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Statistical Consistency of Structural Learning in Networks and graphical models

Statistical Consistency of Structural Learning in Networks a...

引用

作者： Lou, Xingmei University of California Davis

学位级别：Ph.D., Doctor of Philosophy

This dissertation aims to address the statistical consistency for two classical structural learning problems, one is community detection in networks, and the other one is structural learning in probabilistic graphical models. The methods studied in this dissertation are straightforward and widely used. However, their statistical consistency has not been fully revealed, especially under more sophisticated conditions that emerge in modern data analysis. Chapter 2 discusses my joint work with Professor Xiaodong Li and Lihua Lei. We study the hierarchy of communities in real-world networks under a generic stochastic block model, in which the connection probabilities are structured in a binary tree. Under such model, we prove the strong consistency of a standard recursive bi-partitioning algorithm under a wide range of model parameters, which include sparse networks with node degrees as small as O(logn). In addition, unlike most of existing work, our theory covers multi-scale networks where the connection probabilities may differ by orders of magnitude, which comprise an important class of models that are practically relevant but technically challenging to deal with. Finally we demonstrate the performance of our algorithm on synthetic data and real-world examples. Chapter 3 discusses my work supervised by Professor Xiaodong Li and Professor Yu Hu. In this work, we are interested in the problem of learning the directed acyclic graph (DAG) when data are generated from a linear structural equation model (SEM) and the causal structure can be characterized by a polytree. Under the Gaussian polytree models, we study sufficient and necessary conditions on the sample sizes for the well-known Chow-Liu algorithm to exactly recover both the skeleton and the equivalence class of the polytree, which is uniquely represented by a CPDAG. We also consider extensions to the sub-Gaussian case, and then study the estimation of the inverse correlation matrix under such models. Our theoretica

关键词： Statistical consistency Community detection Structural learning probabilistic graphical models

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Building Practical Statistical Relational Learning Systems

Building Practical Statistical Relational Learning Systems

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作者： Augustine, Eriq University of California Santa Cruz

学位级别：Ph.D., Doctor of Philosophy

In our increasingly connected world, data comes from many different sources, in many different forms, and is noisy, complex, and structured. To confront modern data, we need to embrace the structure inherent in the data and in the predictions. Statistical relational learning (SRL) is a subfield of machine learning that provides an effective means of approaching this problem of structured prediction. SRL frameworks use weighted logical and arithmetic expressions to easily create probabilistic graphical models (PGMs) to jointly reason over interdependent data. However, despite being well suited for modern, interconnected data, SRL faces several challenges that keep it from becoming practical and widely used in the machine learning community. In this dissertation, I address four pillars of practicality for SRL systems: scalability, expressivity, model adaptability, and usability. My work in this dissertation uses and extends probabilistic Soft Logic (PSL), a state-of-the-art open-source SRL framework. Scalability in SRL systems is essential for using large datasets and complex models. Because of the complex nature of interconnected data, models can easily outgrow available memory spaces. To address scalability for SRL, I developed methods that more efficiently and intelligently instantiate PGMs from templates and data. I also developed fixed-memory inference methods that can perform inference on very large models without requiring a proportional amount of memory. Expressivity allows SRL systems to represent many different problems and data patterns. Because SRL uses logical and arithmetic expressions to represent structured dependencies, SRL frameworks need to be able to express more than just what is represented by feature vectors. To address expressivity for SRL, I created a system to incorporate neural models with structured SRL inference, and expanded the interpretation of PSL weight hyperparameters to include additional types of distributions. Model adaptability i

关键词： Machine learning probabilistic graphical models probabilistic programming Scalability Statistical relational learning Usability probabilistic Soft Logic

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Spectral Probablistic Modeling and Applications to Natural Language Processing

Spectral Probablistic Modeling and Applications to Natural L...

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作者： Ankur Parikh Carnegie Mellon University

学位级别：博士

probabilistic modeling with latent variables is a powerful paradigm that has led to key advances in many applications such natural language processing, text mining, and computational biology. Unfortunately, while introducing latent variables substantially increases representation power, learning and modeling can become considerably more complicated. Most existing solutions largely ignore non-identifiability issues in modeling and formulate learning as a nonconvex optimization problem, where convergence to the optimal solution is not guaranteed due to local minima. In this thesis, we propose to tackle these problems through the lens of linear/multi-linear algebra. Viewing la- tent variable models from this perspective allows us to approach key problems such as structure learning and parameter learning using tools such as matrix/tensor decompositions, inversion, and additive metrics. These new tools enable us to develop novel solutions to learning in latent variable models with theoretical and prac- tical advantages. For example, our spectral parameter learning methods for latent trees and junction trees are provably consistent, local-optima-free, and 1-2 orders of magnitude faster than EM for large sample sizes. In addition, we focus on applications in Natural Language Processing, using our insights to not only devise new algorithms, but also to propose new models. Our method for unsupervised parsing is the first algorithm that has both theoretical guarantees and is also practical, performing favorably to the CCM method of Klein and Manning. We also developed power low rank ensembles, a framework for language modeling that generalizes existing n-gram techniques to non-integer n. It consistently outperforms state-of-the-art Kneser Ney baselines and can train on billion-word datasets in a few hours.

关键词： probabilistic graphical models spectral methods kernels unsupervised parsing language modeling

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Distributed Learning, Prediction and Detection in probabilistic Graphs

Distributed Learning, Prediction and Detection in Probabilis...

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作者： Meng, Zhaoshi University of Michigan

学位级别：Ph.D., Doctor of Philosophy

Critical to high-dimensional statistical estimation is to exploit the structure in the data distribution. probabilistic graphical models provide an efficient framework for representing complex joint distributions of random variables through their conditional dependency graph, and can be adapted to many high-dimensional machine learning applications. This dissertation develops the probabilistic graphical modeling technique for three statistical estimation problems arising in real-world applications: distributed and parallel learning in networks, missing-value prediction in recommender systems, and emerging topic detection in text corpora. The common theme behind all proposed methods is a combination of parsimonious representation of uncertainties in the data, optimization surrogate that leads to computationally efficient algorithms, and fundamental limits of estimation performance in high dimension. More specifically, the dissertation makes the following theoretical contributions: (1) We propose a distributed and parallel framework for learning the parameters in Gaussian graphical models that is free of iterative global message passing. The proposed distributed estimator is shown to be asymptotically consistent, improve with increasing local neighborhood sizes, and have a high-dimensional error rate comparable to that of the centralized maximum likelihood estimator. (2) We present a family of latent variable Gaussian graphical models whose marginal precision matrix has a “low-rank plus sparse” structure. Under mild conditions, we analyze the high-dimensional parameter error bounds for learning this family of models using regularized maximum likelihood estimation. (3) We consider a hypothesis testing framework for detecting emerging topics in topic models, and propose a novel surrogate test statistic for the standard likelihood ratio. By leveraging the theory of empirical processes, we prove asymptotic consistency for the proposed test and provide guarantees of the de

关键词： Distributed learning Statistical estimation High-dimensional error rate Machine learning probabilistic graphical models Gaussian graphical models

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Learning Gene Networks Underlying Clinical Phenotypes Under SNP Perturbations From Genome-Wide Data

Learning Gene Networks Underlying Clinical Phenotypes Under ...

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作者： Calvin McCarter Carnegie Mellon University

学位级别：博士

Recent technologies are generating an abundance of genome sequence data and molecular and clinical phenotype data, providing an opportunity to understand the genetic architecture and molecular mechanisms underlying diseases. Previous ap- proaches have largely focused on the co-localization of single-nucleotide polymor- phisms (SNPs) associated with clinical and expression traits, each identified from genome-wide association studies and expression quantitative trait locus (eQTL) map- ping, and thus have provided only limited capabilities for uncovering the molecular mechanisms behind the SNPs influencing clinical phenotypes. Here we aim to ex- tract rich information on the functional role of trait-perturbing SNPs that goes far beyond this simple co-localization. We introduce a computational framework called PerturbNet for learning the gene network that modulates the influence of SNPs on phenotypes, using SNPs as naturally occurring perturbation of a biological system. PerturbNet uses a probabilistic graphical model to directly model both the cascade of perturbation from SNPs to the gene network to the phenotype network and the network at each layer of molecular and clinical phenotypes. PerturbNet learns the entire model by solving a single optimization problem with an extremely fast algo- rithm that can analyze human genome-wide data within a few hours. In our analysis of asthma data, for a locus that was previously implicated in asthma susceptibility but for which little is known about the molecular mechanism underlying the asso- ciation, PerturbNet revealed the gene network modules that mediate the influence of the SNP on asthma phenotypes. Many genes in this network module were well supported in the literature as asthma-related.

关键词： probabilistic graphical models sparse learning structure learning convex optimization genomics gene networks systems biology

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Learning Deep Generative models

Learning Deep Generative Models

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作者： Salakhutdinov, Ruslan University of Toronto

学位级别：doctor

Building intelligent systems that are capable of extracting high-level representations from high-dimensional sensory data lies at the core of solving many AI related tasks, including object recognition, speech perception, and language understanding. Theoretical and biological arguments strongly suggest that building such systems requires models with deep architectures that involve many layers of nonlinear processing. The aim of the thesis is to demonstrate that deep generative models that contain many layers of latent variables and millions of parameters can be learned efficiently, and that the learned high-level feature representations can be successfully applied in a wide spectrum of application domains, including visual object recognition, information retrieval, and classification and regression tasks. In addition, similar methods can be used for nonlinear dimensionality reduction

关键词： computer science probabilistic graphical models

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New Algorithms for Predicting Conformational Polymorphismand Inferring Direct Couplings for Side Chains of Proteins

New Algorithms for Predicting Conformational Polymorphismand...

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作者： Soltan Ghoraie, Laleh University of Waterloo

学位级别：doctor

Protein crystals populate diverse conformationalensembles. Despite much evidence that there is widespreadconformational polymorphism in protein side chains, most of thexray crystallography data are modelled by single conformations inthe Protein Data Bank. The ability to extract or to predict theseconformational polymorphisms is of crucial importance, as itfacilitates deeper understanding of protein dynamics andfunctionality. This dissertation describes a computationalstrategy capable of predicting side-chain polymorphisms. Theapplied approach extends a particular class of algorithms forside-chain prediction by modelling the side-chain dihedral anglesmore appropriately as continuous rather than discrete *** a new inferential technique known as particle beliefpropagation (PBP), we predict residue-speci c distributions thatencode information about side-chain polymorphisms. The predictedpolymorphisms are in relatively close agreement with results froma state-of-the-art approach based on x-ray crystallography *** approach characterizes the conformational polymorphisms ofside chains using electron density information, and hassuccessfully discovered previously unmodelled ***, it is known that coupled uctuations and concertedmotions of residues can reveal pathways of communication used forinformation propagation in a molecule and hence, can help inunderstanding the \allostery" phenomenon in proteins. In order tocharacterize the coupled motions, most existing methods inferstructural dependencies among a protein''s residues. However,recent studies have highlighted the role of coupled side-chain uctuations alone in the allosteric behaviour of proteins, incontrast to a common belief that the backbone motions play themain role in allostery. These studies and the aforementionedrecent discoveries about prevalent alternate side-chainconformations (conformational polymorphism) accentuate the need todevise new computational approaches that

关键词： structural bioinformatics protein structure protein function conformational polymorphism side chains allostery long-range information propagatation GLASSO probabilistic graphical models von-Mises distribution canonical correlation analysis kernel function

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A Bayesian Classifier based on Constraints of Ordering of Variables for Fraud Detection 4

A Bayesian Classifier based on Constraints of Ordering of Va...

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4th International Congress of Innovation and Trends in Engineering (CONIITI)

作者： Shiguihara-Juarez, Pedro Murrugarra-Llerena, Nils Univ Peruana Ciencias Aplicadas Dept Comp Sci Lima Peru Univ Pittsburgh Dept Comp Sci Pittsburgh PA 15260 USA

ISBN: (纸本)9781538681312

Fraud detection is important for financial institutions and the society. Supervised machine learning techniques were applied for fraud detection. However, mostly discriminative techniques were applied on these problems. probabilistic graphical models can also detect fraud, providing also a graphical representation of its reasoning scheme as a graph. We proposed a method to generate a probabilistic graphical model for fraud detection, using constraints related to the domain. We achieved 99.272% of accuracy and we outperformed other baselines techniques of probabilistic graphical models. We demonstrated that constraints are important to tackle complex problem such a fraud detection.

关键词： probabilistic graphical models Bayesian Networks Fraud Detection

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Designing Effective Multimodal Behaviors for Robots: A Data-Driven Perspective 13

Designing Effective Multimodal Behaviors for Robots: A Data-...

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15th ACM International Conference on Multimodal Interaction (ICMI)

作者： Huang, Chien-Ming Univ Wisconsin Dept Comp Sci 1210 W Dayton St Madison WI 53706 USA

ISBN: (纸本)9781450321297

Robots need to effectively use multimodal behaviors, including speech, gaze, and gestures, in support of their users to achieve intended interaction goals, such as improved task performance. This proposed research concerns designing effective multimodal behaviors for robots to interact with humans using a data-driven approach. In particular, probabilistic graphical models (PGMs) are used to model the interdependencies among multiple behavioral channels and generate complexly contingent multimodal behaviors for robots to facilitate human-robot interaction. This data-driven approach not only allows the investigation of hidden and temporal relationships among behavioral channels but also provides a holistic perspective on how multimodal behaviors as a whole might shape interaction outcomes. Three studies are proposed to evaluate the proposed data-driven approach and to investigate the dynamics of multimodal behaviors and interpersonal interaction. This research will contribute to the multimodal interaction community in theoretical, methodological, and practical aspects.

关键词： human-robot interaction data-driven multimodal behavior probabilistic graphical models

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A probabilistic Evolutionary Optimization Approach to Compute Quasiparticle Braids

A Probabilistic Evolutionary Optimization Approach to Comput...

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10th International Conference on Simulated Evolution and Learning (SEAL)

作者： Santana, Roberto McDonald, Ross B. Katzgraber, Helmut G. Univ Basque Country UPV EHU Dept Comp Sci & Artificial Intelligence Guipuzcoa 20018 Spain Texas A&M Univ Dept Phys & Astron College Stn TX 77843 USA Santa Fe Inst Santa Fe NM 87501 USA

ISBN: (纸本)9783319135632;9783319135625

This paper proposes the use of estimation of distribution algorithms to deal with the problem of finding an optimal product of braid generators in topological quantum computing. We investigate how the regularities of the braid optimization problem can be translated into statistical regularities by means of the Boltzmann distribution. The introduced algorithm obtains solutions with an accuracy in the order of 10(-6), and lengths up to 9 times shorter than those expected from braids of the same accuracy obtained with other methods.

关键词： topological computing quasiparticle braids probabilistic graphical models EDAs braid optimization Fibonacci anyons

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