Most popular dimension reduction (DR) methods like t-SNE and UMAP are based on minimizing a cost between input and latent pairwise similarities. Though widely used, these approaches lack clear probabilistic foundations to enable a full understanding of their properties and limitations. To that extent, we introduce a unifying statistical framework based on the coupling of hidden graphs using cross entropy. These graphs induce a Markov random field dependency structure among the observations in both input and latent spaces. We show that existing pairwise similarity DR methods can be retrieved from our framework with particular choices of priors for the graphs. Moreover this reveals that these methods relying on shift-invariant kernels suffer from a statistical degeneracy that explains poor performances in conserving coarse-grain dependencies. New links are drawn with PCA which appears as a non-degenerate graph coupling model.

We focus on the estimation of the intensity of a Poisson process in the presence of a uniform noise. We propose a kernel-based procedure fully calibrated in theory and practice. We show that our adaptive estimator is optimal from the oracle and minimax points of view, and provide new lower bounds when the intensity belongs to a Sobolev ball. By developing the Goldenshluger-Lepski methodology in the case of deconvolution for Poisson processes, we propose an optimal data-driven selection of the kernel bandwidth. Our method is illustrated on the spatial distribution of replication origins and sequence motifs along the human genome.

MOTIVATION: The development of high-throughput single-cell sequencing technologies now allows the investigation of the population diversity of cellular transcriptomes. The expression dynamics (gene-to-gene variability) can be quantified more accurately, thanks to the measurement of lowly expressed genes. In addition, the cell-to-cell variability is high, with a low proportion of cells expressing the same genes at the same time/level. Those emerging patterns appear to be very challenging from the statistical point of view, especially to represent a summarized view of single-cell expression data. Principal component analysis (PCA) is a most powerful tool for high dimensional data representation, by searching for latent directions catching the most variability in the data. Unfortunately, classical PCA is based on Euclidean distance and projections that poorly work in presence of over-dispersed count data with dropout events like single-cell expression data. RESULTS: We propose a probabilistic Count Matrix Factorization (pCMF) approach for single-cell expression data analysis that relies on a sparse Gamma-Poisson factor model. This hierarchical model is inferred using a variational EM algorithm. It is able to jointly build a low dimensional representation of cells and genes. We show how this probabilistic framework induces a geometry that is suitable for single-cell data visualization, and produces a compression of the data that is very powerful for clustering purposes. Our method is competed against other standard representation methods like t-SNE, and we illustrate its performance for the representation of single-cell expression data. AVAILABILITY AND IMPLEMENTATION: Our work is implemented in the pCMF R-package (https://github.com/gdurif/pCMF). SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Motivation: The high dimensionality of genomic data calls for the development of specific classification methodologies, especially to prevent over-optimistic predictions. This challenge can be tackled by compression and variable selection, which combined constitute a powerful framework for classification, as well as data visualization and interpretation. However, current proposed combinations lead to unstable and non convergent methods due to inappropriate computational frameworks. We hereby propose a computationally stable and convergent approach for classification in high dimensional based on sparse Partial Least Squares (sparse PLS). Results: We start by proposing a new solution for the sparse PLS problem that is based on proximal operators for the case of univariate responses. Then we develop an adaptive version of the sparse PLS for classification, called logit-SPLS, which combines iterative optimization of logistic regression and sparse PLS to ensure computational convergence and stability. Our results are confirmed on synthetic and experimental data. In particular, we show how crucial convergence and stability can be when cross-validation is involved for calibration purposes. Using gene expression data, we explore the prediction of breast cancer relapse. We also propose a multicategorial version of our method, used to predict cell-types based on single-cell expression data. Availability and implementation: Our approach is implemented in the plsgenomics R-package. Contact: [email protected]. Supplementary information: Supplementary data are available at Bioinformatics online.

High dimensional Poisson regression has become a standard framework for the analysis of massive counts datasets. In this work we estimate the intensity function of the Poisson regression model by using a dictionary approach, which generalizes the classical basis approach, combined with a Lasso or a group-Lasso procedure. Selection depends on penalty weights that need to be calibrated. Standard methodologies developed in the Gaussian framework can not be directly applied to Poisson models due to heteroscedasticity. Here we provide data-driven weights for the Lasso and the group-Lasso derived from concentration inequalities adapted to the Poisson case. We show that the associated Lasso and group-Lasso procedures satisfy fast and slow oracle inequalities. Simulations are used to assess the empirical performance of our procedure, and an original application to the analysis of Next Generation Sequencing data is provided.

MOTIVATION: Proteins can be naturally classified into families of homologous sequences that derive from a common ancestor. The comparison of homologous sequences and the analysis of their phylogenetic relationships provide useful information regarding the function and evolution of genes. One important difficulty of clustering methods is to distinguish highly divergent homologous sequences from sequences that only share partial homology due to evolution by protein domain rearrangements. Existing clustering methods require parameters that have to be set a priori. Given the variability in the evolution pattern among proteins, these parameters cannot be optimal for all gene families. RESULTS: We propose a strategy that aims at clustering sequences homologous over their entire length, and that takes into account the pattern of substitution specific to each gene family. Sequences are first all compared with each other and clustered into pre-families, based on pairwise similarity criteria, with permissive parameters to optimize sensitivity. Pre-families are then divided into homogeneous clusters, based on the topology of the similarity network. Finally, clusters are progressively merged into families, for which we compute multiple alignments, and we use a model selection technique to find the optimal tradeoff between the number of families and multiple alignment likelihood. To evaluate this method, called HiFiX, we analyzed simulated sequences and manually curated datasets. These tests showed that HiFiX is the only method robust to both sequence divergence and domain rearrangements. HiFiX is fast enough to be used on very large datasets. AVAILABILITY AND IMPLEMENTATION: The Python software HiFiX is freely available at http://lbbe.univ-lyon1.fr/hifix.

Analysis of DNA copy number profiles requires methods tailored to the specific nature of these data. The number of available data analysis methods has grown enormously in the last 5 years. We discuss the typical characteristics of DNA copy number data, as measured by microarray technology and review the extensive literature on preprocessing methods such as segmentation and calling. Subsequently, the focus narrows to applications of DNA copy number in cancer, in particular, several downstream analyses of multi-sample data sets such as testing, clustering and classification. Finally, we look ahead: what should we prepare for and which methodology-related topics may deserve attention in the near future?

BACKGROUND: As biological networks often show complex topological features, mathematical methods are required to extract meaningful information. Clustering methods are useful in this setting, as they allow the summary of the network's topology into a small number of relevant classes. Different strategies are possible for clustering, and in this article we focus on a model-based strategy that aims at clustering nodes based on their connectivity profiles. RESULTS: We present MixNet, the first publicly available computer software that analyzes biological networks using mixture models. We apply this method to various networks such as the E. coli transcriptional regulatory network, the macaque cortex network, a foodweb network and the Buchnera aphidicola metabolic network. This method is also compared with other approaches such as module identification or hierarchical clustering. CONCLUSION: We show how MixNet can be used to extract meaningful biological information, and to give a summary of the networks topology that highlights important biological features. This approach is powerful as MixNet is adaptive to the network under study, and finds structural information without any a priori on the structure that is investigated. This makes MixNet a very powerful tool to summarize and decipher the connectivity structure of biological networks.

BACKGROUND: Microarray-CGH experiments are used to detect and map chromosomal imbalances, by hybridizing targets of genomic DNA from a test and a reference sample to sequences immobilized on a slide. These probes are genomic DNA sequences (BACs) that are mapped on the genome. The signal has a spatial coherence that can be handled by specific statistical tools. Segmentation methods seem to be a natural framework for this purpose. A CGH profile can be viewed as a succession of segments that represent homogeneous regions in the genome whose BACs share the same relative copy number on average. We model a CGH profile by a random Gaussian process whose distribution parameters are affected by abrupt changes at unknown coordinates. Two major problems arise: to determine which parameters are affected by the abrupt changes (the mean and the variance, or the mean only), and the selection of the number of segments in the profile. RESULTS: We demonstrate that existing methods for estimating the number of segments are not well adapted in the case of array CGH data, and we propose an adaptive criterion that detects previously mapped chromosomal aberrations. The performances of this method are discussed based on simulations and publicly available data sets. Then we discuss the choice of modeling for array CGH data and show that the model with a homogeneous variance is adapted to this context. CONCLUSIONS: Array CGH data analysis is an emerging field that needs appropriate statistical tools. Process segmentation and model selection provide a theoretical framework that allows precise biological interpretations. Adaptive methods for model selection give promising results concerning the estimation of the number of altered regions on the genome.