arXiv subjects

Pierre Neuvial

Publications and source records attributed to Pierre Neuvial.

27 records · Page 2Linked to original sources

arXiv2018

On the Post Selection Inference constant under Restricted Isometry Properties

Uniformly valid confidence intervals post model selection in regression can be constructed based on Post-Selection Inference (PoSI) constants. PoSI constants are minimal for orthogonal design matrices, and can be upper bounded in function of the sparsity of the set of models under consideration, for generic design matrices. In order to improve on these generic sparse upper bounds, we consider design matrices satisfying a Restricted Isometry Property (RIP) condition. We provide a new upper bound on the PoSI constant in this setting. This upper bound is an explicit function of the RIP constant of the design matrix, thereby giving an interpolation between the orthogonal setting and the generic sparse setting. We show that this upper bound is asymptotically optimal in many settings by constructing a matching lower bound.

math.ST↗

arXiv2018

Post hoc false positive control for spatially structured hypotheses

In a high dimensional multiple testing framework, we present new confidence bounds on the false positives contained in subsets S of selected null hypotheses. The coverage probability holds simultaneously over all subsets S, which means that the obtained confidence bounds are post hoc. Therefore, S can be chosen arbitrarily, possibly by using the data set several times. We focus in this paper specifically on the case where the null hypotheses are spatially structured. Our method is based on recent advances in post hoc inference and particularly on the general methodology of Blanchard et al. (2017); we build confidence bounds for some pre-specified forest-structured subsets {R k , k $\in$ K}, called the reference family, and then we deduce a bound for any subset S by interpolation. The proposed bounds are shown to improve substantially previous ones when the signal is locally structured. Our findings are supported both by theoretical results and numerical experiments. Moreover, we show that our bound can be obtained by a low-complexity algorithm, which makes our approach completely operational for a practical use. The proposed bounds are implemented in the open-source R package sansSouci.

math.ST↗

arXiv2018

Post hoc inference via joint family-wise error rate control

We introduce a general methodology for post hoc inference in a large-scale multiple testing framework. The approach is called "user-agnostic" in the sense that the statistical guarantee on the number of correct rejections holds for any set of candidate items selected by the user (after having seen the data). This task is investigated by defining a suitable criterion, named the joint-family-wise-error rate (JER for short). We propose several procedures for controlling the JER, with a special focus on incorporating dependencies while adapting to the unknown quantity of signal (via a step-down approach). We show that our proposed setting incorporates as particular cases a version of the higher criticism as well as the closed testing based approach of Goeman and Solari (2011). Our theoretical statements are supported by numerical experiments.

math.ST↗

arXiv2016

A model for gene deregulation detection using expression data

In tumoral cells, gene regulation mechanisms are severely altered, and these modifications in the regulations may be characteristic of different subtypes of cancer. However, these alterations do not necessarily induce differential expressions between the subtypes. To answer this question, we propose a statistical methodology to identify the misregulated genes given a reference network and gene expression data. Our model is based on a regulatory process in which all genes are allowed to be deregulated. We derive an EM algorithm where the hidden variables correspond to the status (under/over/normally expressed) of the genes and where the E-step is solved thanks to a message passing algorithm. Our procedure provides posterior probabilities of deregulation in a given sample for each gene. We assess the performance of our method by numerical experiments on simulations and on a bladder cancer data set.

stat.AP↗

arXiv2015

Performance evaluation of DNA copy number segmentation methods

A number of bioinformatic or biostatistical methods are available for analyzing DNA copy number profiles measured from microarray or sequencing technologies. In the absence of rich enough gold standard data sets, the performance of these methods is generally assessed using unrealistic simulation studies, or based on small real data analyses. We have designed and implemented a framework to generate realistic DNA copy number profiles of cancer samples with known truth. These profiles are generated by resampling real SNP microarray data from genomic regions with known copy-number state. The original real data have been extracted from dilutions series of tumor cell lines with matched blood samples at several concentrations. Therefore, the signal-to-noise ratio of the generated profiles can be controlled through the (known) percentage of tumor cells in the sample. In this paper, we describe this framework and illustrate some of the benefits of the proposed data generation approach on a practical use case: a comparison study between methods for segmenting DNA copy number profiles from SNP microarrays. This study indicates that no single method is uniformly better than all others. It also helps identifying pros and cons for the compared methods as a function of biologically informative parameters, such as the fraction of tumor cells in the sample and the proportion of heterozygous markers. Availability: R package jointSeg: http://r-forge.r-project.org/R/?group\_id=1562

q-bio.QM↗

arXiv2013

Asymptotic Results on Adaptive False Discovery Rate Controlling Procedures Based on Kernel Estimators

The False Discovery Rate (FDR) is a commonly used type I error rate in multiple testing problems. It is defined as the expected False Discovery Proportion (FDP), that is, the expected fraction of false positives among rejected hypotheses. When the hypotheses are independent, the Benjamini-Hochberg procedure achieves FDR control at any pre-specified level. By construction, FDR control offers no guarantee in terms of power, or type II error. A number of alternative procedures have been developed, including plug-in procedures that aim at gaining power by incorporating an estimate of the proportion of true null hypotheses. In this paper, we study the asymptotic behavior of a class of plug-in procedures based on kernel estimators of the density of the $p$-values, as the number $m$ of tested hypotheses grows to infinity. In a setting where the hypotheses tested are independent, we prove that these procedures are asymptotically more powerful in two respects: (i) a tighter asymptotic FDR control for any target FDR level and (ii) a broader range of target levels yielding positive asymptotic power. We also show that this increased asymptotic power comes at the price of slower, non-parametric convergence rates for the FDP. These rates are of the form $m^{-k/(2k+1)}$, where $k$ is determined by the regularity of the density of the $p$-value distribution, or, equivalently, of the test statistics distribution. These results are applied to one- and two-sided tests statistics for Gaussian and Laplace location models, and for the Student model.

math.ST↗

arXiv2013

On false discovery rate thresholding for classification under sparsity

We study the properties of false discovery rate (FDR) thresholding, viewed as a classification procedure. The "0"-class (null) is assumed to have a known density while the "1"-class (alternative) is obtained from the "0"-class either by translation or by scaling. Furthermore, the "1"-class is assumed to have a small number of elements w.r.t. the "0"-class (sparsity). We focus on densities of the Subbotin family, including Gaussian and Laplace models. Nonasymptotic oracle inequalities are derived for the excess risk of FDR thresholding. These inequalities lead to explicit rates of convergence of the excess risk to zero, as the number m of items to be classified tends to infinity and in a regime where the power of the Bayes rule is away from 0 and 1. Moreover, these theoretical investigations suggest an explicit choice for the target level $α_m$ of FDR thresholding, as a function of m. Our oracle inequalities show theoretically that the resulting FDR thresholding adapts to the unknown sparsity regime contained in the data. This property is illustrated with numerical experiments.

stat.ME↗

arXiv2010

Gains in Power from Structured Two-Sample Tests of Means on Graphs

We consider multivariate two-sample tests of means, where the location shift between the two populations is expected to be related to a known graph structure. An important application of such tests is the detection of differentially expressed genes between two patient populations, as shifts in expression levels are expected to be coherent with the structure of graphs reflecting gene properties such as biological process, molecular function, regulation, or metabolism. For a fixed graph of interest, we demonstrate that accounting for graph structure can yield more powerful tests under the assumption of smooth distribution shift on the graph. We also investigate the identification of non-homogeneous subgraphs of a given large graph, which poses both computational and multiple testing problems. The relevance and benefits of the proposed approach are illustrated on synthetic data and on breast cancer gene expression data analyzed in context of KEGG pathways.

q-bio.QM↗

arXiv2008

Asymptotic properties of false discovery rate controlling procedures under independence

We investigate the performance of a family of multiple comparison procedures for strong control of the False Discovery Rate ($\mathsf{FDR}$). The $\mathsf{FDR}$ is the expected False Discovery Proportion ($\mathsf{FDP}$), that is, the expected fraction of false rejections among all rejected hypotheses. A number of refinements to the original Benjamini-Hochberg procedure [1] have been proposed, to increase power by estimating the proportion of true null hypotheses, either implicitly, leading to one-stage adaptive procedures [4, 7] or explicitly, leading to two-stage adaptive (or plug-in) procedures [2, 21]. We use a variant of the stochastic process approach proposed by Genovese and Wasserman [11] to study the fluctuations of the $\mathsf{FDP}$ achieved with each of these procedures around its expectation, for independent tested hypotheses. We introduce a framework for the derivation of generic Central Limit Theorems for the $\mathsf{FDP}$ of these procedures, characterizing the associated regularity conditions, and comparing the asymptotic power of the various procedures. We interpret recently proposed one-stage adaptive procedures [4, 7] as fixed points in the iteration of well known two-stage adaptive procedures [2, 21].

math.ST↗