Spectral Learning of Binomial HMMs for DNA Methylation Data

We consider learning parameters of Binomial Hidden Markov Models, which may be used to model DNA methylation data. The standard algorithm for the problem is EM, which is computationally expensive for sequences of the scale of the mammalian genome. Recently developed spectral algorithms can learn parameters of latent variable models via tensor decomposition, and are highly efficient for large data. However, these methods have only been applied to categorial HMMs, and the main challenge is how to extend them to Binomial HMMs while still retaining computational efficiency. We address this challenge by introducing a new feature-map based approach that exploits specific properties of Binomial HMMs. We provide theoretical performance guarantees for our algorithm and evaluate it on real DNA methylation data

Algorithms and Models for Genome Biology

New advances in genomic technology make it possible to address some of the most fundamental questions in biology for the first time. They also highlight a need for new approaches to analyze and model massive amounts of complex data. In this thesis, I present six research projects that illustrate the exciting interaction between high-throughput genomic experiments, new machine learning algorithms, and mathematical modeling. This interdisci- plinary approach gives insights into questions ranging from how variations in the epigenome lead to diseases across human populations to how the slime mold finds the shortest path. The algorithms and models developed here are also of interest to the broader machine learning community, and have applications in other domains such as text modeling.Mathematic

HypoRiPPAtlas as an Atlas of hypothetical natural products for mass spectrometry database search

Recent analyses of public microbial genomes have found over a million biosynthetic gene clusters, the natural products of the majority of which remain unknown. Additionally, GNPS harbors billions of mass spectra of natural products without known structures and biosynthetic genes. We bridge the gap between large-scale genome mining and mass spectral datasets for natural product discovery by developing HypoRiPPAtlas, an Atlas of hypothetical natural product structures, which is ready-to-use for in silico database search of tandem mass spectra. HypoRiPPAtlas is constructed by mining genomes using seq2ripp, a machine-learning tool for the prediction of ribosomally synthesized and post-translationally modified peptides (RiPPs). In HypoRiPPAtlas, we identify RiPPs in microbes and plants. HypoRiPPAtlas could be extended to other natural product classes in the future by implementing corresponding biosynthetic logic. This study paves the way for large-scale explorations of biosynthetic pathways and chemical structures of microbial and plant RiPP classes

Modern Computing Techniques for Solving Genomic Problems

With the advent of high-throughput genomics, biological big data brings challenges to scientists in handling, analyzing, processing and mining this massive data. In this new interdisciplinary field, diverse theories, methods, tools and knowledge are utilized to solve a wide variety of problems. As an exploration, this dissertation project is designed to combine concepts and principles in multiple areas, including signal processing, information-coding theory, artificial intelligence and cloud computing, in order to solve the following problems in computational biology: (1) comparative gene structure detection, (2) DNA sequence annotation, (3) investigation of CpG islands (CGIs) for epigenetic studies. Briefly, in problem #1, sequences are transformed into signal series or binary codes. Similar to the speech/voice recognition, similarity is calculated between two signal series and subsequently signals are stitched/matched into a temporal sequence. In the nature of binary operation, all calculations/steps can be performed in an efficient and accurate way. Improving performance in terms of accuracy and specificity is the key for a comparative method. In problem #2, DNA sequences are encoded and transformed into numeric representations for deep learning methods. Encoding schemes greatly influence the performance of deep learning algorithms. Finding the best encoding scheme for a particular application of deep learning is significant. Three applications (detection of protein-coding splicing sites, detection of lincRNA splicing sites and improvement of comparative gene structure identification) are used to show the computing power of deep neural networks. In problem #3, CpG sites are assigned certain energy and a Gaussian filter is applied to detection of CpG islands. By using the CpG box and Markov model, we investigate the properties of CGIs and redefine the CGIs using the emerging epigenetic data. In summary, these three problems and their solutions are not isolated; they are linked to modern techniques in such diverse areas as signal processing, information-coding theory, artificial intelligence and cloud computing. These novel methods are expected to improve the efficiency and accuracy of computational tools and bridge the gap between biology and scientific computing

Statistical Methods for the Analysis of Epigenomic Data

Epigenomics, the study of the human genome and its interactions with proteins and other cellular elements, has become of significant interest in the past decade. Several landmark studies have shown that these interactions regulate essential cellular processes (gene transcription, gene silencing, etc.) and are associated with multiple complex disorders such as cancer incidence, cardiovascular disease, etc. Chromatin immunoprecipitation followed by massively-parallel sequencing (ChIP-seq) is one of several techniques used to (1) detect protein-DNA interaction sites, (2) classify differential epigenomic activity across conditions, and (3) characterize subpopulations of single-cells in heterogeneous samples. In this dissertation, we present statistical methods to tackle problems (1-3) in contexts where protein-DNA interaction sites expand across broad genomic domains. First, we present a statistical model that integrates data from multiple epigenomic assays and detects protein-DNA interaction sites in consensus across multiple replicates. We introduce a class of zero-inflated mixed-effects hidden Markov models (HMMs) to account for the excess of observed zeros, the latent sample-specific differences, and the local dependency of sequencing read counts. By integrating multiple samples into a statistical model tailored for broad epigenomic marks, our model shows high sensitivity and specificity in both simulated and real datasets. Second, we present an efficient framework for the detection and classification of regions exhibiting differential epigenomic activity in multi-sample multi-condition designs. The presented model utilizes a finite mixture model embedded into a HMM to classify patterns of broad and short differential epigenomic activity across conditions. We utilize a fast rejection-controlled EM algorithm that makes our implementation among the fastest algorithms available, while showing improvement in performance in data from broad epigenomic marks. Lastly, we analyze data from single-cell ChIP-seq assays and present a statistical model that allows the simultaneous clustering and characterization of single-cell subpopulations. The presented framework is robust for the often observed sparsity in single-cell epigenomic data and accounts for the local dependency of counts. We introduce an initialization scheme for the initialization of the EM algorithm as well as the identification of the number of single-cell subpopulations in the data, a common task in current single-cell epigenomic algorithms.Doctor of Philosoph

Hidden Markov Models

Hidden Markov Models (HMMs), although known for decades, have made a big career nowadays and are still in state of development. This book presents theoretical issues and a variety of HMMs applications in speech recognition and synthesis, medicine, neurosciences, computational biology, bioinformatics, seismology, environment protection and engineering. I hope that the reader will find this book useful and helpful for their own research

On Computable Protein Functions

Proteins are biological machines that perform the majority of functions necessary for life. Nature has evolved many different proteins, each of which perform a subset of an organism’s functional repertoire. One aim of biology is to solve the sparse high dimensional problem of annotating all proteins with their true functions. Experimental characterisation remains the gold standard for assigning function, but is a major bottleneck due to resource scarcity. In this thesis, we develop a variety of computational methods to predict protein function, reduce the functional search space for proteins, and guide the design of experimental studies. Our methods take two distinct approaches: protein-centric methods that predict the functions of a given protein, and function-centric methods that predict which proteins perform a given function. We applied our methods to help solve a number of open problems in biology. First, we identified new proteins involved in the progression of Alzheimer’s disease using proteomics data of brains from a fly model of the disease. Second, we predicted novel plastic hydrolase enzymes in a large data set of 1.1 billion protein sequences from metagenomes. Finally, we optimised a neural network method that extracts a small number of informative features from protein networks, which we used to predict functions of fission yeast proteins