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Many organizations require quality improvement initiatives to be based on quantified business cases. This leads some organizations to start measurement programs to collect data about current performance-a lengthy and expensive process that requires a strong commitment from management. This report describes a collaboration between the Software Engineering Institute and Ericsson Research and Development, The Netherlands, to build a business case using high maturity measurement approaches that require limited measurement effort. For this project, a Bayesian belief network (BBN) and Monte Carlo simulation were combined to build a business case for quality improvement. Using a BBN gave quick insight into potential areas of improvement based on relevant quality factors and the current performance level of the organization. Monte Carlo simulation enabled a detailed calculation of the likely business results in the areas of potential improvement. This approach led to the decision to implement agile methods to improve the quality of requirements.

The paper presents a new sampling methodology for Bayesian networks that samples only a subset of variables and applies exact inference to the rest. Cutset sampling is a network structure-exploiting application of the Rao-Blackwellisation principle to sampling in Bayesian networks. It improves convergence by exploiting memory-based inference algorithms. It can also be viewed as an anytime approximation of the exact cutset-conditioning algorithm developed by Pearl. Cutset sampling can be implemented efficiently when the sampled variables constitute a loop-cutset of the Bayesian network and, more generally, when the induced width of the networks graph conditioned on the observed sampled variables is bounded by a constant w. We demonstrate empirically the benefit of this scheme on a range of benchmarks.

Anomaly detection is the process by which low probability events are automatically found against a background of normal activity.By definition there must be many more normal events than anomalous ones. This rare nature of anomalies causes numerical problems for probabilistic methods designed to automatically detect them. This report describes an algorithm that introduces new discretisation levels to support the representation of low probability values in the context of Bayesian network anomaly detection. It is an engineeringsolution to a problem with an extant discretisation tool that represents a data sets fine structure but fails to capture extreme values ornulls between modes in its probability density. It is demonstrated that the limitations of the extant tool can be overcome using examplesof integer and continuous data.

We propose a Multi-Layer Network based on the Bayesian framework of the Factor Graphs in Reduced Normal Form (FGrn) applied to a two-dimensional lattice. The Latent Variable Model (LVM) is the basic building block of a quadtree hierarchy built on top of a bottom layer of random variables that represent pixels of an image, a feature map, or more generally a collection of spatially distributed discrete variables. The multi-layer architecture implements a hierarchical data representation that, via belief propagation, can be used for learning and inference. Typical uses are pattern completion, correction and classification. The FGrn paradigm provides great flexibility and modularity and appears as a promising candidate for building deep networks: the system can be easily extended by introducing new and different (in cardinality and in type) variables. Prior knowledge, or supervised information, can be introduced at different scales. The FGrn paradigm provides a handy way for building all kinds of architectures by interconnecting only three types of units: Single Input Single Output (SISO) blocks, Sources and Replicators. The network is designed like a circuit diagram and the belief messages flow bidirectionally in the whole system. The learning algorithms operate only locally within each block. The framework is demonstrated in this paper in a three-layer structure applied to images extracted from a standard data set.

Bayesian networks are probabilistic graphical models often used in big data analytics. The problem of exact structure learning is to find a network structure that is optimal under certain scoring criteria. The problem is known to be NP-hard and the existing methods are both computationally and memory intensive. In this paper, we introduce a new approach for exact structure learning. Our strategy is to leverage relationship between a partial network structure and the remaining variables to constraint the number of ways in which the partial network can be optimally extended. Via experimental results, we show that the method provides up to three times improvement in runtime, and orders of magnitude reduction in memory consumption over the current best algorithms.

Due to its causal semantics, Bayesian networks (BN) have been widely employed to discover the underlying data relationship in exploratory studies, such as brain research. Despite its success in modeling the probability distribution of variables, BN is naturally a generative model, which is not necessarily discriminative. This may cause the ignorance of subtle but critical network changes that are of investigation values across populations. In this paper, we propose to improve the discriminative power of BN models for continuous variables from two different perspectives. This brings two general discriminative learning frameworks for Gaussian Bayesian networks (GBN). In the first framework, we employ Fisher kernel to bridge the generative models of GBN and the discriminative classifiers of SVMs, and convert the GBN parameter learning to Fisher kernel learning via minimizing a generalization error bound of SVMs. In the second framework, we employ the max-margin criterion and build it directly upon GBN models to explicitly optimize the classification performance of the GBNs. The advantages and disadvantages of the two frameworks are discussed and experimentally compared. Both of them demonstrate strong power in learning discriminative parameters of GBNs for neuroimaging based brain network analysis, as well as maintaining reasonable representation capacity. The contributions of this paper also include a new Directed Acyclic Graph (DAG) constraint with theoretical guarantee to ensure the graph validity of GBN.

The principles of Sun Tzu's Art of War have been widely used by business executives and military officers with much success in the realm of competition and conflict. However, when conflict situations arise in a highly stressful environment coupled with the pressure of time, decision makers may not be able to consider all the key concepts when forming their decisions or strategies. Therefore, a structured reasoning approach may be used to apply Sun Tzu's principles correctly and fully. It is believed that Sun Tzu's principles can be modeled mathematically; hence, a Bayesian Network Model (a form of mathematical tool using probability theory) is used to capture Sun Tzu's principles and provide a structured reasoning approach. Scholars have identified incompleteness in Sun Tzu's appreciation of information in war and his application of secret agents. This incompleteness results in circular reasoning when both sides of the conflict apply his principles. This circular reasoning can be resolved through the use of advanced probability theory. A Bayesian Network Model not only provides a structured reasoning approach, but more importantly, it also can resolve the circular reasoning problem that has been identified.

Feature Markov Decision Processes (PhiMDPs) are well-suited for learning agents in general environments. Nevertheless, unstructured (Phi)MDPs are limited to relatively simple environments. Structured MDPs like Dynamic Bayesian Networks (DBNs) are used for large-scale real-world problems. In this article I extend PhiMDP to PhiDBN. The primary contribution is to derive a cost criterion that allows to automatically extract the most relevant features from the environment, leading to the "best" DBN representation. I discuss all building blocks required for a complete general learning algorithm.

Both intermittent and persistent faults may occur in a wide range of systems. We present in this paper the introduction of intermittent fault handling techniques into ProDiagnose, an algorithm that previously only handled persistent faults. We discuss novel algorithmic techniques as well as how our static Bayesian networks help diagnose, in an integrated manner, a range of intermittent and persistent faults. Through experiments with data from the ADAPT electrical power system test bed, generated as part of the Second International Diagnostic Competition (DXC-10), we show that this novel variant of ProDiagnose diagnoses intermittent faults accurately and quickly, while maintaining strong performance on persistent faults.

The concern for reducing aviation safety risk is rising as the National Airspace System in the United States transforms to the Next Generation Air Transportation System (NextGen). The NASA Aviation Safety Program is committed to developing an effective aviation safety technology portfolio to meet the challenges of this transformation and to mitigate relevant safety risks. The paper focuses on the reasoning of selecting Object-Oriented Bayesian Networks (OOBN) as the technique and commercial software for the accident modeling and portfolio assessment. To illustrate the benefits of OOBN in a large and complex aviation accident model, the in-flight Loss-of-Control Accident Framework (LOCAF) constructed as an influence diagram is presented. An OOBN approach not only simplifies construction and maintenance of complex causal networks for the modelers, but also offers a well-organized hierarchical network that is easier for decision makers to exploit the model examining the effectiveness of risk mitigation strategies through technology insertions.

The data-processing inequality, that is, $I(U;Y) \le I(U;X)$ for a Markov chain $U \to X \to Y$, has been the method of choice for proving impossibility (converse) results in information theory and many other disciplines. Various channel-dependent improvements (called strong data-processing inequalities, or SDPIs) of this inequality have been proposed both classically and more recently. In this note we first survey known results relating various notions of contraction for a single channel. Then we consider the basic extension: given SDPI for each constituent channel in a Bayesian network, how to produce an end-to-end SDPI? Our approach is based on the (extract of the) Evans-Schulman method, which is demonstrated for three different kinds of SDPIs, namely, the usual Ahslwede-G\'acs type contraction coefficients (mutual information), Dobrushin's contraction coefficients (total variation), and finally the $F_I$-curve (the best possible non-linear SDPI for a given channel). Resulting bounds on the contraction coefficients are interpreted as probability of site percolation. As an example, we demonstrate how to obtain SDPI for an $n$-letter memoryless channel with feedback given an SDPI for $n=1$. Finally, we discuss a simple observation on the equivalence of a linear SDPI and comparison to an erasure channel (in the sense of "less noisy" order). This leads to a simple proof of a curious inequality of Samorodnitsky (2015), and sheds light on how information spreads in the subsets of inputs of a memoryless channel.

Learning the network structure of a large graph is computationally demanding, and dynamically monitoring the network over time for any changes in structure threatens to be more challenging still. This paper presents a two-stage method for anomaly detection in dynamic graphs: the first stage uses simple, conjugate Bayesian models for discrete time counting processes to track the pairwise links of all nodes in the graph to assess normality of behavior; the second stage applies standard network inference tools on a greatly reduced subset of potentially anomalous nodes. The utility of the method is demonstrated on simulated and real data sets.

Our research question was whether we could develop a feasible technique, using Bayesian networks, to diagnose gaps in student knowledge. Thirty-four college-age participants completed tasks designed to measure conceptual knowledge, procedural knowledge, and problem-solving skills related to circuit analysis. A Bayesian network was used to model the knowledge dependencies among the circuit analysis concepts. Preliminary results suggested that the Bayesian network was generally working as intended. When high- and low-performing groups were formed on the basis of posterior probabilities, significant group differences were found favoring the high-performing group with respect to circuit definitions and circuit analysis problems, for both actual and self-assessments, and higher major GPA. The Bayesian network was able to predict participants' performance on a problem-solving item on average 75% of the time. The findings of this study are promising for our long-term goal of developing scalable and feasible online automated reasoning techniques to diagnose student knowledge gaps. (Contains 12 tables and 2 figures.) [Appended are: (1) Node-Voltage Analysis Problem-Solving Procedure (Kaiser, 2003); and (2) Bayesian Network.]

Our research question was whether we could develop a feasible technique, using Bayesian networks, to diagnose gaps in student knowledge. Thirty-four college-age participants completed tasks designed to measure conceptual knowledge, procedural knowledge, and problem-solving skills related to circuit analysis. A Bayesian network was used to model the knowledge dependencies among the circuit analysis concepts. Preliminary results suggested that the Bayesian network was generally working as intended. When high- and low-performing groups were formed on the basis of posterior probabilities, significant group differences were found favoring the high-performing group with respect to circuit definitions and circuit analysis problems, for both actual and self-assessments, and higher major GPA. The Bayesian network was able to predict participants' performance on a problem-solving item on average 75% of the time. The findings of this study are promising for our long-term goal of developing scalable and feasible online automated reasoning techniques to diagnose student knowledge gaps. (Contains 12 tables and 2 figures.) [Appended are: (1) Node-Voltage Analysis Problem-Solving Procedure (Kaiser, 2003); and (2) Bayesian Network.]

We investigate the problem of learning Bayesian networks in an agnostic model where an $\epsilon$-fraction of the samples are adversarially corrupted. Our agnostic learning model is similar to -- in fact, stronger than -- Huber's contamination model in robust statistics. In this work, we study the fully observable Bernoulli case where the structure of the network is given. Even in this basic setting, previous learning algorithms either run in exponential time or lose dimension-dependent factors in their error guarantees. We provide the first computationally efficient agnostic learning algorithm for this problem with dimension-independent error guarantees. Our algorithm has polynomial sample complexity, runs in polynomial time, and achieves error that scales nearly-linearly with the fraction of adversarially corrupted samples.

This research is about studying and comparing two different ways of building complex networks. The main goal of our study is to find an effective way to build networks, particularly when we have fewer observations than variables. We construct networks estimating the partial correlation coefficient on Classic Statistics (Inverse Method) and on Bayesian Statistics (Normal - Inverse Wishart conjugate prior). In this current work, in order to solve the problem of having less observations than variables, we propose a new methodology called local partial correlation, which consists of selecting, for each pair of variables, the other variables most correlated to the pair.We applied these methods on simulated data and compared them through ROC curves. The most attractive result is that, even though it has high computational costs, to use Bayesian inference on trees is better when we have less observations than variables. In other cases, both approaches present satisfactory results.

We are concerned with modeling the strength of links in networks by taking into account how often those links are used. Link usage is a strong indicator of how closely two nodes are related, but existing network models in Bayesian Statistics and Machine Learning are able to predict only wether a link exists at all. As priors for latent attributes of network nodes we explore the Chinese Restaurant Process (CRP) and a multivariate Gaussian with fixed dimensionality. The model is applied to a social network dataset and a word coocurrence dataset.

Bayesian graphical modeling provides an appealing way to obtain uncertainty estimates when inferring network structures, and much recent progress has been made for Gaussian models. These models have been used extensively in applications to gene expression data, even in cases where there appears to be significant deviations from the Gaussian model. For more robust inferences, it is natural to consider extensions to t-distribution models. We argue that the classical multivariate t-distribution, defined using a single latent Gamma random variable to rescale a Gaussian random vector, is of little use in highly multivariate settings, and propose other, more flexible t-distributions. Using an independent Gamma-divisor for each component of the random vector defines what we term the alternative t-distribution. The associated model allows one to extract information from highly multivariate data even when most experiments contain outliers for some of their measurements. However, the use of this alternative model comes at increased computational cost and imposes constraints on the achievable correlation structures, raising the need for a compromise between the classical and alternative models. To this end we propose the use of Dirichlet processes for adaptive clustering of the latent Gamma-scalars, each of which may then divide a group of latent Gaussian variables. Dirichlet processes are commonly used to cluster independent observations; here they are used instead to cluster the dependent components of a single observation. The resulting Dirichlet t-distribution interpolates naturally between the two extreme cases of the classical and alternative t-distributions and combines more appealing modeling of the multivariate dependence structure with favorable computational properties.

Unsupervised estimation of latent variable models is a fundamental problem central to numerous applications of machine learning and statistics. This work presents a principled approach for estimating broad classes of such models, including probabilistic topic models and latent linear Bayesian networks, using only second-order observed moments. The sufficient conditions for identifiability of these models are primarily based on weak expansion constraints on the topic-word matrix, for topic models, and on the directed acyclic graph, for Bayesian networks. Because no assumptions are made on the distribution among the latent variables, the approach can handle arbitrary correlations among the topics or latent factors. In addition, a tractable learning method via $\ell_1$ optimization is proposed and studied in numerical experiments.

Existing probabilistic approaches to automated reasoning impose severe restrictions on its knowledge representation scheme. Mainly, this is to ensure that there exists an effective inferencing algorithm. Unfortunately, this makes the application of these approaches to general domains quite difficult. In this paper, we present a new mode' called Bayesian multi-networks which uses a rule-based organization of knowledge quite natural for human experts modeling various domains. Furthermore, strong probabilistic semantics help quantify the knowledge. Combined with the rich structure of rule-based approaches, a general inference engine for Bayesian multi-networks is developed. Probabilistic reasoning, Constraint satisfaction, Linear programming, Temporal reasoning, Abductive explanation.

Existing probabilistic approaches to automated reasoning impose severe restrictions on its knowledge representation scheme. Mainly, this is to ensure that there exists an effective inferencing algorithm. Unfortunately, this makes the application of these approaches to general domains quite difficult. In this paper, we present a new mode' called Bayesian multi-networks which uses a rule-based organization of knowledge quite natural for human experts modeling various domains. Furthermore, strong probabilistic semantics help quantify the knowledge. Combined with the rich structure of rule-based approaches, a general inference engine for Bayesian multi-networks is developed. Probabilistic reasoning, Constraint satisfaction, Linear programming, Temporal reasoning, Abductive explanation.

Complex interactions between genes or proteins contribute a substantial part to phenotypic evolution. Here we develop an evolutionarily grounded method for the cross-species analysis of interaction networks by {\em alignment}, which maps bona fide functional relationships between genes in different organisms. Network alignment is based on a scoring function measuring mutual similarities between networks taking into account their interaction patterns as well as sequence similarities between their nodes. High-scoring alignments and optimal alignment parameters are inferred by a systematic Bayesian analysis. We apply this method to analyze the evolution of co-expression networks between human and mouse. We find evidence for significant conservation of gene expression clusters and give network-based predictions of gene function. We discuss examples where cross-species functional relationships between genes do not concur with sequence similarity.

Directed acyclic graph (DAG) models, also called Bayesian networks, impose conditional independence constraints on a multivariate probability distribution, and are widely used in probabilistic reasoning, machine learning and causal inference. If latent variables are included in such a model, then the set of possible marginal distributions over the remaining (observed) variables is generally complex, and not represented by any DAG. Larger classes of mixed graphical models, which use multiple edge types, have been introduced to overcome this; however, these classes do not represent all the models which can arise as margins of DAGs. In this paper we show that this is because ordinary mixed graphs are fundamentally insufficiently rich to capture the variety of marginal models. We introduce a new class of hyper-graphs, called mDAGs, and a latent projection operation to obtain an mDAG from the margin of a DAG. We show that each distinct marginal of a DAG model is represented by at least one mDAG, and provide graphical results towards characterizing when two such marginal models are the same. Finally we show that mDAGs correctly capture the marginal structure of causally-interpreted DAGs under interventions on the observed variables.

Toxic blooms of Lyngbya majuscula occur in coastal areas worldwide and have major ecological, health and economic consequences. The exact causes and combinations of factors which lead to these blooms are not clearly understood. Lyngbya experts and stakeholders are a particularly diverse group, including ecologists, scientists, state and local government representatives, community organisations, catchment industry groups and local fishermen. An integrated Bayesian network approach was developed to better understand and model this complex environmental problem, identify knowledge gaps, prioritise future research and evaluate management options.

This paper presents new results for the (partial) maximum a posteriori (MAP) problem in Bayesian networks, which is the problem of querying the most probable state configuration of some of the network variables given evidence. First, it is demonstrated that the problem remains hard even in networks with very simple topology, such as binary polytrees and simple trees (including the Naive Bayes structure). Such proofs extend previous complexity results for the problem. Inapproximability results are also derived in the case of trees if the number of states per variable is not bounded. Although the problem is shown to be hard and inapproximable even in very simple scenarios, a new exact algorithm is described that is empirically fast in networks of bounded treewidth and bounded number of states per variable. The same algorithm is used as basis of a Fully Polynomial Time Approximation Scheme for MAP under such assumptions. Approximation schemes were generally thought to be impossible for this problem, but we show otherwise for classes of networks that are important in practice. The algorithms are extensively tested using some well-known networks as well as random generated cases to show their effectiveness.

Observations depending on sums of random variables are common throughout many fields; however, no efficient solution is currently known for performing max-product inference on these sums of general discrete distributions (max-product inference can be used to obtain maximum a posteriori estimates). The limiting step to max-product inference is the max-convolution problem (sometimes presented in log-transformed form and denoted as "infimal convolution", "min-convolution", or "convolution on the tropical semiring"), for which no O(k log(k)) method is currently known. Here I present a O(k log(k)) numerical method for estimating the max-convolution of two nonnegative vectors (e.g., two probability mass functions), where k is the length of the larger vector. This numerical max-convolution method is then demonstrated by performing fast max-product inference on a convolution tree, a data structure for performing fast inference given information on the sum of n discrete random variables in O(n k log(n k) log(n) ) steps (where each random variable has an arbitrary prior distribution on k contiguous possible states). The numerical max-convolution method can be applied to specialized classes of hidden Markov models to reduce the runtime of computing the Viterbi path from n k^2 to n k log(k), and has potential application to the all-pairs shortest paths problem.

In this paper, we discuss how Bayesian networks can be used to develop automated situation-assessment tools suitable for use as decision aids in a command and control system. Inevitably, the introduction of a new technology raises a number of validation, systems integration and human-factors questions. Those issues pertinent to Bayesian network decision aids are identified and their implications discussed. We then describe in detail the implementation of such a system capable of providing Combat-ID and Threat Assessment advisories in the naval anti-air warfare role and its assessment within a realistic (synthetic) human-in-the-loop experiment. We discuss the experimental system, the experimental design and protocol and the experimental results. In a controlled experiment using 14 subjects with relevant military experience we found that the Bayes' net decision aid system was preferred by the majority of the experimental subjects and led to a number of operator performance improvements which could directly contribute to improved operational effectiveness.

This report demonstrates the application of Bayesian networks for modelling and reasoning about uncertainties. A scenario for naval anti-surface warfare is constructed and Bayesian networks are used to represent and update uncertainties encountered in the process of situation assessment. Concepts from information theory are used to provide a measure of uncertainty and understand its flow in a Bayesian network. This in turn yields analytical methods to formulate various effectiveness measures.

We consider the problem of distributed estimation under the Bayesian criterion and explore the design of optimal quantizers in such a system. We show that, for a conditionally unbiased and efficient estimator at the fusion center and when local observations have identical distributions, it is optimal to partition the local sensors into groups, with all sensors within a group using the same quantization rule. When all the sensors use identical number of decision regions, use of identical quantizers at the sensors is optimal. When the network is constrained by the capacity of the wireless multiple access channel over which the sensors transmit their quantized observations, we show that binary quantizers at the local sensors are optimal under certain conditions. Based on these observations, we address the location parameter estimation problem and present our optimal quantizer design approach. We also derive the performance limit for distributed location parameter estimation under the Bayesian criterion and find the conditions when the widely used threshold quantizer achieves this limit. We corroborate this result using simulations. We then relax the assumption of conditionally independent observations and derive the optimality conditions of quantizers for conditionally dependent observations. Using counter-examples, we also show that the previous results do not hold in this setting of dependent observations and, therefore, identical quantizers are not optimal.

In this paper, we present an infinite hierarchical non-parametric Bayesian model to extract the hidden factors over observed data, where the number of hidden factors for each layer is unknown and can be potentially infinite. Moreover, the number of layers can also be infinite. We construct the model structure that allows continuous values for the hidden factors and weights, which makes the model suitable for various applications. We use the Metropolis-Hastings method to infer the model structure. Then the performance of the algorithm is evaluated by the experiments. Simulation results show that the model fits the underlying structure of simulated data.

Process mining is a technique that performs an automatic analysis of business processes from a log of events with the promise of understanding how processes are executed in an organisation. Several models have been proposed to address this problem, however, here we propose a different approach to deal with uncertainty. By uncertainty, we mean estimating the probability of some sequence of tasks occurring in a business process, given that only a subset of tasks may be observable. In this sense, this work proposes a new approach to perform process mining using Bayesian Networks. These structures can take into account the probability of a task being present or absent in the business process. Moreover, Bayesian Networks are able to automatically learn these probabilities through mechanisms such as the maximum likelihood estimate and EM clustering. Experiments made over a Loan Application Case study suggest that Bayesian Networks are adequate structures for process mining and enable a deep analysis of the business process model that can be used to answer queries about that process.

Understanding information exchange and aggregation on networks is a central problem in theoretical economics, probability and statistics. We study a standard model of economic agents on the nodes of a social network graph who learn a binary "state of the world" S, from initial signals, by repeatedly observing each other's best guesses. Asymptotic learning is said to occur on a family of graphs G_n = (V_n, E_n), with |V_n| tending to infinity, if with probability tending to 1 as n tends to infinity all agents in G_n eventually estimate S correctly. We identify sufficient conditions for asymptotic learning and contruct examples where learning does not occur when the conditions do not hold.

Understanding information exchange and aggregation on networks is a central problem in theoretical economics, probability and statistics. We study a standard model of economic agents on the nodes of a social network graph who learn a binary "state of the world" S, from initial signals, by repeatedly observing each other's best guesses. Asymptotic learning is said to occur on a family of graphs G_n = (V_n, E_n), with |V_n| tending to infinity, if with probability tending to 1 as n tends to infinity all agents in G_n eventually estimate S correctly. We identify sufficient conditions for asymptotic learning and contruct examples where learning does not occur when the conditions do not hold.

Recently developed techniques have made it possible to quickly learn accurate probability density functions from data in low-dimensional continuous spaces. In particular. mixtures of Gaussians can be fitted to data very quickly using an accelerated EM algorithm that employs multiresolution kd-trees (Moore 1999). In this paper, we propose a kind of Bayesian network in which low-dimensional mixtures of Gaussians over different subsets of the domain's variables are combined into a coherent joint probability model over the entire domain. The network is also capable of modelling complex dependencies between discrete variables and continuous variables without requiring discretization of the continuous variables. We present efficient heuristic algorithms for automatically learning these networks from data and perform comparative experiments illustrating how well these networks model real scientific data and synthetic data. We also briefly discuss some possible improvements to the networks. as well as their possible application to anomaly detection, classification probabilistic inference, and compression.

Correctly identifying tracks is a difficult but important capability for U.S. Navy ships and aircraft. It is difficult because of the inherent uncertainty, complexity, and short timelines involved. It is important because the price of failure is missed or civilian engagements and fratricide. Today, Navy ships and aircraft primarily use an If-Then rule-based system in evaluating radar and IFF information to perform Combat Identification (CID). To cope with the uncertainty and complexity of CID, Bayesian Networks have been suggested to integrate radar, IFF, and other lower quality sources to perform the identification determination. The goal of this project is to show that Bayesian Networks can be used to support CID investment decisions. Two investments, a new sensor and good maintenance, were compared in a difficult CID scenario in four different environments. The paper applies techniques from decision analysis and Bayesian networks to address the challenges of CID. The CID network was developed using good knowledge engineering practices.

The performed project focused on a new paradigm of planning systems that are based on a combination of Bayesian networks and structural equation models. We focused on theoretical issues that surround combining the two in a practical planning system, developing the foundations for, and building a prototype of such system. The approach and the system built allow for efficient, yet normatively correct, treatment of various types of information, uncertainty, and utility. It is especially powerful in complex situations where the available information is heterogeneous and consists of a mixture of deterministic and uncertain relationships among discrete and continuous variables. Our main contributions are: (1) two state of the art stochastic sampling algorithm for approximate inference in graphical models, both (2) analysis of problems related to combining probabilistic information, (3) an module for interactive construction of causal graphical models and search for opportunities, (4) algorithm for learning graphical models from small data sets, and (5) a prototype of the system, used by over 5,000 people world-wide.

To learn (statistical) dependencies among random variables requires exponentially large sample size in the number of observed random variables if any arbitrary joint probability distribution can occur. We consider the case that sparse data strongly suggest that the probabilities can be described by a simple Bayesian network, i.e., by a graph with small in-degree \Delta. Then this simple law will also explain further data with high confidence. This is shown by calculating bounds on the VC dimension of the set of those probability measures that correspond to simple graphs. This allows to select networks by structural risk minimization and gives reliability bounds on the error of the estimated joint measure without (in contrast to a previous paper) any prior assumptions on the set of possible joint measures. The complexity for searching the optimal Bayesian networks of in-degree \Delta increases only polynomially in the number of random varibales for constant \Delta and the optimal joint measure associated with a given graph can be found by convex optimization.

To learn (statistical) dependencies among random variables requires exponentially large sample size in the number of observed random variables if any arbitrary joint probability distribution can occur. We consider the case that sparse data strongly suggest that the probabilities can be described by a simple Bayesian network, i.e., by a graph with small in-degree \Delta. Then this simple law will also explain further data with high confidence. This is shown by calculating bounds on the VC dimension of the set of those probability measures that correspond to simple graphs. This allows to select networks by structural risk minimization and gives reliability bounds on the error of the estimated joint measure without (in contrast to a previous paper) any prior assumptions on the set of possible joint measures. The complexity for searching the optimal Bayesian networks of in-degree \Delta increases only polynomially in the number of random varibales for constant \Delta and the optimal joint measure associated with a given graph can be found by convex optimization.

In this paper, we establish some theoretical connections between Sum-Product Networks (SPNs) and Bayesian Networks (BNs). We prove that every SPN can be converted into a BN in linear time and space in terms of the network size. The key insight is to use Algebraic Decision Diagrams (ADDs) to compactly represent the local conditional probability distributions at each node in the resulting BN by exploiting context-specific independence (CSI). The generated BN has a simple directed bipartite graphical structure. We show that by applying the Variable Elimination algorithm (VE) to the generated BN with ADD representations, we can recover the original SPN where the SPN can be viewed as a history record or caching of the VE inference process. To help state the proof clearly, we introduce the notion of {\em normal} SPN and present a theoretical analysis of the consistency and decomposability properties. We conclude the paper with some discussion of the implications of the proof and establish a connection between the depth of an SPN and a lower bound of the tree-width of its corresponding BN.

We propose a new inequality that we call the conditional ageing inequality (CAIN). The CAIN is a slight generalization to non-equilibrium situations of the Second Law of thermodynamics. The goal of this paper is to study the consequences of the CAIN. We use the CAIN to discuss Maxwell demon processes (i.e., thermodynamic processes with feedback.) In particular, we apply the CAIN to four cases of the Szilard engine: for a classical or a quantum system with either one or two correlated particles. Besides proposing this new inequality that we call the CAIN, another novel feature of this paper is that we use quantum Bayesian networks for our analysis of Maxwell demon processes.

Network data are increasingly collected along with other variables of interest. Our motivation is drawn from neurophysiology studies measuring brain connectivity networks for a sample of individuals along with their membership to a low or high creative reasoning group. It is of paramount importance to develop statistical methods for testing of global and local changes in the structural interconnections among brain regions across groups. We develop a general Bayesian procedure for inference and testing of group differences in the network structure, which relies on a nonparametric representation for the conditional probability mass function associated with a network-valued random variable. By leveraging a mixture of low-rank factorizations, we allow simple global and local hypothesis testing adjusting for multiplicity. An efficient Gibbs sampler is defined for posterior computation. We provide theoretical results on the flexibility of the model and assess testing performance in simulations. The approach is applied to provide novel insights on the relationships between human brain networks and creativity.

A general notion of algebraic conditional plausibility measures is defined. Probability measures, ranking functions, possibility measures, and (under the appropriate definitions) sets of probability measures can all be viewed as defining algebraic conditional plausibility measures. It is shown that algebraic conditional plausibility measures can be represented using Bayesian networks.

Explains how Bayesian networks can tackle the limitations of pure data-driven statistical machine learning methods when applied to observational data. This is the lecture I was due to present at the NHS Health and Care Analytics Conference, 5 July 2023. For the back story on this see: https://wherearethenumbers.substack.com/p/an-update-on-my-nhs-conference-cancellation

Consistency-based diagnosis relies heavily on the assumption that discrepancies between model predictions and sensor observations can be detected accurately. When sources of uncertainty like sensor noise and model abstraction exist robust schemes have to be designed to make a binary decision on whether predictions are consistent with observations. This risks the occurrence of false alarms and missed alarms when an erroneous decision is made. Moreover when multiple sensors (with differing sensing properties) are available the degree of match between predictions and observations can be used to guide the search for fault candidates. In this paper we propose a novel approach to handle this problem using Bayesian networks. In the consistency- based diagnosis formulation, automatically generated Bayesian networks are used to encode a probabilistic measure of fit between predictions and observations. A Bayesian network inference algorithm is used to compute most probable fault candidates.

Portfolio methods support the combination of different algorithms and heuristics, including stochastic local search (SLS) heuristics, and have been identified as a promising approach to solve computationally hard problems. While successful in experiments, theoretical foundations and analytical results for portfolio-based SLS heuristics are less developed. This article aims to improve the understanding of the role of portfolios of heuristics in SLS. We emphasize the problem of computing most probable explanations (MPEs) in Bayesian networks (BNs). Algorithmically, we discuss a portfolio-based SLS algorithm for MPE computation, Stochastic Greedy Search (SGS). SGS supports the integration of different initialization operators (or initialization heuristics) and different search operators (greedy and noisy heuristics), thereby enabling new analytical and experimental results. Analytically, we introduce a novel Markov chain model tailored to portfolio-based SLS algorithms including SGS, thereby enabling us to analytically form expected hitting time results that explain empirical run time results. For a specific BN, we show the benefit of using a homogenous initialization portfolio. To further illustrate the portfolio approach, we consider novel additive search heuristics for handling determinism in the form of zero entries in conditional probability tables in BNs. Our additive approach adds rather than multiplies probabilities when computing the utility of an explanation. We motivate the additive measure by studying the dramatic impact of zero entries in conditional probability tables on the number of zero-probability explanations, which again complicates the search process. We consider the relationship between MAXSAT and MPE, and show that additive utility (or gain) is a generalization, to the probabilistic setting, of MAXSAT utility (or gain) used in the celebrated GSAT and WalkSAT algorithms and their descendants. Utilizing our Markov chain framework, we show that expected hitting time is a rational function - i.e. a ratio of two polynomials - of the probability of applying an additive search operator. Experimentally, we report on synthetically generated BNs as well as BNs from applications, and compare SGSs performance to that of Hugin, which performs BN inference by compilation to and propagation in clique trees. On synthetic networks, SGS speeds up computation by approximately two orders of magnitude compared to Hugin. In application networks, our approach is highly competitive in Bayesian networks with a high degree of determinism. In addition to showing that stochastic local search can be competitive with clique tree clustering, our empirical results provide an improved understanding of the circumstances under which portfolio-based SLS outperforms clique tree clustering and vice versa.

Since the use of information and communication technologies has now become indispensable for the development of human activity, governments have assumed the responsibility of ensuring access to them, as is the case in Mexico, generating a series of public policies aimed at that end. However, these politics have not generated the expected results since there are yet large differences to internet connectivity. This research presents an analysis of the availability and use of information and communication technologies. Diverse studies indicate that there is a verifiable inequality in terms of access to technologies, this difference is remarkable between municipalities and between regions. The analysis has allowed to know the main activities that the population makes through the ICT with the objective of determining the actions in matters of digital policies that must be considered by the local government. From the analysis performed it can be concluded that the majority of the population that Internet accesses does it through a desktop, laptop computer or a mobile phone. The most actions performed by the population through the internet are actions of entertainment and downloading software, as well as the search for general information, but participating in government affairs is not a priority issue. The population interested in public affairs is the one with the highest educational level, then that the institution requires the development of mechanisms to strengthen citizen participation in the taking of public affairs. It is also required to increase the communications infrastructure then that a greater percentage of the population can access the Internet. The programs on the use of technologies that must be developed by the government must be adapted. The study shows that the completion of procedures is not a priority issue, then that the implementation of electronic services may not have much impact on the Entity. It is necessary at first then to promote the development of the population's capacities to use of communication technologies. As a result, in this moment not have conditions to guarantee the success of an e-government policy such as the implementation of electronic payments and the use of mobile applications. It is necessary to overcome connectivity deficiencies and develop digital literacy actions to ensure the productive use of technologies. Elia Martínez | Guillermo De la Torre-Gea"Analysis of the ICT user Profile for e-goverment through Bayesian Networks" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-2 , February 2018, URL: http://www.ijtsrd.com/papers/ijtsrd2407.pdf Article URL: http://www.ijtsrd.com/other-scientific-research-area/other/2407/analysis-of-the-ict-user-profile-for-e-goverment--through-bayesian-networks/elia-martínez

The IBIS system provides a means of correlating the images of two breech face or firing pin impressions. Cartridges fired by the same gun result in similar images and thus higher scores. The generated scores, together with related firearm and ammunition information were transformed into a Bayesian network. Bayesian networks allow for the assessment of evidence based upon two propositions (same gun ordifferent gun). This allows a forensic scientist to provide insight to courts and investigators as to the value of the evidence.The breech face (BF) and firing pin (FP) scores, and their product, were used to assess the ability of the system to classify an unknowncartridge case into a same-gun or different-gun category. The IBIS system does not provide for an easy means to use the combination of the BF and FP scores. Twenty sets of known and questioned cartridge cases, from a large collection which had been analyzed by operational firearms examiners, were examined and tested using the Bayesian networks. Out of the 20 comparisons, there were eight true positives, seven true negatives, five false negatives, and zero false positives. In all instances of eliminations, the support for the different-gun hypothesis was, at minimum, strong.

The IBIS system provides a means of correlating the images of two breech face or firing pin impressions. Cartridges fired by the same gun result in similar images and thus higher scores. The generated scores, together with related firearm and ammunition information were transformed into a Bayesian network. Bayesian networks allow for the assessment of evidence based upon two propositions (same gun ordifferent gun). This allows a forensic scientist to provide insight to courts and investigators as to the value of the evidence.The breech face (BF) and firing pin (FP) scores, and their product, were used to assess the ability of the system to classify an unknowncartridge case into a same-gun or different-gun category. The IBIS system does not provide for an easy means to use the combination of the BF and FP scores. Twenty sets of known and questioned cartridge cases, from a large collection which had been analyzed by operational firearms examiners, were examined and tested using the Bayesian networks. Out of the 20 comparisons, there were eight true positives, seven true negatives, five false negatives, and zero false positives. In all instances of eliminations, the support for the different-gun hypothesis was, at minimum, strong.

When a posterior distribution has multiple modes, unconditional expectations, such as the posterior mean, may not offer informative summaries of the distribution. Motivated by this problem, we propose to decompose the sample space of a multimodal distribution into domains of attraction of local modes. Domain-based representations are defined to summarize the probability masses of and conditional expectations on domains of attraction, which are much more informative than the mean and other unconditional expectations. A computational method, the multi-domain sampler, is developed to construct domain-based representations for an arbitrary multimodal distribution. The multi-domain sampler is applied to structural learning of protein-signaling networks from high-throughput single-cell data, where a signaling network is modeled as a causal Bayesian network. Not only does our method provide a detailed landscape of the posterior distribution but also improves the accuracy and the predictive power of estimated networks.

Maternal mortality has shown a considerable decrease in countries where the rate of development is higher. This is not the case for Mexico where a large number of annual maternal deaths are still perceived, which turns out to be a public health problem in which the World Health Organization (WHO) considers indigenous populations with a higher rate of maternal deaths, as is the case in the state of Oaxaca. The aim of this paper is to carry out an analysis of maternal deaths during the period 2014-2016 in the municipalities of this state in order to identify the main causes that cause it, factors that intervene in it and municipalities with the highest rate of this problem. The analysis has revealed that the National Institute of Social Security (IMSS) is the site where the highest number of deaths occurred, as well as identifying the main causes that lead to maternal mortality, determining that it is not enough to have Public and Private Health institutions, but they must have a better care system and equipment for care, without leaving aside the cultural aspect of the inhabitants of the municipalities of the state of Oaxaca. Araceli Pinacho-Ríos | Guillermo De la Torre-Gea"Analysis of Maternal Deaths in Oaxaca through Bayesian Networks" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-2 , February 2018, URL: http://www.ijtsrd.com/papers/ijtsrd10758.pdf  http://www.ijtsrd.com/computer-science/data-miining/10758/analysis-of-maternal-deaths-in-oaxaca-through-bayesian-networks/araceli-pinacho-ríos