire, les méthodes de classification et les schémas de ré echantillonnage. Basées sur des arbres de d écision et exploitant les id ées d'agrégation et de bootstrap, les forêts al éatoires introduites par Breiman en 2001, sont une méthode statistique non paramétrique puissante et versatile permettant de prendre en compte dans un cadre unique tant les problemes de régression que les problèmes de classification binaire ou multi-classes. Ce papier examine les propositions disponibles de forêts aléatoires en environnement parallèle ainsi que sur les forêts aléatoires en ligne. Ensuite, nous formulons diverses remarques avant d'esquisser quelques directions alternatives pour les forêts aléatoires dans le contexte du Big Data.

Published
2015

19. Multiple Tests Based on a Gaussian Approximation of the Unitary EventsMethod with Delayed Coincidence Count.

Author

Tuleau-Malot, Christine, Rouis, Amel, Grammont, Franck, and Reynaud-Bouret, Patricia

Subjects
*GAUSSIAN function, *APPROXIMATION theory, *NEURONS, *GENERALIZATION, *DISCRETIZATION methods
Abstract

The unitary events (UE) method is one of the most popular and efficient methods used over the past decade to detect patterns of coincident joint spike activity among simultaneously recorded neurons. The detection of coincidences is usually based on binned coincidence count (Grün, 1996), which is known to be subject to loss in synchrony detection (Grün, Diesmann, Grammont, Riehle, & Aertsen, 1999). This defect has been corrected by the multiple shift coincidence count (Grün et al., 1999). The statistical properties of this count have not been further investigated until this work, the formula being more difficult to deal with than the original binned count. First, we propose a new notion of coincidence count, the delayed coincidence count, which is equal to the multiple shift coincidence count when discretized point processes are involved as models for the spike trains. Moreover, it generalizes this notion to nondiscretized point processes, allowing us to propose a new gaussian approximation of the count. Since unknown parameters are involved in the approximation, we perform a plug-in step, where unknown parameters are replaced by estimated ones, leading to a modification of the approximating distribution. Finally the method takes the multiplicity of the tests into account via a Benjamini and Hochberg approach (Benjamini & Hochberg, 1995), to guarantee a prescribed control of the false discovery rate. We compare our new method,MTGAUE (multiple tests based on a gaussian approximation of the unitary events) and the UE method proposed in Grün et al. (1999) over various simulations, showing that MTGAUE extends the validity of the previous method. In particular, MTGAUE is able to detect both profusion and lack of coincidences with respect to the independence case and is robust to changes in the underlying model. Furthermore MTGAUE is applied on real data. [ABSTRACT FROM AUTHOR]

Published
2014
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