Since their introduction in the 50's, variance component mixed models have been widely used in many application fields. In this context, ReML estimation is by far the most popular procedure to infer the variance components of the model. Although many implementations of the ReML procedure are readily available, there is still need for computational improvements due to the ever-increasing size of the datasets to be handled, and to the complexity of the models to be adjusted. In this paper, we present a Min-Max (MM) algorithm for ReML inference and combine it with several speed-up procedures. The ReML MM algorithm we present is compared to 5 state-of-the-art publicly available algorithms used in statistical genetics. The computational performance of the different algorithms are evaluated on several datasets representing different plant breeding experimental designs. The MM algorithm ranks among the top 2 methods in almost all settings and is more versatile than many of its competitors. The MM algorithm is a promising alternative to the classical AI-ReML algorithm in the context of variance component mixed models. It is available in the MM4LMM R-package.

Abstract Motivation Combining the results of different experiments to exhibit complex patterns or to improve statistical power is a typical aim of data integration. The starting point of the statistical analysis often comes as a set of P-values resulting from previous analyses, that need to be combined flexibly to explore complex hypotheses, while guaranteeing a low proportion of false discoveries. Results We introduce the generic concept of composed hypothesis, which corresponds to an arbitrary complex combination of simple hypotheses. We rephrase the problem of testing a composed hypothesis as a classification task and show that finding items for which the composed null hypothesis is rejected boils down to fitting a mixture model and classifying the items according to their posterior probabilities. We show that inference can be efficiently performed and provide a thorough classification rule to control for type I error. The performance and the usefulness of the approach are illustrated in simulations and on two different applications. The method is scalable, does not require any parameter tuning, and provided valuable biological insight on the considered application cases. Availability and implementation The QCH methodology is available in the qch package hosted on CRAN. Additionally, R codes to reproduce the Einkorn example are available on the personal webpage of the first author: https://www6.inrae.fr/mia-paris/Equipes/Membres/Tristan-Mary-Huard. Supplementary information Supplementary data are available at Bioinformatics online.

The present work aims at deriving theoretical guaranties on the behavior of some cross-validation procedures applied to the $k$-nearest neighbors ($k$NN) rule in the context of binary classification. Here we focus on the leave-$p$-out cross-validation (L$p$O) used to assess the performance of the $k$NN classifier. Remarkably this L$p$O estimator can be efficiently computed in this context using closed-form formulas derived by Celisse and Mary-Huard (2011). We describe a general strategy to derive moment and exponential concentration inequalities for the L$p$O estimator applied to the $k$NN classifier. Such results are obtained first by exploiting the connection between the L$p$O estimator and U-statistics, and second by making an intensive use of the generalized Efron-Stein inequality applied to the L$1$O estimator. One other important contribution is made by deriving new quantifications of the discrepancy between the L$p$O estimator and the classification error/risk of the $k$NN classifier. The optimality of these bounds is discussed by means of several lower bounds as well as simulation experiments.

BACKGROUND: Detecting local correlations in expression between neighboring genes along the genome has proved to be an effective strategy to identify possible causes of transcriptional deregulation in cancer. It has been successfully used to illustrate the role of mechanisms such as copy number variation (CNV) or epigenetic alterations as factors that may significantly alter expression in large chromosomal regions (gene silencing or gene activation). RESULTS: The identification of correlated regions requires segmenting the gene expression correlation matrix into regions of homogeneously correlated genes and assessing whether the observed local correlation is significantly higher than the background chromosomal correlation. A unified statistical framework is proposed to achieve these two tasks, where optimal segmentation is efficiently performed using dynamic programming algorithm, and detection of highly correlated regions is then achieved using an exact test procedure. We also propose a simple and efficient procedure to correct the expression signal for mechanisms already known to impact expression correlation. The performance and robustness of the proposed procedure, called SegCorr, are evaluated on simulated data. The procedure is illustrated on cancer data, where the signal is corrected for correlations caused by copy number variation. It permitted the detection of regions with high correlations linked to epigenetic marks like DNA methylation. CONCLUSIONS: SegCorr is a novel method that performs correlation matrix segmentation and applies a test procedure in order to detect highly correlated regions in gene expression.

MOTIVATION: The spatial conformation of the chromosome has a deep influence on gene regulation and expression. Hi-C technology allows the evaluation of the spatial proximity between any pair of loci along the genome. It results in a data matrix where blocks corresponding to (self-)interacting regions appear. The delimitation of such blocks is critical to better understand the spatial organization of the chromatin. From a computational point of view, it results in a 2D segmentation problem. RESULTS: We focus on the detection of cis-interacting regions, which appear to be prominent in observed data. We define a block-wise segmentation model for the detection of such regions. We prove that the maximization of the likelihood with respect to the block boundaries can be rephrased in terms of a 1D segmentation problem, for which the standard dynamic programming applies. The performance of the proposed methods is assessed by a simulation study on both synthetic and resampled data. A comparative study on public data shows good concordance with biologically confirmed regions. AVAILABILITY AND IMPLEMENTATION: The HiCseg R package is available from the Comprehensive R Archive Network and from the Web page of the corresponding author.

The problems of model and variable selections for classification trees are jointly considered. A penalized criterion is proposed which explicitly takes into account the number of variables, and a risk bound inequality is provided for the tree classifier minimizing this criterion. This penalized criterion is compared to the one used during the pruning step of the CART algorithm. It is shown that the two criteria are similar under some specific margin assumptions. In practice, the tuning parameter of the CART penalty has to be calibrated by hold-out or cross-validation. A simulation study is performed to compare the form of the theoretical penalized criterion we propose with the form obtained after tuning the regularization parameter via cross-validation.

BACKGROUND: Chromatin immunoprecipitation coupled with hybridization to a tiling array (ChIP-chip) is a cost-effective and routinely used method to identify protein-DNA interactions or chromatin/histone modifications. The robust identification of ChIP-enriched regions is frequently complicated by noisy measurements. This identification can be improved by accounting for dependencies between adjacent probes on chromosomes and by modeling of biological replicates. RESULTS: MultiChIPmixHMM is a user-friendly R package to analyse ChIP-chip data modeling spatial dependencies between directly adjacent probes on a chromosome and enabling a simultaneous analysis of replicates. It is based on a linear regression mixture model, designed to perform a joint modeling of immunoprecipitated and input measurements. CONCLUSION: We show the utility of MultiChIPmixHMM by analyzing histone modifications of Arabidopsis thaliana. MultiChIPmixHMM is implemented in R and including functions in C, freely available from the CRAN web site: http://cran.r-project.org.

Compression and variable selection are two classical strategies to deal with large-dimension data sets in classification. We propose an alternative strategy, called aggregation, which consists of a clustering step of redundant variables and a compression step within each group. We develop a statistical framework to define tailored aggregation methods that can be combined with selection methods to build reliable classifiers that benefit from the information contained in redundant variables. Two algorithms are proposed for ordered and nonordered variables, respectively. Applications to the kNN and CART algorithms are presented.

BACKGROUND: In individually dye-balanced microarray designs, each biological sample is hybridized on two different slides, once with Cy3 and once with Cy5. While this strategy ensures an automatic correction of the gene-specific labelling bias, it also induces dependencies between log-ratio measurements that must be taken into account in the statistical analysis. RESULTS: We present two original statistical procedures for the statistical analysis of individually balanced designs. These procedures are compared with the usual ML and REML mixed model procedures proposed in most statistical toolboxes, on both simulated and real data. CONCLUSION: The UP procedure we propose as an alternative to usual mixed model procedures is more efficient and significantly faster to compute. This result provides some useful guidelines for the analysis of complex designs.

BACKGROUND: Microarray data must be normalized because they suffer from multiple biases. We have identified a source of spatial experimental variability that significantly affects data obtained with Cy3/Cy5 spotted glass arrays. It yields a periodic pattern altering both signal (Cy3/Cy5 ratio) and intensity across the array. RESULTS: Using the variogram, a geostatistical tool, we characterized the observed variability, called here the spotting effect because it most probably arises during steps in the array printing procedure. CONCLUSIONS: The spotting effect is not appropriately corrected by current normalization methods, even by those addressing spatial variability. Importantly, the spotting effect may alter differential and clustering analysis.