The Statistical Physics Of Data Assimilation And Machine Learning

The theory of data assimilation and machine learning is introduced in an accessible manner for undergraduate and graduate students.

This book bridges the gap between advances in the communities of computer science and physics--namely machine learning and statistical physics. It contains diverse but relevant topics in statistical physics, complex systems, network theory, and machine learning. Examples of such topics are: predicting missing links, higher-order generative modeling of networks, inferring network structure by tracking the evolution and dynamics of digital traces, recommender systems, and diffusion processes. The book contains extended versions of high-quality submissions received at the workshop, Dynamics On and Of Complex Networks (doocn.org), together with new invited contributions. The chapters will benefit a diverse community of researchers. The book is suitable for graduate students, postdoctoral researchers and professors of various disciplines including sociology, physics, mathematics, and computer science.

Networks are ubiquitous in science and have become a focal point for discussion in everyday life. Formal statistical models for the analysis of network data have emerged as a major topic of interest in diverse areas of study, and most of these involve a form of graphical representation. Probability models on graphs date back to 1959. Along with empirical studies in social psychology and sociology from the 1960s, these early works generated an active network community and a substantial literature in the 1970s. This effort moved into the statistical literature in the late 1970s and 1980s, and the past decade has seen a burgeoning network literature in statistical physics and computer science. The growth of the World Wide Web and the emergence of online networking communities such as Facebook, MySpace, and LinkedIn, and a host of more specialized professional network communities has intensified interest in the study of networks and network data. Our goal in this review is to provide the reader with an entry point to this burgeoning literature. We begin with an overview of the historical development of statistical network modeling and then we introduce a number of examples that have been studied in the network literature. Our subsequent discussion focuses on a number of prominent static and dynamic network models and their interconnections. We emphasize formal model descriptions, and pay special attention to the interpretation of parameters and their estimation. We end with a description of some open problems and challenges for machine learning and statistics.

This graduate text covers a variety of mathematical and statistical tools for the analysis of big data coming from biology, medicine and economics. Neural networks, Markov chains, tools from statistical physics and wavelet analysis are used to develop efficient computational algorithms, which are then used for the processing of real-life data using Matlab.

This modern and self-contained book offers a clear and accessible introduction to the important topic of machine learning with neural networks. In addition to describing the mathematical principles of the topic, and its historical evolution, strong connections are drawn with underlying methods from statistical physics and current applications within science and engineering. Closely based around a well-established undergraduate course, this pedagogical text provides a solid understanding of the key aspects of modern machine learning with artificial neural networks, for students in physics, mathematics, and engineering. Numerous exercises expand and reinforce key concepts within the book and allow students to hone their programming skills. Frequent references to current research develop a detailed perspective on the state-of-the-art in machine learning research.

Focuses on mathematical understanding Presentation is self-contained, accessible, and comprehensive Full color throughout Extensive list of exercises and worked-out examples Many concrete algorithms with actual code

The understanding of complex systems is a key element to predict and control the system’s dynamics. To gain deeper insights into the underlying actions of complex systems today, more and more data of diverse types are analyzed that mirror the systems dynamics, whereas system models are still hard to derive. Data assimilation merges both data and model to an optimal description of complex systems’ dynamics. The present eBook brings together both recent theoretical work in data assimilation and control and demonstrates applications in diverse research fields.

Informatics and Machine Learning Discover a thorough exploration of how to use computational, algorithmic, statistical, and informatics methods to analyze digital data Informatics and Machine Learning: From Martingales to Metaheuristics delivers an interdisciplinary presentation on how analyze any data captured in digital form. The book describes how readers can conduct analyses of text, general sequential data, experimental observations over time, stock market and econometric histories, or symbolic data, like genomes. It contains large amounts of sample code to demonstrate the concepts contained within and assist with various levels of project work. The book offers a complete presentation of the mathematical underpinnings of a wide variety of forms of data analysis and provides extensive examples of programming implementations. It is based on two decades worth of the distinguished author’s teaching and industry experience. A thorough introduction to probabilistic reasoning and bioinformatics, including Python shell scripting to obtain data counts, frequencies, probabilities, and anomalous statistics, or use with Bayes’ rule An exploration of information entropy and statistical measures, including Shannon entropy, relative entropy, maximum entropy (maxent), and mutual information A practical discussion of ad hoc, ab initio, and bootstrap signal acquisition methods, with examples from genome analytics and signal analytics Perfect for undergraduate and graduate students in machine learning and data analytics programs, Informatics and Machine Learning: From Martingales to Metaheuristics will also earn a place in the libraries of mathematicians, engineers, computer scientists, and life scientists with an interest in those subjects.