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"A biological system is a complex network of heterogeneous molecular entities and their interactions contributing to various biological characteristics of the system. Although the biological networks not only provide an elegant theoretical framework but also offer a mathematical foundation to analyze, understand, and learn from complex biological systems, the reconstruction of biological networks is an important and unsolved problem. Current biological networks are noisy, sparse and incomplete, limiting the ability to create a holistic view of the biological reconstructions and thus fail to provide a system-level understanding of the biological phenomena. Experimental identification of missing interactions is both time-consuming and expensive. Recent advancements in high-throughput data generation and significant improvement in computational power have led to novel computational methods to predict missing interactions. However, these methods still suffer from several unresolved challenges. It is challenging to extract information about interactions and incorporate that information into the computational model. Furthermore, the biological data are not only heterogeneous but also high-dimensional and sparse presenting the difficulty of modeling from indirect measurements. The heterogeneous nature and sparsity of biological data pose significant challenges to the design of deep neural network structures which use essentially either empirical or heuristic model selection methods. These unscalable methods heavily rely on expertise and experimentation, which is a time-consuming and error-prone process and are prone to overfitting. Furthermore, the complex deep networks tend to be poorly calibrated with high confidence on incorrect predictions. In this dissertation, we describe novel algorithms that address these challenges. In Part I, we design novel neural network structures to learn representation for biological entities and further expand the model to integrate heterogeneous biological data for biological interaction prediction. In part II, we develop a novel Bayesian model selection method to infer the most plausible network structures warranted by data. We demonstrate that our methods achieve the state-of-the-art performance on the tasks across various domains including interaction prediction. Experimental studies on various interaction networks show that our method makes accurate and calibrated predictions. Our novel probabilistic model selection approach enables the network structures to dynamically evolve to accommodate incrementally available data. In conclusion, we discuss the limitations and future directions for proposed works."--Abstract.
Probabilistic modeling, as known as probabilistic machine learning, provides a principled framework for learning from data, with the key advantage of offering rigorous solutions for uncertainty quantification. In the era of big and complex data, there is an urgent need for new inference methods in probabilistic modeling to extract information from data effectively and efficiently. This thesis shows how to do theoretically-guaranteed scalable and reliable inference for modern machine learning. Considering both theory and practice, we provide foundational understanding of scalable and reliable inference methods and practical algorithms of new inference methods, as well as extensive empirical evaluation on common machine learning and deep learning tasks. Classical inference algorithms, such as Markov chain Monte Carlo, have enabled probabilistic modeling to achieve gold standard results on many machine learning tasks. However, these algorithms are rarely used in modern machine learning due to the difficulty of scaling up to large datasets. Existing work suggests that there is an inherent trade-off between scalability and reliability, forcing practitioners to choose between expensive exact methods and biased scalable ones. To overcome the current trade-off, we introduce general and theoretically grounded frameworks to enable fast and asymptotically correct inference, with applications to Gibbs sampling, Metropolis-Hastings and Langevin dynamics. Deep neural networks (DNNs) have achieved impressive success on a variety of learning problems in recent years. However, DNNs have been criticized for being unable to estimate uncertainty accurately. Probabilistic modeling provides a principled alternative that can mitigate this issue; they are able to account for model uncertainty and achieve automatic complexity control. In this thesis, we analyze the key challenges of probabilistic inference in deep learning, and present novel approaches for fast posterior inference of neural network weights.
This is the first comprehensive treatment of probabilistic Boolean networks (PBNs), an important model class for studying genetic regulatory networks. This book covers basic model properties, including the relationships between network structure and dynamics, steady-state analysis, and relationships to other model classes." "Researchers in mathematics, computer science, and engineering are exposed to important applications in systems biology and presented with ample opportunities for developing new approaches and methods. The book is also appropriate for advanced undergraduates, graduate students, and scientists working in the fields of computational biology, genomic signal processing, control and systems theory, and computer science.
Graph-structured data is ubiquitous throughout the natural and social sciences, from telecommunication networks to quantum chemistry. Building relational inductive biases into deep learning architectures is crucial for creating systems that can learn, reason, and generalize from this kind of data. Recent years have seen a surge in research on graph representation learning, including techniques for deep graph embeddings, generalizations of convolutional neural networks to graph-structured data, and neural message-passing approaches inspired by belief propagation. These advances in graph representation learning have led to new state-of-the-art results in numerous domains, including chemical synthesis, 3D vision, recommender systems, question answering, and social network analysis. This book provides a synthesis and overview of graph representation learning. It begins with a discussion of the goals of graph representation learning as well as key methodological foundations in graph theory and network analysis. Following this, the book introduces and reviews methods for learning node embeddings, including random-walk-based methods and applications to knowledge graphs. It then provides a technical synthesis and introduction to the highly successful graph neural network (GNN) formalism, which has become a dominant and fast-growing paradigm for deep learning with graph data. The book concludes with a synthesis of recent advancements in deep generative models for graphs—a nascent but quickly growing subset of graph representation learning.
This book presents an exciting new synthesis of directed and undirected, discrete and continuous graphical models. Combining elements of Bayesian networks and Markov random fields, the newly introduced hybrid random fields are an interesting approach to get the best of both these worlds, with an added promise of modularity and scalability. The authors have written an enjoyable book---rigorous in the treatment of the mathematical background, but also enlivened by interesting and original historical and philosophical perspectives. -- Manfred Jaeger, Aalborg Universitet The book not only marks an effective direction of investigation with significant experimental advances, but it is also---and perhaps primarily---a guide for the reader through an original trip in the space of probabilistic modeling. While digesting the book, one is enriched with a very open view of the field, with full of stimulating connections. [...] Everyone specifically interested in Bayesian networks and Markov random fields should not miss it. -- Marco Gori, Università degli Studi di Siena Graphical models are sometimes regarded---incorrectly---as an impractical approach to machine learning, assuming that they only work well for low-dimensional applications and discrete-valued domains. While guiding the reader through the major achievements of this research area in a technically detailed yet accessible way, the book is concerned with the presentation and thorough (mathematical and experimental) investigation of a novel paradigm for probabilistic graphical modeling, the hybrid random field. This model subsumes and extends both Bayesian networks and Markov random fields. Moreover, it comes with well-defined learning algorithms, both for discrete and continuous-valued domains, which fit the needs of real-world applications involving large-scale, high-dimensional data.
Written for researchers and students in statistics, machine learning, and the biological sciences. This book provides a self-contained introduction to the methodology of Bayesian networks. It offers both elementary tutorials as well as more advanced applications and case studies.
How can we automate and scale up the processes of learning accurate probabilistic models of complex data and obtaining principled solutions to probabilistic inference and analysis queries? This thesis presents efficient techniques for addressing these fundamental challenges grounded in probabilistic programming, that is, by representing probabilistic models as computer programs in specialized programming languages. First, I introduce scalable methods for real-time synthesis of probabilistic programs in domain-specific data modeling languages, by performing Bayesian structure learning over hierarchies of symbolic program representations. These methods let us automatically discover accurate and interpretable models in a variety of settings, including cross-sectional data, relational data, and univariate and multivariate time series data; as well as models whose structures are generated by probabilistic context-free grammars. Second, I describe SPPL, a probabilistic programming language that integrates knowledge compilation and symbolic analysis to compute sound exact answers to many Bayesian inference queries about both hand-written and machine-synthesized probabilistic programs. Third, I present fast algorithms for analyzing statistical properties of probabilistic programs in cases where exact inference is intractable. These algorithms operate entirely through black-box computational interfaces to probabilistic programs and solve challenging problems such as estimating bounds on the information flow between arbitrary sets of program variables and testing the convergence of sampling-based algorithms for approximate posterior inference. A large collection of empirical evaluations establish that, taken together, these techniques can outperform multiple state-of-the-art systems across diverse real-world data science problems, which include adapting to extreme novelty in streaming time series data; imputing and forecasting sparse multivariate flu rates; discovering commonsense clusters in relational and temporal macroeconomic data; generating synthetic satellite records with realistic orbital physics; finding information-theoretically optimal medical tests for liver disease and diabetes; and verifying the fairness of machine learning classifiers.
Bayesian Networks in R with Applications in Systems Biology is unique as it introduces the reader to the essential concepts in Bayesian network modeling and inference in conjunction with examples in the open-source statistical environment R. The level of sophistication is also gradually increased across the chapters with exercises and solutions for enhanced understanding for hands-on experimentation of the theory and concepts. The application focuses on systems biology with emphasis on modeling pathways and signaling mechanisms from high-throughput molecular data. Bayesian networks have proven to be especially useful abstractions in this regard. Their usefulness is especially exemplified by their ability to discover new associations in addition to validating known ones across the molecules of interest. It is also expected that the prevalence of publicly available high-throughput biological data sets may encourage the audience to explore investigating novel paradigms using the approaches presented in the book.
Biological Network Analysis: Trends, Approaches, Graph Theory, and Algorithms considers three major biological networks, including Gene Regulatory Networks (GRN), Protein-Protein Interaction Networks (PPIN), and Human Brain Connectomes. The book's authors discuss various graph theoretic and data analytics approaches used to analyze these networks with respect to available tools, technologies, standards, algorithms and databases for generating, representing and analyzing graphical data. As a wide variety of algorithms have been developed to analyze and compare networks, this book is a timely resource. Presents recent advances in biological network analysis, combining Graph Theory, Graph Analysis, and various network models Discusses three major biological networks, including Gene Regulatory Networks (GRN), Protein-Protein Interaction Networks (PPIN) and Human Brain Connectomes Includes a discussion of various graph theoretic and data analytics approaches