Query-specific learning and inference for probabilistic graphical models

A probabilistic graphical model approach to stochastic multiscale partial differential equations

: Graphical models fuse probability theory and graph theory in such a way as to permit efficient representation and computation with probability distributions. They intuitively capture statistical relationships among random variables and provide a succinct formalism that allows for the development of tractable algorithms for statistical inference. In recent years, certain types of graphical models, particularly Bayesian networks and dynamic Bayesian networks (DBNs), have been applied to various problems in missile defense that involve decision making under uncertainty and estimation in dynamic systems, such as data association, multitarget tracking, and classification. While the set of problems addressed in the missile defense arena is quite diverse, all require mathematically sound machinery for dealing with uncertainty. The graphical model regime provides a robust, flexible framework for representing and computationally handling uncertainty in real-world problems. While the graphical model regime is relatively new, it has deep roots in many fields, as the formalism generalizes many commonly used stochastic models, including Kalman filters and hidden Markov models. In this report, we describe the mathematical foundations of graphical models and statistical inference, focusing on the concepts and techniques that are most useful to the problem of decision making in dynamic systems under uncertainty. In general, statistical inference on a graphical model is an NP-Hard problem, so there have been large research efforts that involve developing algorithms for performing inference efficiently for certain classes of models, or obtaining approximations for quantities of interest using algorithms for approximate inference. Due to the breadth of problems, a broad class of algorithms has been of interest to researchers over the past several years. As such, the need arose for an extensible and efficient software library for performing statistical inference on graphical models.

Inference is a central problem in probabilistic graphical models, and is often the main sub-step in probabilistic learning procedures. Thus, accurate inference algorithms are essential to both answer queries on a learned model, as well as to learn a robust model. Gibbs sampling is arguably one of the most popular approximate inference methods that has been widely used for probabilistic inference in several different domains including natural language processing, computer vision. etc. Here, we develop an approach that improves the performance of blocked Gibbs sampling, an advanced variant of the Gibbs sampling algorithm. Specifically, we utilize correlation among variables in the probabilistic graphical model to develop an adaptive blocked Gibbs sampler that automatically tunes its proposal distribution based on statistics derived from previous samples. Specifically, we adapt the proposal such that we sample blocks containing highly correlated variables more often than the others. This in turn helps improve probability estimates given by the sampler, by selecting hard-to-sample variables more often during the sampling procedure. Further, since adaptation breaks the Markovian property of the sampler, we develop a method to guarantee that our sampler converges to the correct stationary distribution despite being non-Markovian, by diminishing the adaptation of the selection probabilities over time. We evaluate our method with several discrete probabilistic graphical models taken from UAI challenge problems corresponding to different domains, and show that our approach is superior in terms of accuracy as compared to methods that ignore correlation information in the proposal distribution of the sampler.

Probabilistic graphical models are a fundamental tool in probabilistic modeling, machine learning and artificial intelligence. They allow us to integrate in a natural way expert knowledge, physical modeling, heterogeneous and correlated data and quantities of interest. For exactly this reason, multiple sources of model uncertainty are inherent within the modular structure of the graphical model. In this paper we develop information-theoretic, robust uncertainty quantification methods and non-parametric stress tests for directed graphical models to assess the effect and the propagation through the graph of multi-sourced model uncertainties to quantities of interest. These methods allow us to rank the different sources of uncertainty and correct the graphical model by targeting its most impactful components with respect to the quantities of interest. Thus, from a machine learning perspective, we provide a mathematically rigorous approach to correctability that guarantees a systematic selection for improvement of components of a graphical model while controlling potential new errors created in the process in other parts of the model. We demonstrate our methods in two physico-chemical examples, namely quantum scale-informed chemical kinetics and materials screening to improve the efficiency of fuel cells.

Graphical modelling is an important tool for the efficient representation and analysis of uncertain information in knowledge-based systems. While Bayesian networks and Markov networks from probabilistic graphical modelling are well-known for a couple of years, the field of possibilistic graphical modelling occurs as a new promising area of research. Possibilistic networks provide an alternative approach compared to probabilistic networks, whenever it is necessary to model uncertainty and imprecision as two different kinds of imperfect information. Imprecision in the sense of set-valued data has often to be considered in situations where data are obtained from human observations or non-precise measurement units. In this contribution we present a comparison of the background and perspectives of probabilistic and possibilistic graphical models, and give an overview on the current state of the art of possibilistic networks with respect to propagation and learning algorithms, applicable to data mining and data fusion problems.

Probabilistic graphical models (PGM) are one of the rich frameworks. These models are used over complex domains for coding probability distributions. The joint distributions interact with each other over large numbers of random variables and are the combination of statistics and computer science. These concepts are dependent on theories such as probability theory, graph algorithms, machine learning, which make a basic tool in devising many machine learning problems. These are the origin for the contemporary methods in an extensive range of applications. These applications range as medical diagnosis, image understanding, speech recognition, natural language processing, etc. Graphical models are one of dominant tools for handling image processing applications. On the other hand, the volume of image data gives rise to a problem. The representation of all possible graphical model node variables with that of discrete states heads to the number of states for the model. This leads to interpretation computationally obstinate. Many projects involve a human intervention or an automated system to obtain the consensus established on existing information. The PGM, discussed in this chapter, offers a variety of approaches. The approach is based on models and allows interpretable models to be built which then is employed by reasoning algorithms. These models are also studied significantly from data and allow the approaches for cases where the model is manually built. Most real-world applications are of uncertain data which makes a model building more challenging. This chapter emphasizes on PGM where the uncertainty of data is obvious. PGM provides models that are more realistic. These are extended from Bayesian networks, undirected Markov networks, discrete and continuous models, and extensions to deal with dynamical systems and relational data also. For each class of models, the chapter describes the fundamental bases: representation, inference, and learning. Finally, the chapter considers the decision making under the uncertainty of the data.

Representing and processing lineages over uncertain data based on the Bayesian network

As genomics becomes increasingly relevant to medicine, medical informatics and bioinformatics are gradually converging into a larger field that we call computational biomedicine. Developing a computational framework that is common to the different disciplines that compose computational biomedicine will be a major enabler of the further development and integration of this research domain. Probabilistic graphical models such as Hidden Markov Models, belief networks, and missing-data models together with computational methods such as dynamic programming, Expectation-Maximization, data-augmentation Gibbs sampling, and the Metropolis-Hastings algorithm provide the tools for an integrated probabilistic approach to computational biomedicine. We show how graphical models have already found a broad application in different fields composing computational biomedicine. We also indicate several challenges that lie at the interface between medical informatics, statistical genomics, and bioinformatics. We also argue that graphical models offer a unified framework making it possible to integrate in a statistically meaningful way multiple models ranging from the molecular level to cellular and to clinical levels. Because of their versatility and firm statistical underpinning, we assert that probabilistic graphical models can serve as the lingua franca for many computationally intensive approaches to biology and medicine. As such, graphical models should be a foundation of the curriculum of students in these fields. From such a foundation, students could then build towards specific computational methods in medical informatics, medical image analysis, statistical genetics, or bioinformatics while keeping the communication open between these areas.

Aiming at a comprehensive and concise tutorial survey, recap of variational inference and reinforcement learning with Probabilistic Graphical Models are given with detailed derivations. Reviews and comparisons on recent advances in deep reinforcement learning are made from various aspects. We offer detailed derivations to a taxonomy of Probabilistic Graphical Model and Variational Inference methods in deep reinforcement learning, which serves as a complementary material on top of the original contributions.

Probabilistic graphical modeling (PGM) provides a framework for formulating an interpretable generative process of data and expressing uncertainty about unknowns. This makes PGM very useful for understanding phenomena underlying data and for decision making. PGM has seen great success in domains where interpretable inferences are key, e.g. marketing, medicine, neuroscience, and social science. However, PGM tends to lack flexibility, which has hindered its use when it comes to modeling large scale high-dimensional complex data and performing tasks that require flexibility (e.g. in vision and language applications.)\n\nDeep learning (DL) is another framework for modeling and learning from data that has seen great empirical success in recent years. DL is very powerful and offers great flexibility, but it lacks the interpretability and calibration of PGM. \n\nThis thesis develops deep probabilistic graphical modeling (DPGM). DPGM consists in leveraging DL to make PGM more flexible. DPGM brings about new methods for learning from data that exhibit the advantages of both PGM and DL. \n\nWe use DL within PGM to build flexible models endowed with an interpretable latent structure. One family of models we develop extends exponential family principal component analysis (EF-PCA) using neural networks to improve predictive performance while enforcing the interpretability of the latent factors. Another model class we introduce enables accounting for long-term dependencies when modeling sequential data, which is a challenge when using purely DL or PGM approaches. This model class for sequential data was successfully applied to language modeling, unsupervised document representation learning for sentiment analysis, conversation modeling, and patient representation learning for hospital readmission prediction. Finally, DPGM successfully solves several outstanding problems of probabilistic topic models. \n\nLeveraging DL within PGM also brings about new algorithms for learning with complex data. For example, we develop entropy-regularized adversarial learning, a learning paradigm that deviates from the traditional maximum likelihood approach used in PGM. From the DL perspective, entropy-regularized adversarial learning provides a solution to the long-standing mode collapse problem of generative adversarial networks.

Fingerprint matching is the most important part in the field of fingerprint recognition. In this paper, a novel fingerprint matching algorithm based on the probabilistic graphical model and 3-tree model is proposed. First, minutiae matching problems are considered as a special point-set matching. Fingerprint minutiae are viewed as random variables. Each minutia pairs have some probability to be matched. Second, an algorithm is proposed to generate the graphical model and choose "signal points", which dynamically have corresponding points in other point set. We choose three base minutiae pairs as signal pairs. Third, the model is converted into a Junction Tree. A 3-tree model is built and the potentials of other minutiae pairs are calculated through Junction Tree (J.T.) algorithm. Then we translate the matching problem into the best matching problem of a weighted bipartite graph. Finally, the number of common matching pairs can be got through maximum flow algorithm. The similarity of two fingerprints is evaluated using the number of common matching pairs and the maximal posteriori probability. In order to deal with part-matching problems, we use the smallest convex hull which contains all the matched minutiae. Experiments evaluated on FVC 2004 show both effectiveness and efficiency of our methods.

Dependence is a universal phenomenon which can be observed everywhere. In machine learning, probabilistic graphical models (PGMs) represent dependence relations with graphs. PGMs find wide applications in natural language processing (NLP), speech processing, computer vision, biomedicine, information retrieval, etc. Many traditional models, such as hidden Markov models (HMMs), Kalman filters, can be put under the umbrella of PGMs. The central idea of PGMs is to decompose (factorize) a joint probability into a product of local factors. Learning, inference and storage can be conducted efficiently over the factorization representation. In this thesis, we propose a novel framework motivated by the Minimum Shared Information Principle (MSIP): We try to find a factorization in which the information shared between factors is minimum. In other words, we try to make factors as independent as possible. The benefit by doing this is that we can train factors separately without paying a lot of efforts to guarantee consistency between them. To achieve this goal, we develop a theoretical framework called co-occurrence rate networks (CRNs) to obtain such a factorization. Experimental results on three important natural language processing tasks show that our separate training method is two orders of magnitude faster than conditional random fields, while achieving competitive quality (often better on the overall quality metric F1). The second contribution of this thesis is applying PGMs to a real-world NLP application: open relation extraction (ORE). In open relation extraction, two entities in a sentence are given, and the goal is to automatically extract their relation expression. ORE is a core technique, especially in the age of big data, for transforming unstructured information into structured data. We propose our model SimpleIE for this task. The basic idea is to decompose an extraction pattern into a sequence of simplification operations (components). The benefit by doing this is that these components can be re-combined in a new way to generate new extraction patterns. Experimental results on three benchmark data sets show that SimpleIE boosts recall and F1 by at least 15% comparing with seven ORE systems.

This chapter introduces graphical models as a powerful tool to derive efficient algorithms for inference problems. When dealing with complex interdependent variables, inference problems may become of huge complexity. In this context, the structure of the variables is of great interest. In this chapter, directed and undirected graphical models are first defined, before some crucial results are stated, such as the Hammersley–Clifford theorem of Markov random fields and the junction tree property aimed at finding groupings under which a graphical model becomes a tree. Taking advantage of the structure of the variables, belief propagation is then described, including two particular instances: the sum–product and max–sum algorithms. In the final section, the learning problem is addressed in three different contexts: parameter learning, graphical model learning, and latent graphical model learning.

A graphical model represents the data distribution of a data generating process and inherently captures its feature relationships. This stochastic model can be used to perform inference, to calculate posterior probabilities, in various applications such as classification. Exact inference algorithms are known to be intractable on large networks due to exponential time and space complexity. Approximate inference algorithms are instead widely used in practice to overcome this constraint, with a trade off in accuracy. Stochastic sampling is one such method where an approximate probability distribution is empirically evaluated using various sampling techniques. However, these algorithms may still suffer from scalability issues on large and complex networks. To address this challenge, we have designed and implemented several MapReduce based distributed versions of a specific type of approximate inference algorithm called Adaptive Importance Sampling (AIS). We compare and evaluate the proposed approaches using benchmark networks. Experimental result shows that our approach achieves significant scaleup and speedup compared to the sequential algorithm, while achieving similar accuracy asymptotically.

Proteins, the basic structural and functional building blocks of cellular machinery, evolve under significant constraint. Evolutionary pressures limit the acceptable variation and covariation of amino acids in a protein. As such, these evolutionary pressures yield constraints manifested in the sequence record of a family of evolutionarily related proteins. Some of these sequence constraints arise from within the proteins themselves (intramolecular constraints), while others are imposed externally (intermolecular constraints). This thesis addresses how to identify both intramolecular and intermolecular sequence constraints, represent these constraints with probabilistic graphical models, and use the models predictively and generatively. Our probabilistic graphical models support a general and powerful mechanism for representing and utilizing sequence constraints, providing a sound semantics, an efficient and transparent means of evaluating consistency with the underlying constraints, and an effective framework for exploring the space of satisfying sequences. For intramolecular constraints, our graphical models of residue coupling (GMRCs) identify and encode both residue conservation (individual residue variation) and residue coupling (pairwise residue covariation). Our GMRCs identify biologically relevant constraints and can be used to predict with high accuracy the functional class of a protein. Algorithms we have developed for sampling from GMRCs generate novel sequences that meet the underlying constraints. For intermolecular constraints, our graphical models of residue cross-coupling (GMRCCs) identify and encode residue cross-coupling (covariation between residues in two different proteins). Our GMRCCs identify cross-coupled residues that are known to confer specificity in protein-protein interactions. Using these constraints, our models are able to predict whether or not two proteins will interact. Algorithms we have developed are able to generate the sequences most likely to interact (or not) with particular design targets.