Adaptive blocked Gibbs sampling for inference in probabilistic graphical models

In numerous real world applications, from sensor networks to computer vision to natural text processing, one needs to reason about the system in question in the face of uncertainty. A key problem in all those settings is to compute the probability distribution over the variables of interest (the query) given the observed values of other random variables (the evidence). Probabilistic graphical models (PGMs) have become the approach of choice for representing and reasoning with high-dimensional probability distributions. However, for most models capable of accurately representing real-life distributions, inference is fundamentally intractable. As a result, optimally balancing the expressive power and inference complexity of the models, as well as designing better approximate inference algorithms, remain important open problems with potential to significantly improve the quality of answers to probabilistic queries. This thesis contributes algorithms for learning and approximate inference in probabilistic graphical models that improve on the state of the art by emphasizing the computational aspects of inference over the representational properties of the models. Our contributions fall into two categories: learning accurate models where exact inference is tractable and speeding up approximate inference by focusing computation on the query variables and only spending as much effort on the remaining parts of the model as needed to answer the query accurately. First, for a case when the set of evidence variables is not known in advance and a single model is needed that can be used to answer any query well, we propose a polynomial time algorithm for learning the structure of tractable graphical models with quality guarantees, including PAC learnability and graceful degradation guarantees. Ours is the first efficient algorithm to provide this type of guarantees. A key theoretical insight of our approach is a tractable upper bound on the mutual information of arbitrarily large sets of random variables that yields exponential speedups over the exact computation. Second, for a setting where the set of evidence variables is known in advance, we propose an approach for learning tractable models that tailors the structure of the model for the particular value of evidence that become known at test time. By avoiding a commitment to a single tractable structure during learning, we are able to expand the representation power of the model without sacrificing efficient exact inference and parameter learning. We provide a general framework that allows one to leverage existing structure learning algorithms for discovering high-quality evidence-specific structures. Empirically, we demonstrate state of the art accuracy on real-life datasets and an order of magnitude speedup. Finally, for applications where the intractable model structure is a given and approximate inference is needed, we propose a principled way to speed up convergence of belief propagation by focusing the computation on the query variables and away from the variables that are of no direct interest to the user. We demonstrate significant speedups over the state of the art on large-scale relational models. Unlike existing approaches, ours does not involve model simplification, and thus has an advantage of converging to the fixed point of the full model. More generally, we argue that the common approach of concentrating on the structure of representation provided by PGMs, and only structuring the computation as representation allows, is suboptimal because of the fundamental computational problems. It is the computation that eventually yields answers to the queries, so directly focusing on structure of computation is a natural direction for improving the quality of the answers. The results of this thesis are a step towards adapting the structure of computation as a foundation of graphical models.

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 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.

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.

A probabilistic graphical model approach to stochastic multiscale partial differential equations

In this work, we present a novel approach for predicting the perception performance of an optical aerial surveillance system. We outline our use case in multi-target tracking motivating this work before giving some background on related work in sensor performance estimation. After explaining the reasoning behind selecting a Bayesian network against other machine learning classifiers, we present relevant underlying concepts of sample-based inference and parameter learning in probabilistic graphical models. We present the modular architecture of our performance estimator and reason through the model input nodes based on system, object, and scene parameters. Further, we describe the extensive flight experiment performed using a crewed ultralight aircraft equipped with a state-of-the-art aerial surveillance gimbal to collect imagery of target vehicles under carefully specified conditions. We describe the implemented post-processing of the recorded data, the method used to sample a reasonably sized dataset for learning, the criteria followed while labeling the dataset, and the technique used to learn a usable model based on a Bayesian network. Next, we analyze the classification performance of the model on an independent validation dataset and compare it against two additional machine-learning classifiers trained on the same dataset. We discuss the limitations of the proposed model and the presented validation. We wrap up by giving an outlook on various opportunities for possible future improvements to enhance the prediction performance of our network. Finally, we present other use cases benefitting from a similarly structured sensor performance prediction model, such as search planning.

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.

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.

Ranking evaluation of institutions based on a Bayesian network having a latent variable

Wallace and colleagues’ 1 article on tagging audio-recorded patient-physician interactions is intriguing, because they bring state-of-the-art machine-learning methods to a relatively prosaic problem that has potentially great implications for medical decision-making research and clinical decision support. Understanding the patient-physician interaction must be a first step to supporting shared decision making between these two participants, whether we model it formally, with decision analytic models based on maximizing expected utility, or whether we pay attention to the psychological aspects of that interaction. The physician’s opinion probably matters the most to patients, but how that opinion is communicated or could be modulated, through a decision-making intervention, depends on the type of empirical research conducted by Wallace and colleagues. The prosaic problem they address is straightforward. The best research on the patient-physician interaction requires video recording and tagging of the video at multiple levels. Second best is audio recording. As the authors point out, the dimensions for tagging were initially articulated by Roter in her Roter Interactional Analysis (RIAS) framework over 35 years ago, where dimensions of coding include gathering data, education and counseling, building a relationship, activating, and partnership building. Wallace and colleagues’ General Medical Interaction Analysis System (GMIAS) aims to include greater domain knowledge (e.g., the domain of HIV treatment) to enable the computer to perform automated tagging. As a student might say, ‘‘Wouldn’t it be great if we could get the computer to do the tedious job of coding?’’ And this is the task that Wallace and colleagues set for themselves. Their effort begins after the recording has been transcribed and divided into ‘‘utterances,’’ sequences of words spoken by a participant (physician or patient) before the switching of speakers. Thus, issues of tone, pauses, and timing are not represented. Further, they restrict the coding to just the topic level—that is, the content of the utterance, not its ‘‘speech act,’’ the interpersonal component. Their topic scheme is still broad, including tags for biomedical, psychosocial, logistics, socializing, antiretroviral (HIV) treatment, and missing/other. The heart of their contribution is the algorithm that ‘‘reads’’ the utterances and applies these topic tags. The algorithm is based on conditional random fields (CRFs), a type of probabilistic graphical model (PGM). PGMs have a long history, with either path analysis in the 1920s or hidden Markov models from 1966 as progenitors. The Society was involved in some of these developments in the 1980s, when uncertainty in the artificial intelligence community overlapped with that in the medical decision-making community because of the common interest in making high-stakes decisions in contexts of uncertainty. The key product of that turmoil was the Bayesian (belief) network, because the posteriors calculated from those models could be fed into expected-value decision analytic models. Pearl’s book on these models was influential in providing many researchers with a concrete basis for extending this work. But GPMs proved important in many other domains beyond medical diagnosis and decision making, such as computer vision, spatial analysis, bioinformatics, and natural language processing (NLP). The latter two have many affinities, since so many bioinformatics problems involve sequences of nucleotides or high-order motifs, and NLP involves sequence of phonemes, words, or utterances. Received 2 January 2014 from Johns Hopkins, Baltimore, MD (HPL). Revision accepted for publication 7 March 2014.

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.

In continuous domain, how to efficiently learn the complex probabilistic graphical model is a bottleneck problem for estimation of distribution algorithms (EDAs). The predominant researches focus on Gaussian probabilistic model instead of histogram distribution model because of its comparative superiority in the computational complexity. In this paper, however, we find that using the histogram model does not necessarily bring into exponential computational complexity. Based on the fact many bins are zero-height, we propose a novel method that can learn the multivariate dependency histogram based probabilistic graphical model with acceptable polynomial computational complexity. Several strategies previously used in the HEDA are combined into the new algorithm to improve the convergence and diversity. Experiments showed the superior performance of the new algorithm on several continuous problems compared with UMDA <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> , IDEA-G and sur-shr-HEDA.

Most clustering and classification methods are based on the assumption that the objects to be clustered are independent. However, in more and more modern applications, data are structured in a way that makes this assumption not realistic and potentially misleading. A typical example that can be viewed as a clustering task is image segmentation where the objects are the pixels on a regular grid and depend on neighbouring pixels on this grid. Also, when data are geographically located, it is of interest to cluster data with an underlying dependence structure accounting for some spatial localisation. These spatial interactions can be naturally encoded via a graph not necessarily regular as a grid. Data sets can then be modelled via Markov random fields and mixture models (e.g. the so-called MRF and Hidden MRF). More generally, probabilistic graphical models are tools that can be used to represent and manipulate data in a structured way while modeling uncertainty. This chapter introduces the basic concepts. The two main classes of probabilistic graphical models are considered: Bayesian networks and Markov networks. The key concept of conditional independence and its link to Markov properties is presented. The main problems that can be solved with such tools are described. Some illustrations are given associated with some practical work.

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.

Our daily life is full of challenges, and the biggest challenge is the unpredictability of many of our significant life events. To deal with this unpredictability, analysing the probability of events has become very important. In particular, the theorem of English statistician Thomas Bayes has been revolutionary. Numerous theories and techniques have been proposed, and many tools have been developed to solve real-life problems based on the theorem, yet it is still very much an area of active research. It still attracts researchers dealing with cutting-edge technologies. One tool that has been used extensively in modelling probabilistic analysis for decades is the Probabilistic Graphical Model (PGM). PGMs have very challenging childhood but glorious youth. The vast applicability of the models in cutting-edge technologies attracts researchers, modellers and scientists of diversified fields. Hence there are numerous models with their respective features, merits and backlogs. To date, there have been very few surveys conducted among the wide range of models and their associated tools. More specifically, those few reviews are highly application and domain focused, and limited to three to four very popular and widely used models and their associated learning and inference algorithms. To the best of our knowledge, this paper is the first that presents the features, limitations, design and implementation platforms, research challenges and applicability of the models based on a common framework that consists of some essential attributes of the popular PGMs and tools for probabilistic analysis. The study helps deciding an appropriate tool as per the perspective of the application and feature of the tool. This paper concludes with future research scope and a non-exhaustive list of applications of PGMs. DUJASE Vol. 6 (2) 82-93, 2021 (July)