Graphical Models and Symmetries : Loopy Belief Propagation Approaches

Whenever a person or an automated system has to reason in uncertain domains, probability theory is necessary. Probabilistic graphical models allow us to build statistical models that capture complex dependencies between random variables. Inference in these models, however, can easily become intractable. Typical ways to address this scaling issue are inference by approximate message-passing, stochastic gradients, and MapReduce, among others. Exploiting the symmetries of graphical models, however, has not yet been considered for scaling statistical machine learning applications. One instance of graphical models that are inherently symmetric are statistical relational models. These have recently gained attraction within the machine learning and AI communities and combine probability theory with first-order logic, thereby allowing for an efficient representation of structured relational domains. The provided formalisms to compactly represent complex real-world domains enable us to effectively describe large problem instances. Inference within and training of graphical models, however, have not been able to keep pace with the increased representational power. This thesis tackles two major aspects of graphical models and shows that both inference and training can indeed benefit from exploiting symmetries. It first deals with efficient inference exploiting symmetries in graphical models for various query types. We introduce lifted loopy belief propagation (lifted LBP), the first lifted parallel inference approach for relational as well as propositional graphical models. Lifted LBP can effectively speed up marginal inference, but cannot straightforwardly be applied to other types of queries. Thus we also demonstrate efficient lifted algorithms for MAP inference and higher order marginals, as well as the efficient handling of multiple inference tasks. Then we turn to the training of graphical models and introduce the first lifted online training for relational models. Our training procedure and the MapReduce lifting for loopy belief propagation combine lifting with the traditional statistical approaches to scaling, thereby bridging the gap between statistical relational learning and traditional statistical machine learning

Accelerating Iterative Computations for Large-Scale Data Processing

Recent advances in sensing, storage, and networking technologies are creating massive amounts of data at an unprecedented scale and pace. Large-scale data processing is commonly leveraged to make sense of these data, which will enable companies, governments, and organizations, to make better decisions and bring convenience to our daily life. However, the massive amount of data involved makes it challenging to perform data processing in a timely manner. On the one hand, huge volumes of data might not even fit into the disk of a single machine. On the other hand, data mining and machine learning algorithms, which are usually involved in large-scale data processing, typically require time-consuming iterative computations. Therefore, it is imperative to efficiently perform iterative computations on large computer clusters or cloud using highly-parallel and shared-nothing distributed systems. This research aims to explore new forms of iterative computations that reduce unnecessary computations so as to accelerate large-scale data processing in a distributed environment. We propose the iterative computation transformation for well-known data mining and machine learning algorithms, such as expectation-maximization, nonnegative matrix factorization, belief propagation, and graph algorithms (e.g., PageRank). These algorithms have been used in a wide range of application domains. First, we show how to accelerate expectation-maximization algorithms with frequent updates in a distributed environment. Then, we illustrate the way of efficiently scaling distributed nonnegative matrix factorization with block-wise updates. Next, our approach of scaling distributed belief propagation with prioritized block updates is presented. Last, we illustrate how to efficiently perform distributed incremental computation on evolving graphs. We will elaborate how to implement these transformed iterative computations on existing distributed programming models such as the MapReduce-based model, as well as develop new scalable and efficient distributed programming models and frameworks when necessary. The goal of these supporting distributed frameworks is to lift the burden of the programmers in specifying transformation of iterative computations and communication mechanisms, and automatically optimize the execution of the computation. Our techniques are evaluated extensively to demonstrate their efficiency. While the techniques we propose are in the context of specific algorithms, they address the challenges commonly faced in many other algorithms

mARC: Memory by Association and Reinforcement of Contexts

This paper introduces the memory by Association and Reinforcement of Contexts (mARC). mARC is a novel data modeling technology rooted in the second quantization formulation of quantum mechanics. It is an all-purpose incremental and unsupervised data storage and retrieval system which can be applied to all types of signal or data, structured or unstructured, textual or not. mARC can be applied to a wide range of information clas-sification and retrieval problems like e-Discovery or contextual navigation. It can also for-mulated in the artificial life framework a.k.a Conway "Game Of Life" Theory. In contrast to Conway approach, the objects evolve in a massively multidimensional space. In order to start evaluating the potential of mARC we have built a mARC-based Internet search en-gine demonstrator with contextual functionality. We compare the behavior of the mARC demonstrator with Google search both in terms of performance and relevance. In the study we find that the mARC search engine demonstrator outperforms Google search by an order of magnitude in response time while providing more relevant results for some classes of queries

Models, Inference, and Implementation for Scalable Probabilistic Models of Text

Unsupervised probabilistic Bayesian models are powerful tools for statistical analysis, especially in the area of information retrieval, document analysis and text processing. Despite their success, unsupervised probabilistic Bayesian models are often slow in inference due to inter-entangled mutually dependent latent variables. In addition, the parameter space of these models is usually very large. As the data from various different media sources--for example, internet, electronic books, digital films, etc--become widely accessible, lack of scalability for these unsupervised probabilistic Bayesian models becomes a critical bottleneck. The primary focus of this dissertation is to speed up the inference process in unsupervised probabilistic Bayesian models. There are two common solutions to scale the algorithm up to large data: parallelization or streaming. The former achieves scalability by distributing the data and the computation to multiple machines. The latter assumes data come in a stream and updates the model gradually after seeing each data observation. It is able to scale to larger datasets because it usually takes only one pass over the entire data. In this dissertation, we examine both approaches. We first demonstrate the effectiveness of the parallelization approach on a class of unsupervised Bayesian models--topic models, which are exemplified by latent Dirichlet allocation (LDA). We propose a fast parallel implementation using variational inference on the MapRe- duce framework, referred to as Mr. LDA. We show that parallelization enables topic models to handle significantly larger datasets. We further show that our implementation--unlike highly tuned and specialized implementations--is easily extensible. We demonstrate two extensions possible with this scalable framework: 1) informed priors to guide topic discovery and 2) extracting topics from a multilingual corpus. We propose polylingual tree-based topic models to infer topics in multilingual corpora. We then propose three different inference methods to infer the latent variables. We examine the effectiveness of different inference methods on the task of machine translation in which we use the proposed model to extract domain knowledge that considers both source and target languages. We apply it on a large collection of aligned Chinese-English sentences and show that our model yields significant improvement on BLEU score over strong baselines. Other than parallelization, another approach to deal with scalability is to learn parameters in an online streaming setting. Although many online algorithms have been proposed for LDA, they all overlook a fundamental but challenging problem-- the vocabulary is constantly evolving over time. To address this problem, we propose an online LDA with infinite vocabulary--infvoc LDA. We derive online hybrid inference for our model and propose heuristics to dynamically order, expand, and contract the set of words in our vocabulary. We show that our algorithm is able to discover better topics by incorporating new words into the vocabulary and constantly refining the topics over time. In addition to LDA, we also show generality of the online hybrid inference framework by applying it to adaptor grammars, which are a broader class of models subsuming LDA. With proper grammar rules, it simplifies to the exact LDA model, however, it provides more flexibility to alter or extend LDA with different grammar rules. We develop online hybrid inference for adaptor grammar, and show that our method discovers high-quality structure more quickly than both MCMC and variational inference methods

An optimization framework for the capacity allocation and admission control of MapReduce jobs in cloud systems

Nowadays, we live in a Big Data world and many sectors of our economy are guided by data-driven decision processes. Big Data and Business Intelligence applications are facilitated by the MapReduce programming model, while, at infrastructural layer, cloud computing provides flexible and cost-effective solutions to provide on-demand large clusters. Capacity allocation in such systems, meant as the problem of providing computational power to support concurrent MapReduce applications in a cost-effective fashion, represents a challenge of paramount importance. In this paper we lay the foundation for a solution implementing admission control and capacity allocation for MapReduce jobs with a priori deadline guarantees. In particular, shared Hadoop 2.x clusters supporting batch and/or interactive jobs are targeted. We formulate a linear programming model able to minimize cloud resources costs and rejection penalties for the execution of jobs belonging to multiple classes with deadline guarantees. Scalability analyses demonstrated that the proposed method is able to determine the global optimal solution of the linear problem for systems including up to 10,000 classes in less than 1 s