Estimating Object Perception Performance in Aerial Imagery Using a Bayesian Approach

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.

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.

Sophisticated course projects in senior computer science classes have raised great challenges to educators. Students now have stronger needs for instant and individualized guidance when exposed to the complexity of software development. In this paper, we describe the application of Bayesian Network, a probabilistic graphic model, to automated project failure analysis. Students can make multiple project submissions to an automated grader before the project deadline. Each submission will be graded immediately, by running a collection of test cases prepared by instructors in advance. Then failure behaviors of test cases are piped to a Bayesian Network (BN) inference engine. The BN engine generates a report on the most probable failure causes, and helps students in removing software bugs. The analysis of the BN engine can be improved by parameter learning. A case study is presented to illustrate the effectiveness of the approach.

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.

A Bayesian network (BN) is a probabilistic graphical model that represents a set of variables and their probabilistic dependencies. Formally, BNs are directed acyclic graphs whose nodes represent variables, and whose arcs encode the conditional dependencies among the variables. Nodes can represent any kind of variable, be it a measured parameter, a latent variable, or a hypothesis. They are not restricted to represent random variables, which form the “Bayesian” aspect of a BN. Efficient algorithms exist that perform inference and learning in BNs. BNs that model sequences of variables are called dynamic BNs. In this context, [A. Harel, R. Kenett, and F. Ruggeri, Modeling web usability diagnostics on the basis of usage statistics, in Statistical Methods in eCommerce Research, W. Jank and G. Shmueli, eds., Wiley, 2008] provide a comparison between Markov Chains and BNs in the analysis of web usability from e-commerce data. A comparison of regression models, structural equation models, and BNs is presented in Anderson et al. [R.D. Anderson, R.D. Mackoy, V.B. Thompson, and G. Harrell, A bayesian network estimation of the service–profit Chain for transport service satisfaction, Decision Sciences 35(4), (2004), pp. 665–689]. In this article we apply BNs to the analysis of customer satisfaction surveys and demonstrate the potential of the approach. In particular, BNs offer advantages in implementing models of cause and effect over other statistical techniques designed primarily for testing hypotheses. Other advantages include the ability to conduct probabilistic inference for prediction and diagnostic purposes with an output that can be intuitively understood by managers.

Fault diagnosis is useful in helping technicians detect, isolate, and identify faults, and troubleshoot. Bayesian network (BN) is a probabilistic graphical model that effectively deals with various uncertainty problems. This model is increasingly utilized in fault diagnosis. This paper presents bibliographical review on use of BNs in fault diagnosis in the last decades with focus on engineering systems. This work also presents general procedure of fault diagnosis modeling with BNs; processes include BN structure modeling, BN parameter modeling, BN inference, fault identification, validation, and verification. The paper provides series of classification schemes for BNs for fault diagnosis, BNs combined with other techniques, and domain of fault diagnosis with BN. This study finally explores current gaps and challenges and several directions for future research.

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.

Non-parametric Bayesian networks: Improving theory and reviewing applications

In this chapter we will introduce two probabilistic graphical models -Bayesian networks and Gaussian networks-that will be used to carry out factorization of the probability distribution of the selected individuals in the Estimation of Distribution Algorithms based approaches. For both paradigms we will present different algorithms to induce the underlying model from data, as well as some methods to simulate such models.

: 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.

A probabilistic expert system for predicting the risk of Legionella in evaporative installations

PyBNesian: An extensible python package for Bayesian networks

Bayesian network (BN) is the main model for solving probabilistic inference problem. The current research of BN just focuses on structure learning or parameter learning. And it still lacked algorithm which can implement the consistence of structure building, parameter learning and knowledge inference, so that knowledge construction and application are not associated and cannot be verified. This paper proposes a novel approach of Bayesian network adaptive knowledge construction and inference which is based on genetic algorithm. This algorithm, which designs a new BN learning encodement, crossover and mutation operators with adjusted strategies and the fitness function with inferential error feedback, implements BN building in all processes of structure building, parameter learning, knowledge inference and feedback revise with samples supported. Results show that the new approach not only can optimize the structure and parameters learning synchronously, but also can revise inferential error adaptively, and has more satisfied and accurate inference result.

Bayesian network (BN) is a probabilistic graphical model which describes the joint probability distribution over a set of random variables. Finding an optimal network structure based on an available training dataset is one of the most important challenges in the field of BNs. Since the problem of searching the optimal BN structure belongs to the class of NP-hard problems, typically greedy algorithms are used to solve it. In this paper two novel learning automata-based algorithms are proposed to solve the BNs’ structure learning problem. In both, there is a learning automaton corresponding with each possible edge to determine the appearance and the direction of that edge in the constructed network; therefore, we have a game of learning automata, at each stage of the proposed algorithms. Two special cases of the game of the learning automata have been discussed, namely, the game with a common payoff and the competitive game. In the former, all the automata in the game receive a unique payoff from the environment, but in the latter, each automaton receives its own payoff. As the algorithms proceed, the learning processes focus on the BN structures with higher scores. The use of learning automata has led to design the algorithms with a guided search scheme, which can avoid getting stuck in local maxima. Experimental results show that the proposed algorithms are capable of finding the optimal structure of BN in an acceptable execution time; and compared with other search-based methods, they outperform them.