28 results on '"Collier, Olivier"'
Search Results
2. Minimax optimal estimators for general additive functional estimation
- Author
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Collier, Olivier and Comminges, Laëtitia
- Subjects
Mathematics - Statistics Theory - Abstract
In this paper, we observe a sparse mean vector through Gaussian noise and we aim at estimating some additive functional of the mean in the minimax sense. More precisely, we generalize the results of (Collier et al., 2017, 2019) to a very large class of functionals. The optimal minimax rate is shown to depend on the polynomial approximation rate of the marginal functional, and optimal estimators achieving this rate are built.
- Published
- 2019
3. On estimation of nonsmooth functionals of sparse normal means
- Author
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Collier, Olivier, Comminges, Laëtitia, and Tsybakov, Alexandre B.
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Mathematics - Statistics Theory - Abstract
We study the problem of estimation of the value N_gamma(\theta) = sum(i=1)^d |\theta_i|^gamma for 0 < gamma <= 1 based on the observations y_i = \theta_i + \epsilon\xi_i, i = 1,...,d, where \theta = (\theta_1,...,\theta_d) are unknown parameters, \epsilon>0 is known, and \xi_i are i.i.d. standard normal random variables. We prove that the non-asymptotic minimax risk on the class B_0(s) of s-sparse vectors and we propose estimators achieving the minimax rate.
- Published
- 2018
4. Minimax rate of testing in sparse linear regression
- Author
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Carpentier, Alexandra, Collier, Olivier, Comminges, Laëtitia, Tsybakov, Alexandre B., and Wang, Yuhao
- Subjects
Mathematics - Statistics Theory - Abstract
We consider the problem of testing the hypothesis that the parameter of linear regression model is 0 against an s-sparse alternative separated from 0 in the l2-distance. We show that, in Gaussian linear regression model with p < n, where p is the dimension of the parameter and n is the sample size, the non-asymptotic minimax rate of testing has the form sqrt((s/n) log(1 + sqrt(p)/s )). We also show that this is the minimax rate of estimation of the l2-norm of the regression parameter.
- Published
- 2018
5. Adaptive robust estimation in sparse vector model
- Author
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Comminges, Laëtitia, Collier, Olivier, Ndaoud, Mohamed, and Tsybakov, Alexandre B.
- Subjects
Mathematics - Statistics Theory - Abstract
For the sparse vector model, we consider estimation of the target vector, of its L2-norm and of the noise variance. We construct adaptive estimators and establish the optimal rates of adaptive estimation when adaptation is considered with respect to the triplet "noise level - noise distribution - sparsity". We consider classes of noise distributions with polynomially and exponentially decreasing tails as well as the case of Gaussian noise. The obtained rates turn out to be different from the minimax non-adaptive rates when the triplet is known. A crucial issue is the ignorance of the noise variance. Moreover, knowing or not knowing the noise distribution can also influence the rate. For example, the rates of estimation of the noise variance can differ depending on whether the noise is Gaussian or sub-Gaussian without a precise knowledge of the distribution. Estimation of noise variance in our setting can be viewed as an adaptive variant of robust estimation of scale in the contamination model, where instead of fixing the "nominal" distribution in advance, we assume that it belongs to some class of distributions.
- Published
- 2018
6. Minimax estimation of a p-dimensional linear functional in sparse Gaussian models and robust estimation of the mean
- Author
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Collier, Olivier and Dalalyan, Arnak S.
- Subjects
Mathematics - Statistics Theory - Abstract
We consider two problems of estimation in high-dimensional Gaussian models. The first problem is that of estimating a linear functional of the means of $n$ independent $p$-dimensional Gaussian vectors, under the assumption that most of these means are equal to zero. We show that, up to a logarithmic factor, the minimax rate of estimation in squared Euclidean norm is between $(s^2\wedge n) +sp$ and $(s^2\wedge np)+sp$. The estimator that attains the upper bound being computationally demanding, we investigate suitable versions of group thresholding estimators that are efficiently computable even when the dimension and the sample size are very large. An interesting new phenomenon revealed by this investigation is that the group thresholding leads to a substantial improvement in the rate as compared to the element-wise thresholding. Thus, the rate of the group thresholding is $s^2\sqrt{p}+sp$, while the element-wise thresholding has an error of order $s^2p+sp$. To the best of our knowledge, this is the first known setting in which leveraging the group structure leads to a polynomial improvement in the rate. The second problem studied in this work is the estimation of the common $p$-dimensional mean of the inliers among $n$ independent Gaussian vectors. We show that there is a strong analogy between this problem and the first one. Exploiting it, we propose new strategies of robust estimation that are computationally tractable and have better rates of convergence than the other computationally tractable robust (with respect to the presence of the outliers in the data) estimators studied in the literature. However, this tractability comes with a loss of the minimax-rate-optimality in some regimes.
- Published
- 2017
7. Estimating linear functionals of a sparse family of Poisson means
- Author
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Collier, Olivier and Dalalyan, Arnak
- Subjects
Mathematics - Statistics Theory - Abstract
Assume that we observe a sample of size n composed of p-dimensional signals, each signal having independent entries drawn from a scaled Poisson distribution with an unknown intensity. We are interested in estimating the sum of the n unknown intensity vectors, under the assumption that most of them coincide with a given 'background' signal. The number s of p-dimensional signals different from the background signal plays the role of sparsity and the goal is to leverage this sparsity assumption in order to improve the quality of estimation as compared to the naive estimator that computes the sum of the observed signals. We first introduce the group hard thresholding estimator and analyze its mean squared error measured by the squared Euclidean norm. We establish a nonasymptotic upper bound showing that the risk is at most of the order of {\sigma}^2(sp + s^2sqrt(p)) log^3/2(np). We then establish lower bounds on the minimax risk over a properly defined class of collections of s-sparse signals. These lower bounds match with the upper bound, up to logarithmic terms, when the dimension p is fixed or of larger order than s^2. In the case where the dimension p increases but remains of smaller order than s^2, our results show a gap between the lower and the upper bounds, which can be up to order sqrt(p).
- Published
- 2017
8. Optimal adaptive estimation of linear functionals under sparsity
- Author
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Collier, Olivier, Comminges, Laëtitia, Tsybakov, Alexandre B., and Verzélen, Nicolas
- Subjects
Mathematics - Statistics Theory - Abstract
We consider the problem of estimation of a linear functional in the Gaussian sequence model where the unknown vector theta in R^d belongs to a class of s-sparse vectors with unknown s. We suggest an adaptive estimator achieving a non-asymptotic rate of convergence that differs from the minimax rate at most by a logarithmic factor. We also show that this optimal adaptive rate cannot be improved when s is unknown. Furthermore, we address the issue of simultaneous adaptation to s and to the variance sigma^2 of the noise. We suggest an estimator that achieves the optimal adaptive rate when both s and sigma^2 are unknown.
- Published
- 2016
9. Minimax estimation of linear and quadratic functionals on sparsity classes
- Author
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Collier, Olivier, Comminges, Laëtitia, and Tsybakov, Alexandre B.
- Subjects
Mathematics - Statistics Theory - Abstract
For the Gaussian sequence model, we obtain non-asymptotic minimax rates of estimation of the linear, quadratic and the L2-norm functionals on classes of sparse vectors and construct optimal estimators that attain these rates. The main object of interest is the class s-sparse vectors for which we also provide completely adaptive estimators (independent of s and of the noise variance) having only logarithmically slower rates than the minimax ones. Furthermore, we obtain the minimax rates on the Lq-balls where 0 < q < 2. This analysis shows that there are, in general, three zones in the rates of convergence that we call the sparse zone, the dense zone and the degenerate zone, while a fourth zone appears for estimation of the quadratic functional. We show that, as opposed to estimation of the vector, the correct logarithmic terms in the optimal rates for the sparse zone scale as log(d/s^2) and not as log(d/s). For the sparse class, the rates of estimation of the linear functional and of the L2-norm have a simple elbow at s = sqrt(d) (boundary between the sparse and the dense zones) and exhibit similar performances, whereas the estimation of the quadratic functional reveals more complex effects and is not possible only on the basis of sparsity described by the sparsity condition on the vector. Finally, we apply our results on estimation of the L2-norm to the problem of testing against sparse alternatives. In particular, we obtain a non-asymptotic analog of the Ingster-Donoho-Jin theory revealing some effects that were not captured by the previous asymptotic analysis., Comment: 32 pages
- Published
- 2015
10. A Network of 17 Microtubule-Related Genes Highlights Functional Deregulations in Breast Cancer
- Author
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Rodrigues-Ferreira, Sylvie, primary, Morin, Morgane, additional, Guichaoua, Gwenn, additional, Moindjie, Hadia, additional, Haykal, Maria M., additional, Collier, Olivier, additional, Stoven, Véronique, additional, and Nahmias, Clara, additional
- Published
- 2023
- Full Text
- View/download PDF
11. Minimax rates in permutation estimation for feature matching
- Author
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Collier, Olivier and Dalalyan, Arnak S.
- Subjects
Mathematics - Statistics Theory ,Computer Science - Learning - Abstract
The problem of matching two sets of features appears in various tasks of computer vision and can be often formalized as a problem of permutation estimation. We address this problem from a statistical point of view and provide a theoretical analysis of the accuracy of several natural estimators. To this end, the minimax rate of separation is investigated and its expression is obtained as a function of the sample size, noise level and dimension. We consider the cases of homoscedastic and heteroscedastic noise and establish, in each case, tight upper bounds on the separation distance of several estimators. These upper bounds are shown to be unimprovable both in the homoscedastic and heteroscedastic settings. Interestingly, these bounds demonstrate that a phase transition occurs when the dimension $d$ of the features is of the order of the logarithm of the number of features $n$. For $d=O(\log n)$, the rate is dimension free and equals $\sigma (\log n)^{1/2}$, where $\sigma$ is the noise level. In contrast, when $d$ is larger than $c\log n$ for some constant $c>0$, the minimax rate increases with $d$ and is of the order $\sigma(d\log n)^{1/4}$. We also discuss the computational aspects of the estimators and provide empirical evidence of their consistency on synthetic data. Finally, we show that our results extend to more general matching criteria.
- Published
- 2013
12. OPTIMAL ADAPTIVE ESTIMATION OF LINEAR FUNCTIONALS UNDER SPARSITY
- Author
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Collier, Olivier, Comminges, Laëtitia, Tsybakov, Alexandre B., and Verzelen, Nicolas
- Published
- 2018
13. Minimax hypothesis testing for curve registration
- Author
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Collier, Olivier
- Subjects
Mathematics - Statistics Theory - Abstract
This paper is concerned with the problem of goodness-of-fit for curve registration, and more precisely for the shifted curve model, whose application field reaches from computer vision and road traffic prediction to medicine. We give bounds for the asymptotic minimax separation rate, when the functions in the alternative lie in Sobolev balls and the separation from the null hypothesis is measured by the l2-norm. We use the generalized likelihood ratio to build a nonadaptive procedure depending on a tuning parameter, which we choose in an optimal way according to the smoothness of the ambient space. Then, a Bonferroni procedure is applied to give an adaptive test over a range of Sobolev balls. Both achieve the asymptotic minimax separation rates, up to possible logarithmic factors.
- Published
- 2011
14. Curve registration by nonparametric goodness-of-fit testing
- Author
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Collier, Olivier and Dalalyan, Arnak S.
- Subjects
Mathematics - Statistics Theory - Abstract
The problem of curve registration appears in many different areas of applications ranging from neuroscience to road traffic modeling. In the present work, we propose a nonparametric testing framework in which we develop a generalized likelihood ratio test to perform curve registration. We first prove that, under the null hypothesis, the resulting test statistic is asymptotically distributed as a chi-squared random variable. This result, often referred to as Wilks' phenomenon, provides a natural threshold for the test of a prescribed asymptotic significance level and a natural measure of lack-of-fit in terms of the $p$-value of the $\chi^2$-test. We also prove that the proposed test is consistent, \textit{i.e.}, its power is asymptotically equal to $1$. Finite sample properties of the proposed methodology are demonstrated by numerical simulations. As an application, a new local descriptor for digital images is introduced and an experimental evaluation of its discriminative power is conducted.
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- 2011
15. MINIMAX ESTIMATION OF LINEAR AND QUADRATIC FUNCTIONALS ON SPARSITY CLASSES
- Author
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Collier, Olivier, Comminges, Laëtitia, and Tsybakov, Alexandre B.
- Published
- 2017
16. Estimating linear functionals of a sparse family of Poisson means
- Author
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Collier, Olivier and Dalalyan, Arnak S.
- Published
- 2018
- Full Text
- View/download PDF
17. Curve registration by nonparametric goodness-of-fit testing
- Author
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Collier, Olivier and Dalalyan, Arnak S.
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- 2015
- Full Text
- View/download PDF
18. Estimation of the ℓ2-norm and testing in sparse linear regression with unknown variance
- Author
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Carpentier, Alexandra, primary, Collier, Olivier, additional, Comminges, Laetitia, additional, Tsybakov, Alexandre B., additional, and Wang, Yuhao, additional
- Published
- 2022
- Full Text
- View/download PDF
19. LOTUS: a single-and multi-task machine-learning algorithm for the prediction of cancer driver genes
- Author
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Collier, Olivier, Stoven, Véronique, Vert, Jean-Philippe, Modélisation aléatoire de Paris X (MODAL'X), Université Paris Nanterre (UPN), Centre de Bioinformatique (CBIO), Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Institut Curie [Paris], Cancer et génome: Bioinformatique, biostatistiques et épidémiologie d'un système complexe, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut Curie [Paris]-Institut National de la Santé et de la Recherche Médicale (INSERM), ANR-10-LABX-0023,UnivEarthS,Earth - Planets - Universe: observation, modeling, transfer(2010), MINES ParisTech - École nationale supérieure des mines de Paris, Institut Curie [Paris]-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de la Santé et de la Recherche Médicale (INSERM), Collier, Olivier, and Earth - Planets - Universe: observation, modeling, transfer - - UnivEarthS2010 - ANR-10-LABX-0023 - LABX - VALID
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[STAT.AP]Statistics [stat]/Applications [stat.AP] ,[STAT.AP] Statistics [stat]/Applications [stat.AP] ,[SDV.GEN.GH]Life Sciences [q-bio]/Genetics/Human genetics ,[SDV.GEN.GH] Life Sciences [q-bio]/Genetics/Human genetics - Abstract
Cancer driver genes, i.e., oncogenes and tumor suppressor genes, are involved in the acquisition of important functions in tumors, providing a selective growth advantage, allowing uncontrolled proliferation and avoiding apoptosis. It is therefore important to identify these driver genes, both for the fundamental understanding of cancer and to help finding new therapeutic targets. Although the most frequently mutated driver genes have been identified, it is believed that many more remain to be discovered, particularly for driver genes specific to some cancer types. In this paper we propose a new computational method called LOTUS to predict new driver genes. LOTUS is a machine-learning based approach which allows to integrate various types of data in a versatile manner, including informations about gene mutations and protein-protein interactions. In addition, LOTUS can predict cancer driver genes in a pan-cancer setting as well as for specific cancer types, using a 1 multitask learning strategy to share information across cancer types. We empirically show that LOTUS outperforms three other state-of-the-art driver gene prediction methods, both in terms of intrinsic consistency and prediction accuracy, and provide predictions of new cancer genes across many cancer types. Author summary Cancer development is thought to be driven by some important genes that should be targeted by new treatments. Unfortunately, there is a small number of such genes, so that it is of crucial importance to design algorithms capable of finding genes with the highest oncogenic potential. Our new method analyses in particular data of mutations but also other sources of informations to establish a list of genes that should be investigated in priority. Moreover, our algorithm can differentiate between several types of cancer and share information between them to improve the prediction for every disease. We showed that in several contexts our algorithm beats its concurrents.
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- 2018
20. LOTUS: A single- and multitask machine learning algorithm for the prediction of cancer driver genes
- Author
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Collier, Olivier, primary, Stoven, Véronique, additional, and Vert, Jean-Philippe, additional
- Published
- 2019
- Full Text
- View/download PDF
21. Multidimensional linear functional estimation in sparse Gaussian models and robust estimation of the mean
- Author
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Collier, Olivier, primary and Dalalyan, Arnak S., additional
- Published
- 2019
- Full Text
- View/download PDF
22. LOTUS: a Single- and Multitask Machine Learning Algorithm for the Prediction of Cancer Driver Genes
- Author
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Collier, Olivier, primary, Stoven, Véronique, additional, and Vert, Jean-Philippe, additional
- Published
- 2018
- Full Text
- View/download PDF
23. Permutation estimation and minimax rates of identifiability
- Author
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Collier, Olivier, Dalalyan, Arnak S., imagine [Marne-la-Vallée], Laboratoire d'Informatique Gaspard-Monge (LIGM), Université Paris-Est Marne-la-Vallée (UPEM)-École des Ponts ParisTech (ENPC)-ESIEE Paris-Fédération de Recherche Bézout-Centre National de la Recherche Scientifique (CNRS)-Université Paris-Est Marne-la-Vallée (UPEM)-École des Ponts ParisTech (ENPC)-ESIEE Paris-Fédération de Recherche Bézout-Centre National de la Recherche Scientifique (CNRS)-Centre Scientifique et Technique du Bâtiment (CSTB), Université Paris-Est Marne-la-Vallée (UPEM)-École des Ponts ParisTech (ENPC)-ESIEE Paris-Fédération de Recherche Bézout-Centre National de la Recherche Scientifique (CNRS), Centre de Recherche en Économie et Statistique (CREST), Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] (ENSAI)-École polytechnique (X)-École Nationale de la Statistique et de l'Administration Économique (ENSAE Paris)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-École des Ponts ParisTech (ENPC)-Université Paris-Est Marne-la-Vallée (UPEM)-Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-École des Ponts ParisTech (ENPC)-Université Paris-Est Marne-la-Vallée (UPEM)-Centre Scientifique et Technique du Bâtiment (CSTB), Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-École des Ponts ParisTech (ENPC)-Université Paris-Est Marne-la-Vallée (UPEM), and Collier, Olivier
- Subjects
minimax ,[STAT.TH] Statistics [stat]/Statistics Theory [stat.TH] ,Gaussian sequence model ,[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] ,[STAT.TH]Statistics [stat]/Statistics Theory [stat.TH] ,permutation estimation ,[MATH.MATH-ST] Mathematics [math]/Statistics [math.ST] - Abstract
International audience; The problem of matching two sets of features appears in various tasks of computer vision and can be often formalized as a problem of permutation estimation. We address this problem from a statistical point of view and provide a theoretical analysis of the accuracy of several natural estimators. To this end, the notion of the minimax rate of identifiability is introduced and its expression is obtained as a function of the sample size, noise level and dimensionality. We consider the cases of homoscedastic and heteroscedastic noise and carry out, in each case, upper bounds on the identifiability threshold of several estimators. This upper bounds are shown to be unimprovable in the homoscedastic setting. We also discuss the computational aspects of the estimators and provide empirical evidence of their consistency on synthetic data.
- Published
- 2013
24. Statistical methods for descriptor matching
- Author
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Collier, Olivier, Laboratoire d'Informatique Gaspard-Monge (LIGM), Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-École des Ponts ParisTech (ENPC)-Université Paris-Est Marne-la-Vallée (UPEM), imagine [Marne-la-Vallée], Centre Scientifique et Technique du Bâtiment (CSTB)-École des Ponts ParisTech (ENPC)-Laboratoire d'Informatique Gaspard-Monge (LIGM), Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-École des Ponts ParisTech (ENPC)-Université Paris-Est Marne-la-Vallée (UPEM)-Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-Université Paris-Est Marne-la-Vallée (UPEM), Université Paris-Est, Arnak S. Dalalyan, Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-École des Ponts ParisTech (ENPC)-Université Paris-Est Marne-la-Vallée (UPEM)-Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-École des Ponts ParisTech (ENPC)-Université Paris-Est Marne-la-Vallée (UPEM)-Centre Scientifique et Technique du Bâtiment (CSTB), and STAR, ABES
- Subjects
Minimax testing ,[MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM] ,Problème non-paramétrique ,Minimax estimation ,Tests minimax ,[MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM] ,Nonparametric problem ,Estimation minimax - Abstract
Many applications, as in computer vision or medicine, aim at identifying the similarities between several images or signals. There after, it is possible to detect objects, to follow them, or to overlap different pictures. In every case, the algorithmic procedures that treat the images use a selection of key points that they try to match by pairs. The most popular algorithm nowadays is SIFT, that performs key point selection, descriptor calculation, and provides a criterion for global descriptor matching. In the first part, we aim at improving this procedure by changing the original descriptor, that requires to find the argument of the maximum of a histogram: its computation is indeed statistically unstable. So we also have to change the criterion to match two descriptors. This yields a nonparametric hypothesis testing problem, in which both the null and the alternative hypotheses are composite, even nonparametric. We use the generalized likelihood ratio test to get consistent testing procedures, and carry out a minimax study. In the second part, we are interested in the optimality of the procedure of global matching. We give a statistical model in which some descriptors are present in a given order in a first image, and in another order in a second image. Descriptor matching is equivalent in this case to the estimation of a permutation. We give an optimality criterion for the estimators in the minimax sense. In particular, we use the likelihood to find several consistent estimators, which are even optimal under some conditions. Finally, we tackled some practical aspects and showed that our estimators are computable in reasonable time, so that we could then illustrate the hierarchy of our estimators by some simulations, De nombreuses applications, en vision par ordinateur ou en médecine notamment,ont pour but d'identifier des similarités entre plusieurs images ou signaux. On peut alors détecter des objets, les suivre, ou recouper des prises de vue. Dans tous les cas, les procédures algorithmiques qui traitent les images utilisent une sélection de points-clefs qu'elles essayent ensuite de mettre en correspondance par paire. Elles calculent pour chaque point un descripteur qui le caractérise, le discrimine des autres. Parmi toutes les procédures possibles,la plus utilisée aujourd'hui est SIFT, qui sélectionne les points-clefs, calcule des descripteurs et propose un critère de mise en correspondance globale. Dans une première partie, nous tentons d'améliorer cet algorithme en changeant le descripteur original qui nécessite de trouver l'argument du maximum d'un histogramme : en effet, son calcul est statistiquement instable. Nous devons alors également changer le critère de mise en correspondance de deux descripteurs. Il en résulte un problème de test non paramétrique dans lequel à la fois l'hypothèse nulle et alternative sont composites, et même non paramétriques. Nous utilisons le test du rapport de vraisemblance généralisé afin d'exhiber des procédures de test consistantes, et proposons une étude minimax du problème. Dans une seconde partie, nous nous intéressons à l'optimalité d'une procédure globale de mise en correspondance. Nous énonçons un modèle statistique dans lequel des descripteurs sont présents dans un certain ordre dans une première image, et dans un autre dans une seconde image. La mise en correspondance revient alors à l'estimation d'une permutation. Nous donnons un critère d'optimalité au sens minimax pour les estimateurs. Nous utilisons en particulier la vraisemblance afin de trouver plusieurs estimateurs consistants, et même optimaux sous certaines conditions. Enfin, nous nous sommes intéressés à des aspects pratiques en montrant que nos estimateurs étaient calculables en temps raisonnable, ce qui nous a permis ensuite d'illustrer la hiérarchie de nos estimateurs par des simulations
- Published
- 2013
25. Wilks' phenomenon and penalized likelihood-ratio test for nonparametric curve registration
- Author
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Collier, Olivier, Dalalyan, Arnak S., imagine [Marne-la-Vallée], Laboratoire d'Informatique Gaspard-Monge (LIGM), Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-École des Ponts ParisTech (ENPC)-Université Paris-Est Marne-la-Vallée (UPEM)-Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-École des Ponts ParisTech (ENPC)-Université Paris-Est Marne-la-Vallée (UPEM)-Centre Scientifique et Technique du Bâtiment (CSTB), Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-École des Ponts ParisTech (ENPC)-Université Paris-Est Marne-la-Vallée (UPEM), Centre de Recherche en Économie et Statistique (CREST), Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] (ENSAI)-École polytechnique (X)-École Nationale de la Statistique et de l'Administration Économique (ENSAE Paris)-Centre National de la Recherche Scientifique (CNRS), Dalalyan, Arnak, Université Paris-Est Marne-la-Vallée (UPEM)-École des Ponts ParisTech (ENPC)-ESIEE Paris-Fédération de Recherche Bézout-Centre National de la Recherche Scientifique (CNRS)-Université Paris-Est Marne-la-Vallée (UPEM)-École des Ponts ParisTech (ENPC)-ESIEE Paris-Fédération de Recherche Bézout-Centre National de la Recherche Scientifique (CNRS)-Centre Scientifique et Technique du Bâtiment (CSTB), and Université Paris-Est Marne-la-Vallée (UPEM)-École des Ponts ParisTech (ENPC)-ESIEE Paris-Fédération de Recherche Bézout-Centre National de la Recherche Scientifique (CNRS)
- Subjects
[STAT.ML]Statistics [stat]/Machine Learning [stat.ML] ,[STAT.ML] Statistics [stat]/Machine Learning [stat.ML] - Abstract
International audience; The problem of curve registration appears in many different areas of applications ranging from neuroscience to road traffic modeling. In the present work, we propose a nonparametric testing framework in which we develop a generalized likelihood ratio test to perform curve registration. We first prove that, under the null hypothesis, the resulting test statistic is asymptotically distributed as a chi-squared random variable. This result, often referred to as Wilks' phenomenon, provides a natural threshold for the test of a prescribed asymptotic significance level and a natural measure of lack-of-fit in terms of the p-value of the $\chi^2$-test. We also prove that the proposed test is consistent, i.e., its power is asymptotically equal to 1. Finite sample properties of the proposed methodology are demonstrated by numerical simulations.
- Published
- 2012
26. Minimax Rates in Permutation Estimation for Feature Matching.
- Author
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Collier, Olivier and Dalalyan, Arnak S.
- Subjects
- *
COMPUTER algorithms , *MACHINE learning , *MACHINE theory , *DATA mining , *ARTIFICIAL intelligence , *COMPUTER software - Abstract
The problem of matching two sets of features appears in various tasks of computer vision and can be often formalized as a problem of permutation estimation. We address this problem from a statistical point of view and provide a theoretical analysis of the accuracy of several natural estimators. To this end, the minimax rate of separation is investigated and its expression is obtained as a function of the sample size, noise level and dimension of the features. We consider the cases of homoscedastic and heteroscedastic noise and establish, in each case, tight upper bounds on the separation distance of several estimators. These upper bounds are shown to be unimprovable both in the homoscedastic and heteroscedastic settings. Interestingly, these bounds demonstrate that a phase transition occurs when the dimension d of the features is of the order of the logarithm of the number of features n. For d = O(log n), the rate is dimension free and equals σ(log n)1/2, where σ is the noise level. In contrast, when d is larger than c log n for some constant c > 0, the minimax rate increases with d and is of the order of σ(d log n)1/4. We also discuss the computational aspects of the estimators and provide empirical evidence of their consistency on synthetic data. Finally, we show that our results extend to more general matching criteria. [ABSTRACT FROM AUTHOR]
- Published
- 2016
27. Minimax hypothesis testing for curve registration
- Author
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Collier, Olivier, primary
- Published
- 2012
- Full Text
- View/download PDF
28. Human Fetal Cell Therapy in Huntington's Disease: A Randomized, Multicenter, Phase <scp>II</scp> Trial
- Author
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Bachoud-Lévi, Anne-Catherine, Schramm, Catherine, Remy, Philippe, Aubin, Ghislaine, Blond, Serge, Bocket, Laurence, Brugières, Pierre, Calvas, Fabienne, Calvier, Elisabeth, Cassim, François, Challine, Dominique, Gagou, Clarisse Scherer, De Langavant, Laurent Cleret, Collier, Francis, Cottencin, Olivier, David, Philippe, Damier, Philippe, Delliaux, Marie, Delmaire, Christine, Delval, Arnaud, Démonet, Jean‐François, Descamps, Philippe, Gaura, Véronique, Gohier, Bénédicte, Goldman, Serge, Haddad, Bassam, Izopet, Jacques, Jeny, Roland, Kerr-Conte, Julie, Krystowiak, Pierre, Lalanne, Christophe, Lavisse, Sonia, Lefaucheur, Jean‐Pascal, Lemoine, Laurie, Levivier, Marc, Lotterie, Jean‐Albert, Lunel‐Fabiani, Françoise, Maison, Patrick, Massager, Nicolas, Massart, Renaud, Menei, Philippe, Montero‐Menei, Claudia, Neveu, Isabelle, Parant, Olivier, Pautot, Vivien, Payoux, Pierre, Péréon, Yann, Rialland, Amandine, Rosser, Anne, Rouard, Hélène HR, Schmitz, David, Simonetta‐Moreau, Marion, Simonin, Clémence, Slama, Hichem, Sol, Jean‐Christophe, Supiot, Frédéric, Tanguy, Jean‐Yves, Tenenbaum, Liliane, Verny, Christophe, Youssov, Katia, Peschanski, Marc, Audureau, Etienne, Palfi, Stéphane, Hantraye, Philippe, Centre de référence maladie de Huntington, Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Hôpital Henri Mondor-CHU Pitié-Salpêtrière [AP-HP], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Sorbonne Université (SU)-CHU Trousseau [APHP], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU), IMRB - 'NeuroPsychologie Interventionnelle' [Créteil] (U955 Inserm - UPEC), Institut Mondor de Recherche Biomédicale (IMRB), Institut National de la Santé et de la Recherche Médicale (INSERM)-IFR10-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Institut National de la Santé et de la Recherche Médicale (INSERM)-IFR10-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12), Université Paris sciences et lettres (PSL), Université Paris-Est Créteil Val-de-Marne - Faculté de médecine (UPEC Médecine), Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12), AOM00139 and AOM04021 Direction de la Recherche Clinique, Association Française contre les Myopathies., Collaborators : on behalf the Multicentric Intracerebral Grafting in Huntington's Disease Group : Catherine Schramm, Philippe Remy, Ghislaine Aubin, Serge Blond, Laurence Bocket, Pierre Brugières, Fabienne Calvas, Elisabeth Calvier, François Cassim, Dominique Challine, Clarisse Scherer Gagou, Laurent Cleret de Langavant, Francis Collier, Olivier Cottencin, Philippe David, Philippe Damier, Marie Delliaux, Christine Delmaire, Arnaud Delval, Jean-François Démonet, Philippe Descamps, Véronique Gaura, Bénédicte Gohier, Serge Goldman, Bassam Haddad, Jacques Izopet, Roland Jeny, Julie Kerr-Conte, Pierre Krystowiak, Christophe Lalanne, Sonia Lavisse, Jean-Pascal Lefaucheur, Laurie Lemoine, Marc Levivier, Jean-Albert Lotterie, Françoise Lunel-Fabiani, Patrick Maison, Nicolas Massager, Renaud Massart, Philippe Menei, Claudia Montero-Menei, Isabelle Neveu, Olivier Parant, Vivien Pautot, Pierre Payoux, Yann Pereon, Amandine Rialland, Anne Rosser, Hélène Rouard, David Schmitz, Marion Simonetta-Moreau, Clémence Simonin, Hichem Slama, Jean-Christophe Sol, Frédéric Supiot, Jean-Yves Tanguy, Liliane Tenenbaum, Christophe Verny, Katia Youssov, Marc Peschanski, Etienne Audureau, Stéphane Palfi, Philippe Hantraye., and Montero-Menei, claudia
- Subjects
0301 basic medicine ,medicine.medical_specialty ,Neurology ,Huntington s disease ,MIG-' HD ,Cell- and Tissue-Based Therapy ,[SDV.BC]Life Sciences [q-bio]/Cellular Biology ,Disease ,law.invention ,03 medical and health sciences ,0302 clinical medicine ,Huntington's disease ,Randomized controlled trial ,law ,Internal medicine ,medicine ,Humans ,Stage (cooking) ,Adverse effect ,[SDV.BC] Life Sciences [q-bio]/Cellular Biology ,business.industry ,phase 2 trial ,Neurodegenerative Diseases ,Sciences bio-médicales et agricoles ,medicine.disease ,Confidence interval ,Transplantation ,Huntington Disease ,030104 developmental biology ,Neurology (clinical) ,cell therapy ,business ,030217 neurology & neurosurgery - Abstract
Background\ud Huntington's disease is a rare, severe, inherited neurodegenerative disease in which we assessed the safety and efficacy of grafting human fetal ganglionic eminence intrastriatally.\ud \ud Methods\ud Patients at the early stage of the disease were enrolled in the Multicentric Intracerebral Grafting in Huntington's Disease trial, a delayed‐start phase II randomized study. After a run‐in period of 12 months, patients were randomized at month 12 to either the treatment group (transplanted at month 13–month 14) or the control group and secondarily treated 20 months later (month 33–month 34). The primary outcome was total motor score compared between both groups 20 months postrandomization (month 32). Secondary outcomes included clinical, imaging, and electrophysiological findings and a comparison of pregraft and postgraft total motor score slopes during the entire study period (month 0–month 52) regardless of the time of transplant.\ud \ud Results\ud Of 54 randomized patients, 45 were transplanted; 26 immediately (treatment) and 19 delayed (control). Mean total motor score at month 32 did not differ between groups (treated controls difference in means adjusted for M12: +2.9 [95% confidence interval, −2.8 to 8.6]; P = 0.31). Its rate of decline after transplantation was similar to that before transplantation. A total of 27 severe adverse events were recorded in the randomized patients, 10 of which were related to the transplant procedure. Improvement of procedures during the trial significantly decreased the frequency of surgical events.We found antihuman leucocytes antigen antibodies in 40% of the patients.\ud \ud Conclusion\ud No clinical benefit was found in this trial. This may have been related to graft rejection. Ectopia and high track number negatively influence the graft outcome. Procedural adjustments substantially improved surgical safety. (ClinicalTrials.gov NCT00190450.) © 2020 International Parkinson and Movement Disorder Society
- Published
- 2020
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