New efficient algorithms for multiple change-point detection with kernels

Several statistical approaches based on reproducing kernels have been proposed to detect abrupt changes arising in the full distribution of the observations and not only in the mean or variance. Some of these approaches enjoy good statistical properties (oracle inequality, \ldots). Nonetheless, they have a high computational cost both in terms of time and memory. This makes their application difficult even for small and medium sample sizes ($n< 10^4$). This computational issue is addressed by first describing a new efficient and exact algorithm for kernel multiple change-point detection with an improved worst-case complexity that is quadratic in time and linear in space. It allows dealing with medium size signals (up to $n \approx 10^5$). Second, a faster but approximation algorithm is described. It is based on a low-rank approximation to the Gram matrix. It is linear in time and space. This approximation algorithm can be applied to large-scale signals ($n \geq 10^6$). These exact and approximation algorithms have been implemented in \texttt{R} and \texttt{C} for various kernels. The computational and statistical performances of these new algorithms have been assessed through empirical experiments. The runtime of the new algorithms is observed to be faster than that of other considered procedures. Finally, simulations confirmed the higher statistical accuracy of kernel-based approaches to detect changes that are not only in the mean. These simulations also illustrate the flexibility of kernel-based approaches to analyze complex biological profiles made of DNA copy number and allele B frequencies. An R package implementing the approach will be made available on github

Penalized inference of the hematopoietic cell differentiation network via high-dimensional clonal tracking

Abstract Background During their lifespan, stem- or progenitor cells have the ability to differentiate into more committed cell lineages. Understanding this process can be key in treating certain diseases. However, up until now only limited information about the cell differentiation process is known. Aim The goal of this paper is to present a statistical framework able to describe the cell differentiation process at the single clone level and to provide a corresponding inferential procedure for parameters estimation and structure reconstruction of the differentiation network. Approach We propose a multidimensional, continuous-time Markov model with density-dependent transition probabilities linear in sub-population sizes and rates. The inferential procedure is based on an iterative calculation of approximated solutions for two systems of ordinary differential equations, describing process moments evolution over time, that are analytically derived from the process' master equation. Network sparsity is induced by adding a SCAD-based penalization term in the generalized least squares objective function. Results The methods proposed here have been tested by means of a simulation study and then applied to a data set derived from a gene therapy clinical trial, in order to investigate hematopoiesis in humans, in-vivo. The hematopoietic structure estimated contradicts the classical dichotomy theory of cell differentiation and supports a novel myeloid-based model recently proposed in the literature

Statistical Methods for Human Microbiome Data Analysis

The human microbiome is the totality of the microbes, their genetic elements and the interactions they have with surrounding environments throughout the human body. Studies have implicated the human microbiome in health and disease. Two central themes of human microbiome studies are to identify potential factors influencing the microbiome composition, and to define the relationship between microbiome features and biological or clinical outcomes. With the development of next generation sequencing technologies, the human microbiome composition can be interrogated using high-throughput DNA sequencing. One strategy sequences the bacterial 16S ribosomal RNA gene for species identification. These 16S sequences are usually clustered into Operational Taxonomic Units (OTUs). Analysis of such OTU data raises several important statistical challenges, including taking into account the phylogenetic relationship among OTUs and modeling high-dimensional overdispersed count data. This dissertation presents three statistical methods developed specifically for 16S data analysis centering around the two themes. To test the association between overall microbiome composition and a covariate/an outcome, a testing procedure based on a generalized UniFrac distance was developed. The generalized UniFrac distance corrects the unduly weighting of classic UniFrac distances on either highly abundant or rare lineages, and was shown to be more powerful than the classic UniFracs. Under the framework of canonical correlation analysis (CCA), a structure-constrained sparse CCA was proposed to select the OTUs and their correlated covariates. A phylogenetic structure-constrained penalty function was imposed to induce certain smoothness on the linear coefficients according to the OTU phylogenetic relationship. Structure-constrained sparse CCA performed much better than sparse CCA in selecting relevant OTUs. Finally, a sparse Dirichlet-multinomial regression (SDMR) model was developed to link the microbiome composition to environmental covariates and to select the most important covariates and their affected OTUs. SDMR accounts for the overdispersion of OTU counts and uses a sparse group L1 penalty function to facilitate selection of covariates and OTUs simultaneously. These methods were illustrated using simulations as well as a real human gut microbiome data set from a study of dietary effects on gut microbiome composition

Machine learning and computational methods to identify molecular and clinical markers for complex diseases – case studies in cancer and obesity

In biomedical research, applied machine learning and bioinformatics are the essential disciplines heavily involved in translating data-driven findings into medical practice. This task is especially accomplished by developing computational tools and algorithms assisting in detection and clarification of underlying causes of the diseases. The continuous advancements in high-throughput technologies coupled with the recently promoted data sharing policies have contributed to presence of a massive wealth of data with remarkable potential to improve human health care. In concordance with this massive boost in data production, innovative data analysis tools and methods are required to meet the growing demand. The data analyzed by bioinformaticians and computational biology experts can be broadly divided into molecular and conventional clinical data categories. The aim of this thesis was to develop novel statistical and machine learning tools and to incorporate the existing state-of-the-art methods to analyze bio-clinical data with medical applications. The findings of the studies demonstrate the impact of computational approaches in clinical decision making by improving patients risk stratification and prediction of disease outcomes. This thesis is comprised of five studies explaining method development for 1) genomic data, 2) conventional clinical data and 3) integration of genomic and clinical data. With genomic data, the main focus is detection of differentially expressed genes as the most common task in transcriptome profiling projects. In addition to reviewing available differential expression tools, a data-adaptive statistical method called Reproducibility Optimized Test Statistic (ROTS) is proposed for detecting differential expression in RNA-sequencing studies. In order to prove the efficacy of ROTS in real biomedical applications, the method is used to identify prognostic markers in clear cell renal cell carcinoma (ccRCC). In addition to previously known markers, novel genes with potential prognostic and therapeutic role in ccRCC are detected. For conventional clinical data, ensemble based predictive models are developed to provide clinical decision support in treatment of patients with metastatic castration resistant prostate cancer (mCRPC). The proposed predictive models cover treatment and survival stratification tasks for both trial-based and realworld patient cohorts. Finally, genomic and conventional clinical data are integrated to demonstrate the importance of inclusion of genomic data in predictive ability of clinical models. Again, utilizing ensemble-based learners, a novel model is proposed to predict adulthood obesity using both genetic and social-environmental factors. Overall, the ultimate objective of this work is to demonstrate the importance of clinical bioinformatics and machine learning for bio-clinical marker discovery in complex disease with high heterogeneity. In case of cancer, the interpretability of clinical models strongly depends on predictive markers with high reproducibility supported by validation data. The discovery of these markers would increase chance of early detection and improve prognosis assessment and treatment choice