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This dissertation focuses on Markov logic networks (MLNs), a knowledge representation tool that elegantly unifies first-order logic (FOL) and probabilistic graphical models (PGMs). FOL enables compact representation while probability allows the user to model uncertainty in a principled manner. Unfortunately, although the representation is compact, inference in MLNs is quite challenging, as PGMs generated from MLNs typically have millions of random variables and features. As a result, even linear time algorithms are computationally infeasible. Recently, there has been burgeoning interest in developing "lifted" algorithms to scale up inference in MLNs. These algorithms exploit symmetries in the PGM associated with an MLN, detecting them in many cases by analyzing the first-order structure without constructing the PGM, and thus have time and space requirements that are sub-linear when symmetries are present and can be detected. However, previous research has focused primarily on lifted marginal inference while algorithms for optimization tasks such as maximum-a-posteriori (MAP) inference are far less advanced. This dissertation fills this void, by developing next generation algorithms for MAP inference. This dissertation presents several novel, scalable algorithms for MAP inference in MLNs. The new algorithms exploit both exact and approximate symmetries, and experimentally are orders of magnitude faster than existing algorithms on a wide variety of real-world MLNs. Specifically, this dissertation makes the following contributions: A key issue with existing lifted approaches is that one has to make substantial modifications to highly engineered, well-researched inference algorithms and software, developed in the PGM community over the last few decades. We address this problem by developing the ``lifting as pre-processing'' paradigm, where we show that lifted inference can be reduced to a series of pre-processing operations that compresses a large PGM to a much smaller PGM. Another problem with current lifted algorithms is that they only exploit exact symmetries. In many real-world problems, very few exact symmetries are present while approximate symmetries are abundant. We address this limitation by developing a general framework for exploiting approximate symmetries that elegantly trades solution quality with time and space complexity. Inference and weight learning algorithms for MLNs need to solve complex combinatorial counting problems. We propose a novel approach for formulating and efficiently solving these problems. We scale-up two approximate inference algorithms, Gibbs sampling and MaxWalkSAT and three weight learning algorithms, Contrastive Divergence, Voted Perceptron, and, Pseudo-log-likelihood learning. We propose novel approximate inference algorithms for accurate, scalable inference in PGMs having shared sub-structures but no shared parameters. We demonstrate both theoretically and experimentally that they outperform state-of-the-art approaches.
Determinantal Point Processes (DPPs) are probability distributions on subsets of a collection of points that tend to generate diverse configurations of points. This feature makes them suitable as a probabilistic model of diversity. Recently this idea has been exploited extensively in subset selection problems, where given a large set of items such as images, documents, or any other form of collected data, the goal is to select a small, yet diverse and representative subset. However, with the rapid growth of datasets size, in order to utilize DPPs for real-world tasks, we need to design new primitives and inference algorithms that can be run efficiently in these settings. This thesis focuses on two inference tasks for DPPs: In the first part, we study sampling algorithms for DPPs and offer efficient MCMC based algorithms which can be applied in both discrete and continuous domains. In the second part, we consider the problem of determinant maximization which is equivalent to the Maximum a Posteriori encoding for DPPs, and present scalable algorithms in a distributed setting which assumes the input data are arbitrarily split among numerous nodes.
Probabilistic topic models have proven to be an extremely versatile class of mixed-membership models for discovering the thematic structure of text collections. There are many possible applications, covering a broad range of areas of study: technology, natural science, social science and the humanities. In this thesis, a new efficient parallel Markov Chain Monte Carlo inference algorithm is proposed for Bayesian inference in large topic models. The proposed methods scale well with the corpus size and can be used for other probabilistic topic models and other natural language processing applications. The proposed methods are fast, efficient, scalable, and will converge to the true posterior distribution. In addition, in this thesis a supervised topic model for high-dimensional text classification is also proposed, with emphasis on interpretable document prediction using the horseshoe shrinkage prior in supervised topic models. Finally, we develop a model and inference algorithm that can model agenda and framing of political speeches over time with a priori defined topics. We apply the approach to analyze the evolution of immigration discourse in the Swedish parliament by combining theory from political science and communication science with a probabilistic topic model. Probabilistiska ämnesmodeller (topic models) är en mångsidig klass av modeller för att estimera ämnessammansättningar i större corpusar. Applikationer finns i ett flertal vetenskapsområden som teknik, naturvetenskap, samhällsvetenskap och humaniora. I denna avhandling föreslås nya effektiva och parallella Markov Chain Monte Carlo algoritmer för Bayesianska ämnesmodeller. De föreslagna metoderna skalar väl med storleken på corpuset och kan användas för flera olika ämnesmodeller och liknande modeller inom språkteknologi. De föreslagna metoderna är snabba, effektiva, skalbara och konvergerar till den sanna posteriorfördelningen. Dessutom föreslås en ämnesmodell för högdimensionell textklassificering, med tonvikt på tolkningsbar dokumentklassificering genom att använda en kraftigt regulariserande priorifördelningar. Slutligen utvecklas en ämnesmodell för att analyzera "agenda" och "framing" för ett förutbestämt ämne. Med denna metod analyserar vi invandringsdiskursen i Sveriges Riksdag över tid, genom att kombinera teori från statsvetenskap, kommunikationsvetenskap och probabilistiska ämnesmodeller.
In this dissertation, we focus on Markov logic networks (MLNs), an advanced modeling language that combines first-order logic, the cornerstone of traditional Artificial Intelligence (AI), with probabilistic graphical models, the cornerstone of modern AI. MLNs are routinely used in a wide variety of application domains including natural language processing and computer vision, and are preferred over propositional representations because unlike the latter they yield compact, interpretable models that can be easily modified and tuned. Unfortunately, even though the MLN representation is compact and efficient, inference in them is notoriously difficult and despite great progress, several inference tasks in complex real-world MLNs are beyond the reach of existing technology. In this dissertation, we greatly advance the state-of-the-art in MLN inference, enabling it to solve much harder and larger problems than existing approaches. We develop several domain-independent principles, techniques and algorithms for fast, scalable and accurate inference that fully exploit both probabilistic and logical structure. This dissertation makes the following five contributions. First, we propose two approaches that respectively address two fundamental problems with Gibbs sampling, a popular approximate inference algorithm: it does not converge in presence of determinism and it exhibits poor accuracy when the MLN contains a large number of strongly correlated variables. Second, we lift sampling-based approximate inference algorithms to the first-order level, enabling them to take full advantage of symmetries and relational structure in MLNs. Third, we develop novel approaches for exploiting approximate symmetries. These approaches help scale up inference to large, complex MLNs, which are not amenable to conventional lifting techniques that exploit only exact symmetries. Fourth, we propose a new, efficient algorithm for solving a major bottleneck in all inference algorithms for MLNs: counting the number of true groundings of each formula. We demonstrate empirically that our new counting approach yields orders of magnitude improvements in both the speed and quality of inference. Finally, we demonstrate the power and promise of our approaches on Biomedical event extraction, a challenging real-world information extraction task, on which our system achieved state-of-the-art results.
This book provides a straightforward look at the concepts, algorithms and advantages of Bayesian Deep Learning and Deep Generative Models. Starting from the model-based approach to Machine Learning, the authors motivate Probabilistic Graphical Models and show how Bayesian inference naturally lends itself to this framework. The authors present detailed explanations of the main modern algorithms on variational approximations for Bayesian inference in neural networks. Each algorithm of this selected set develops a distinct aspect of the theory. The book builds from the ground-up well-known deep generative models, such as Variational Autoencoder and subsequent theoretical developments. By also exposing the main issues of the algorithms together with different methods to mitigate such issues, the book supplies the necessary knowledge on generative models for the reader to handle a wide range of data types: sequential or not, continuous or not, labelled or not. The book is self-contained, promptly covering all necessary theory so that the reader does not have to search for additional information elsewhere. Offers a concise self-contained resource, covering the basic concepts to the algorithms for Bayesian Deep Learning; Presents Statistical Inference concepts, offering a set of elucidative examples, practical aspects, and pseudo-codes; Every chapter includes hands-on examples and exercises and a website features lecture slides, additional examples, and other support material.
Now in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors—all leaders in the statistics community—introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice. New to the Third Edition Four new chapters on nonparametric modeling Coverage of weakly informative priors and boundary-avoiding priors Updated discussion of cross-validation and predictive information criteria Improved convergence monitoring and effective sample size calculations for iterative simulation Presentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation New and revised software code The book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page.
Information theory and inference, taught together in this exciting textbook, lie at the heart of many important areas of modern technology - communication, signal processing, data mining, machine learning, pattern recognition, computational neuroscience, bioinformatics and cryptography. The book introduces theory in tandem with applications. Information theory is taught alongside practical communication systems such as arithmetic coding for data compression and sparse-graph codes for error-correction. Inference techniques, including message-passing algorithms, Monte Carlo methods and variational approximations, are developed alongside applications to clustering, convolutional codes, independent component analysis, and neural networks. Uniquely, the book covers state-of-the-art error-correcting codes, including low-density-parity-check codes, turbo codes, and digital fountain codes - the twenty-first-century standards for satellite communications, disk drives, and data broadcast. Richly illustrated, filled with worked examples and over 400 exercises, some with detailed solutions, the book is ideal for self-learning, and for undergraduate or graduate courses. It also provides an unparalleled entry point for professionals in areas as diverse as computational biology, financial engineering and machine learning.
Statistical Rethinking: A Bayesian Course with Examples in R and Stan builds readers’ knowledge of and confidence in statistical modeling. Reflecting the need for even minor programming in today’s model-based statistics, the book pushes readers to perform step-by-step calculations that are usually automated. This unique computational approach ensures that readers understand enough of the details to make reasonable choices and interpretations in their own modeling work. The text presents generalized linear multilevel models from a Bayesian perspective, relying on a simple logical interpretation of Bayesian probability and maximum entropy. It covers from the basics of regression to multilevel models. The author also discusses measurement error, missing data, and Gaussian process models for spatial and network autocorrelation. By using complete R code examples throughout, this book provides a practical foundation for performing statistical inference. Designed for both PhD students and seasoned professionals in the natural and social sciences, it prepares them for more advanced or specialized statistical modeling. Web Resource The book is accompanied by an R package (rethinking) that is available on the author’s website and GitHub. The two core functions (map and map2stan) of this package allow a variety of statistical models to be constructed from standard model formulas.
Recent advances in the area of lifted inference, which exploits the structure inherent in relational probabilistic models. Statistical relational AI (StaRAI) studies the integration of reasoning under uncertainty with reasoning about individuals and relations. The representations used are often called relational probabilistic models. Lifted inference is about how to exploit the structure inherent in relational probabilistic models, either in the way they are expressed or by extracting structure from observations. This book covers recent significant advances in the area of lifted inference, providing a unifying introduction to this very active field. After providing necessary background on probabilistic graphical models, relational probabilistic models, and learning inside these models, the book turns to lifted inference, first covering exact inference and then approximate inference. In addition, the book considers the theory of liftability and acting in relational domains, which allows the connection of learning and reasoning in relational domains.