arXiv subjects

Irène Gannaz

Publications and source records attributed to Irène Gannaz.

At least 19 recordsLinked to original sources

arXiv2026

Deepest voting on rankings

This article aims to present a unified framework for ranking-based voting rules based on the use of depth functions on permutations, as a counterpart of deepest voting rules on evaluation introduced in Aubin et al. [2022]. It introduces the notion of depth functions, in continuous sets and in permutation sets, the later using the notion of Fr{é}chet means. Deepest voting procedures are then formally defined, and some classical voting rules are expressed as deepest voting procedures, using a large variety of distances on the set of permutations. Links are done between the depth functions mathematical properties and some behaviours of the voting rule, such as Neutrality, Anonymity, Universality, Condorcet winner/loser property and so on.

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arXiv2025

G{é}n{é}ration de Matrices de Corr{é}lation avec des Structures de Graphe par Optimisation Convexe

This work deals with the generation of theoretical correlation matrices with specific sparsity patterns, associated to graph structures. We present a novel approach based on convex optimization, offering greater flexibility compared to existing techniques, notably by controlling the mean of the entry distribution in the generated correlation matrices. This allows for the generation of correlation matrices that better represent realistic data and can be used to benchmark statistical methods for graph inference.

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arXiv2025

Benchmarking Brain Connectivity Graph Inference: A Novel Validation Approach

Inferring a binary connectivity graph from resting-state fMRI data for a single subject requires making several methodological choices and assumptions that can significantly affect the results. In this study, we investigate the robustness of existing edge detection methods when relaxing a common assumption: the sparsity of the graph. We propose a new pipeline to generate synthetic data and to benchmark the state of the art in graph inference. Simulated correlation matrices are designed to have a set of given zeros and a constraint on the signal-to-noise ratio. We compare approaches based on covariance or precision matrices, emphasizing their implications for connectivity inference. This framework allows us to assess the sensitivity of connectivity estimations and edge detection methods to different parameters.

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arXiv2025

Generating Correlation Matrices with Graph Structures Using Convex Optimization

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arXiv2024

A non-asymptotic upper bound in prediction for the PLS estimator

We investigate the theoretical performances of the Partial Least Square (PLS) algorithm in a high dimensional context. We provide upper bounds on the risk in prediction for the statistical linear model when considering the PLS estimator. Our bounds are non-asymptotic and are expressed in terms of the number of observations, the noise level, the properties of the design matrix, and the number of considered PLS components. In particular, we exhibit some scenarios where the variability of the PLS may explode and prove that we can get round of these situations by introducing a Ridge regularization step. These theoretical findings are illustrated by some numerical simulations.

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arXiv2024

Probabilistic Models of Profiles for Voting by Evaluation

Considering voting rules based on evaluation inputs rather than preference rankings modifies the paradigm of probabilistic studies of voting procedures. This article proposes several simulation models for generating evaluation-based voting inputs. These models can cope with dependent and non identical marginal distributions of the evaluations received by the candidates. A last part is devoted to fitting these models to real data sets.

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arXiv2023

A non-asymptotic analysis of the single component PLS regression

This paper investigates some theoretical properties of the Partial Least Square (PLS) method. We focus our attention on the single component case, that provides a useful framework to understand the underlying mechanism. We provide a non-asymptotic upper bound on the quadratic loss in prediction with high probability in a high dimensional regression context. The bound is attained thanks to a preliminary test on the first PLS component. In a second time, we extend these results to the sparse partial least squares (sPLS) approach. In particular, we exhibit upper bounds similar to those obtained with the lasso algorithm, up to an additional restricted eigenvalue constraint on the design matrix.

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arXiv2023

Local Whittle estimation with (quasi-)analytic wavelets

In the general setting of long-memory multivariate time series, the long-memory characteristics are defined by two components. The long-memory parameters describe the autocorrelation of each time series. And the long-run covariance measures the coupling between time series, with general phase parameters. It is of interest to estimate the long-memory, long-run covariance and general phase parameters of time series generated by this wide class of models although they are not necessarily Gaussian nor stationary. This estimation is thus not directly possible using real wavelets decomposition or Fourier analysis. Our purpose is to define an inference approach based on a representation using quasi-analytic wavelets. We first show that the covariance of the wavelet coefficients provides an adequate estimator of the covariance structure including the phase term. Consistent estimators based on a local Whittle approximation are then proposed. Simulations highlight a satisfactory behavior of the estimation on finite samples on linear time series and on multivariate fractional Brownian motions. An application on a real neuroscience dataset is presented, where long-memory and brain connectivity are inferred.

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arXiv2022

Asymptotic normality of wavelet covariances and of multivariate wavelet Whittle estimators

Multivariate processes with long-range dependence properties can be encountered in many fields of application. Two fundamental characteristics in such frameworks are long-range dependence parameters and correlations between component time series. We consider multivariate long-range dependent linear processes, not necessarily Gaussian. We show that the covariances between the wavelet coefficients in this setting are asymptotically Gaussian. We also study the asymptotic distributions of the estimators of the long-range dependence parameter and the long-run covariance by a wavelet-based Whittle procedure. We prove the asymptotic normality of the estimators, and we provide an explicit expression for the asymptotic covariances. An empirical illustration of this result is proposed on a real dataset of rat brain connectivity.

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arXiv2022

Outlier detection in multivariate functional data through a contaminated mixture model

In an industrial context, the activity of sensors is recorded at a high frequency. A challenge is to automatically detect abnormal measurement behavior. Considering the sensor measures as functional data, the problem can be formulated as the detection of outliers in a multivariate functional data set. Due to the heterogeneity of this data set, the proposed contaminated mixture model both clusters the multivariate functional data into homogeneous groups and detects outliers. The main advantage of this procedure over its competitors is that it does not require to specify the proportion of outliers. Model inference is performed through an Expectation-Conditional Maximization algorithm, and the BIC is used to select the number of clusters. Numerical experiments on simulated data demonstrate the high performance achieved by the inference algorithm. In particular, the proposed model outperforms the competitors. Its application on the real data which motivated this study allows to correctly detect abnormal behaviors.

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arXiv2021

Deepest Voting: a new way of electing

This article aims to present a unified framework for grading-based voting processes. The idea is to represent the grades of each voter on d candidates as a point in R^d and to define the winner of the vote using the deepest point of the scatter plot. The deepest point is obtained by the maximization of a depth function. Universality, unanimity, and neutrality properties are proved to be satisfied. Monotonicity and Independence to Irrelevant Alternatives are also studied. It is shown that usual voting processes correspond to specific choices of depth functions. Finally, some basic paradoxes are explored for these voting processes.

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arXiv2021

A Note on Data Simulations for Voting by Evaluation

Voting rules based on evaluation inputs rather than preference orders have been recently proposed, like majority judgement, range voting or approval voting. Traditionally, probabilistic analysis of voting rules supposes the use of simulation models to generate preferences data, like the Impartial Culture (IC) or Impartial and Anonymous Culture (IAC) models. But these simulation models are not suitable for the analysis of evaluation-based voting rules as they generate preference orders instead of the needed evaluations. We propose in this paper several simulation models for generating evaluation-based voting inputs. These models, inspired by classical ones, are defined, tested and compared for recommendation purpose.

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arXiv2020

Asymptotic control of FWER under Gaussian assumption: application to correlation tests

In many applications, hypothesis testing is based on an asymptotic distribution of statistics. The aim of this paper is to clarify and extend multiple correction procedures when the statistics are asymptotically Gaussian. We propose a unified framework to prove their asymptotic behavior which is valid in the case of highly correlated tests. We focus on correlation tests where several test statistics are proposed. All these multiple testing procedures on correlations are shown to control FWER. An extensive simulation study on correlation-based graph estimation highlights finite sample behavior, independence on the sparsity of graphs and dependence on the values of correlations. Empirical evaluation of power provides comparisons of the proposed methods. Finally validation of our procedures is proposed on real dataset of rats brain connectivity measured by fMRI. We confirm our theoretical findings by applying our procedures on a full null hypotheses with data from dead rats. Data on alive rats show the performance of the proposed procedures to correctly identify brain connectivity graphs with controlled errors.

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arXiv2018

Wavelet-based and Fourier-based multivariate Whittle estimation: multiwave

Multivariate time series with long-dependence are observed in many applications such as finance , geophysics or neuroscience. Many packages provide estimation tools for univariate settings but few are addressing the problem of long-dependence estimation for multivariate settings. The package multiwave is providing efficient estimation procedures for multivariate time series. Two semi-parametric estimation methods of the long-memory exponents and long-run covariance matrix of time series are implemented. The first one is the Fourier-based estimation proposed by [18] and the second one is a wavelet-based estimation described in [4]. The objective of this paper is to provide an overview of the R package multiwave with its practical application perspectives.

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arXiv2017

New results on approximate Hilbert pairs of wavelet filters with common factors

In this paper, we consider the design of wavelet filters based on the Thiran common-factor approach proposed in Selesnick [2001]. This approach aims at building finite impulseresponse filters of a Hilbert-pair of wavelets serving as real and imaginary part of a complexwavelet. Unfortunately it is not possible to construct wavelets which are both finitelysupported and analytic. The wavelet filters constructed using the common-factor approachare then approximately analytic. Thus, it is of interest to control their analyticity. Thepurpose of this paper is to first provide precise and explicit expressions as well as easilyexploitable bounds for quantifying the analytic approximation of this complex wavelet.Then, we prove the existence of such filters enjoying the classical perfect reconstructionconditions, with arbitrarily many vanishing moments.

stat.ME↗

arXiv2015

Multivariate wavelet Whittle estimation in long-range dependence

Multivariate processes with long-range dependent properties are found in a large number of applications including finance, geophysics and neuroscience. For real data applications, the correlation between time series is crucial. Usual estimations of correlation can be highly biased due to phase-shifts caused by the differences in the properties of autocorrelation in the processes. To address this issue, we introduce a semiparametric estimation of multivariate long-range dependent processes. The parameters of interest in the model are the vector of the long-range dependence parameters and the long-run covariance matrix, also called functional connectivity in neuroscience. This matrix characterizes coupling between time series. The proposed multivariate wavelet-based Whittle estimation is shown to be consistent for the estimation of both the long-range dependence and the covariance matrix and to encompass both stationary and nonstationary processes. A simulation study and a real data example are presented to illustrate the finite sample behaviour.

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arXiv2014

Classification of EEG recordings in auditory brain activity via a logistic functional linear regression model

We want to analyse EEG recordings in order to investigate the phonemic categorization at a very early stage of auditory processing. This problem can be modelled by a supervised classification of functional data. Discrimination is explored via a logistic functional linear model, using a wavelet representation of the data. Different procedures are investigated, based on penalized likelihood and principal component reduction or partial least squares reduction.

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arXiv2013

Wavelet penalized likelihood estimation in generalized functional models

The paper deals with generalized functional regression. The aim is to estimate the influence of covariates on observations, drawn from an exponential distribution. The link considered has a semiparametric expression: if we are interested in a functional influence of some covariates, we authorize others to be modeled linearly. We thus consider a generalized partially linear regression model with unknown regression coefficients and an unknown nonparametric function. We present a maximum penalized likelihood procedure to estimate the components of the model introducing penalty based wavelet estimators. Asymptotic rates of the estimates of both the parametric and the nonparametric part of the model are given and quasi-minimax optimality is obtained under usual conditions in literature. We establish in particular that the LASSO penalty leads to an adaptive estimation with respect to the regularity of the estimated function. An algorithm based on backfitting and Fisher-scoring is also proposed for implementation. Simulations are used to illustrate the finite sample behaviour, including a comparison with kernel and splines based methods.

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