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This thesis discusses novel statistical methods for analyzing high-dimensional multimodal data. Part one discusses three methods for multimodal data learning. First, we propose a model-based probabilistic approach for correlation and canonical correlation estimation for two sparse count datasets motivated by integer-valued data from next-generation sequencing platforms. Second, in many scientific problems such as video surveillance, modern genomics, and finance, data are often collected from diverse domains across time that exhibits time-dependent heterogeneous properties. We propose a generative model based on variational autoencoder and recurrent neural network to infer the latent dynamics for multi-view longitudinal data. This method allows us to identify the disentangled latent embeddings across multiple modalities while accounting for the time factor to achieve interpretable results. Third, we propose a deep interpretable variational canonical correlation analysis model for multi-view learning. This model is designed to disentangle both the shared and view-specific variations for multi-view data and achieve model interpretability. For all the methods, simulated and real experiments show our algorithms' advantages across domains. Part two discusses two methods for multiple hypothesis testing. First, we propose incorporating the feature hierarchy in a probabilistic black-box model to control FDR for two-group multiple hypothesis testing problems. The deep learning architecture enables efficient optimization and gracefully handles high-dimensional hypothesis features. The extensive simulation studies on synthetic and real datasets demonstrate that our algorithm yields more discoveries while controlling the FDR than state-of-the-art methods. Further, we propose a Bayesian differential analysis framework for multiple group problems. The simulation studies demonstrate that this model can recover the truth from learning the data very well. We conclude the thesis with discussions and future works.
Multi-source data refers to data that are collected from multiple sources or modalities. With the increasing availability of digital data, multi-source data has been applied to a wide range of applications, including sentiment analysis, object recognition, and recommendation systems. For example, in sentiment analysis, multi-source data has been used to combine text, images, and audio to improve the accuracy of sentiment classification. In recommendation systems, multi-source data has been used to combine data from different sources, such as text, images, and audio, to improve the quality of recommendations. The integration of these diverse and heterogeneous sources of data can provide a more comprehensive understanding of a particular phenomenon or problem. However, there are many challenges for learning multi-source data, such as dealing with heterogeneous data and developing interpretable models. To address these challenges, a number of statistical and machine learning methods have been developed, including multi-view learning and transfer learning. Multi-view learning is a technique that involves the analysis of data from multiple sources or views to learn a common representation of the data. Transfer learning is a machine learning technique that enables the transfer of knowledge from one domain or task to another. This dissertation develops new methods on multi-view learning and transfer learning. Chapter 3 presents a weighted multi-view NMF algorithm, termed as WM- NMF, to conduct integrative clustering of multi-view heterogeneous or corrupted data. We improve the existing multi-view NMF algorithms and propose to perform multi-view clustering by quantifying each view's content through learning both the view-specific and reconstruction weights. Our proposed algorithm can enlarge the positive effects and alleviate the adverse effects of the important and unnecessary views, respectively. We further demonstrate the competing performance of WM- NMF with regard to clustering performance. Using several datasets, we show that our algorithm significantly outperforms the existing multi-view algorithms in terms of six evaluation metrics. In Chapters 4 and 5, we propose a novel, interpretable, one-step, and unified framework for transfer learning. We first apply it to the high-dimensional linear regression in Chapter 4 and extend it to the generalized linear models in Chapter 5. More specifically, we propose a novel unified transfer learning model by re-defining the design matrix and the response vector in the context of the high-dimensional statistical models. To the best of our knowledge, this is the first work on unified transfer learning. The theoretical results show that it attains tighter upper bounds of the estimation errors than Lasso using the target data only, assuming the target data and source data are sufficiently close to some extent. We also prove that our bound is better than the existing methods, including a tighter minimax rate and a wider range of values for the transferring level. Detecting the transferable data, including the transferable source data and the transferable variables, is a major task in transfer learning. Our unified model is able to automatically identify the transferable variables due to its nature. We develop a hypothesis testing method and a data-driven method for source detection in Chapter 4 and Chapter 5, respectively. To the best of our knowledge, this is the first work for identifying the transferable variables by the model's nature and the first work to incorporate statistical inference in transfer 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.
Abstract: "An important problem in statistical machine learning is how to effectively model the predictions of multiple related tasks, which is known as multi-task learning. Different from single-task learning where tasks are learned separately, multi-task learning aims to jointly model those tasks. The main benefit of multi-task learning is that it can more effectively use training resources from all tasks and achieve better generalization performance when tasks are related. To be more specific, successfully addressing multi-task learning can not only allay the data paucity problem given many tasks, but also generalize to future tasks by transferring knowledge learned from existing tasks. Multiple tasks naturally exist in many applications, such as text classification, email anti-spam filtering, image classification, etc. We present a novel probabilistic framework for multi-task learning where task relatedness is modeled using a shared structure through latent variables. Within such a framework, we study a series of important multi-task learning scenarios and propose suitable models accordingly, and show that the flexibility of the framework is achieved by allowing different assumptions about latent variables and the shared structure. In particular, we present sparsity models which are parsimonious and suitable for high-dimensional tasks; we propose the l1 o l[subscript p] regularization method which is suitable for joint feature selection; we propose to use mixture models as the solution of the clusters of tasks scenario; we also extend our framework to unsupervised learning and show its connection to existing topic models. Furthermore, model selection techniques for multi-task learning are investigated since they play important roles in choosing the best joint model and generalizing to future tasks. Experiments are conducted to support our methods using both simulated datasets and real datasets from text classification, anti-spam filtering, handwritten letter recognition and collaborative filtering."
“IAS has been held every two years since 1986 providing venue for the latest accomplishments and innovations in advanced intelligent autonomous systems. New technologies and application domains continuously pose new challenges to be overcome in order to apply intelligent autonomous systems in a reliable and user-independent way in areas ranging from industrial applications to professional service and household domains. The present book contains the papers presented at the 17th International Conference on Intelligent Autonomous Systems (IAS-17), which was held from June 13–16, 2022, in Zagreb, Croatia. In our view, 62 papers, authored by 196 authors from 19 countries, are a testimony to the appeal of the conference considering travel restrictions imposed by the COVID-19 pandemic. Our special thanks go to the authors and the reviewers for their effort—the results of their joint work are visible in this book. We look forward to seeing you at IAS-18 in 2023 in Suwon, South Korea!”
Machine learning allows computers to learn and discern patterns without actually being programmed. When Statistical techniques and machine learning are combined together they are a powerful tool for analysing various kinds of data in many computer science/engineering areas including, image processing, speech processing, natural language processing, robot control, as well as in fundamental sciences such as biology, medicine, astronomy, physics, and materials. Introduction to Statistical Machine Learning provides a general introduction to machine learning that covers a wide range of topics concisely and will help you bridge the gap between theory and practice. Part I discusses the fundamental concepts of statistics and probability that are used in describing machine learning algorithms. Part II and Part III explain the two major approaches of machine learning techniques; generative methods and discriminative methods. While Part III provides an in-depth look at advanced topics that play essential roles in making machine learning algorithms more useful in practice. The accompanying MATLAB/Octave programs provide you with the necessary practical skills needed to accomplish a wide range of data analysis tasks. Provides the necessary background material to understand machine learning such as statistics, probability, linear algebra, and calculus Complete coverage of the generative approach to statistical pattern recognition and the discriminative approach to statistical machine learning Includes MATLAB/Octave programs so that readers can test the algorithms numerically and acquire both mathematical and practical skills in a wide range of data analysis tasks Discusses a wide range of applications in machine learning and statistics and provides examples drawn from image processing, speech processing, natural language processing, robot control, as well as biology, medicine, astronomy, physics, and materials
An advanced book for researchers and graduate students working in machine learning and statistics who want to learn about deep learning, Bayesian inference, generative models, and decision making under uncertainty. An advanced counterpart to Probabilistic Machine Learning: An Introduction, this high-level textbook provides researchers and graduate students detailed coverage of cutting-edge topics in machine learning, including deep generative modeling, graphical models, Bayesian inference, reinforcement learning, and causality. This volume puts deep learning into a larger statistical context and unifies approaches based on deep learning with ones based on probabilistic modeling and inference. With contributions from top scientists and domain experts from places such as Google, DeepMind, Amazon, Purdue University, NYU, and the University of Washington, this rigorous book is essential to understanding the vital issues in machine learning. Covers generation of high dimensional outputs, such as images, text, and graphs Discusses methods for discovering insights about data, based on latent variable models Considers training and testing under different distributions Explores how to use probabilistic models and inference for causal inference and decision making Features online Python code accompaniment
The recent rapid growth in the variety and complexity of new machine learning architectures requires the development of improved methods for designing, analyzing, evaluating, and communicating machine learning technologies. Statistical Machine Learning: A Unified Framework provides students, engineers, and scientists with tools from mathematical statistics and nonlinear optimization theory to become experts in the field of machine learning. In particular, the material in this text directly supports the mathematical analysis and design of old, new, and not-yet-invented nonlinear high-dimensional machine learning algorithms. Features: Unified empirical risk minimization framework supports rigorous mathematical analyses of widely used supervised, unsupervised, and reinforcement machine learning algorithms Matrix calculus methods for supporting machine learning analysis and design applications Explicit conditions for ensuring convergence of adaptive, batch, minibatch, MCEM, and MCMC learning algorithms that minimize both unimodal and multimodal objective functions Explicit conditions for characterizing asymptotic properties of M-estimators and model selection criteria such as AIC and BIC in the presence of possible model misspecification This advanced text is suitable for graduate students or highly motivated undergraduate students in statistics, computer science, electrical engineering, and applied mathematics. The text is self-contained and only assumes knowledge of lower-division linear algebra and upper-division probability theory. Students, professional engineers, and multidisciplinary scientists possessing these minimal prerequisites will find this text challenging yet accessible. About the Author: Richard M. Golden (Ph.D., M.S.E.E., B.S.E.E.) is Professor of Cognitive Science and Participating Faculty Member in Electrical Engineering at the University of Texas at Dallas. Dr. Golden has published articles and given talks at scientific conferences on a wide range of topics in the fields of both statistics and machine learning over the past three decades. His long-term research interests include identifying conditions for the convergence of deterministic and stochastic machine learning algorithms and investigating estimation and inference in the presence of possibly misspecified probability models.
The aim of this book is to discuss the fundamental ideas which lie behind the statistical theory of learning and generalization. It considers learning as a general problem of function estimation based on empirical data. Omitting proofs and technical details, the author concentrates on discussing the main results of learning theory and their connections to fundamental problems in statistics. This second edition contains three new chapters devoted to further development of the learning theory and SVM techniques. Written in a readable and concise style, the book is intended for statisticians, mathematicians, physicists, and computer scientists.