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

A complex hardware system experiences several different types of failure modes when deployed in its field of use. Although each failure mode merits its very own root cause analysis, experience has shown us that a majority of root cause analyses require us to answer a very similar set of questions. These recurring questions often use very similar type of field data to be answered. For example, usage parameters such as hours of operation, total power cycles, vibration fatigue, etc. are used almost always while trying to figure out the failure mechanism. By taking advantage of this, we can automate the process of finding the most likely failure mechanism for a given failure mode. In the current work, we start by computing what we believe are parameters that are most relevant across all different types of failure modes. Once these parameters are computed, we will build a Bayesian Network to model the cause-effect relationship between the degradation parameters (cause) and failure modes(effect) that occur on the field. Bayesian Network is a probabilistic graphical model which concisely describes the relationship between many random variables and their conditional independence via an acyclic directed graph. Once the topology of the Bayesian network is laid out by a domain expert, the conditional probabilities can be learnt from existing data, thereby completely describing the system using the notion of joint probabilities. Two real life field issues are used as examples to demonstrate the accuracy of the network once it is modelled and built. This paper demonstrates that accurately modelling the hardware system as a Bayesian Network substantially accelerates the process of root cause analysis.

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.

Use of a Bayesian network for Red Listing under uncertainty

Chapter 11 Bayesian Networks

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.

This paper gives an approach for fusing the directed acyclic graphs (DAGs) of BNs, an important and popular probabilistic graphical model (PGM). Considering conditional independence as the semantics implied in a BN, we focus on the DAG fusion while preserving the semantics in all participating BNs. Based on the concept and properties of Markov equivalence, we respectively give the algorithms for fusing equivalent and inequivalent common subgraphs of all participating BNs.KeywordsProbabilistic graphical model (PGM)Bayesian network (BN)FusionConditional independenceMarkov equivalence

Query processing over uncertain data has gained growing attention, because it is necessary to deal with uncertain data in many real-life applications. In this paper, we investigate skyline queries over uncertain data in distributed environments (DSUD query) whose research is only in an early stage. The state-of-the-art algorithm, called e-DSUD algorithm, is designed for processing this query. It has the desirable characteristics of progressiveness and minimum bandwidth consumption. However, it still needs to be perfected in three aspects. (1) Progressiveness. Each time it only returns one query result at most. (2) Efficiency. There are a significant amount of redundant I/O cost and numerous iterations which causes a long total query time. (3) Universality. It is restricted to the case where local skyline tuples are incomparability. To address these concerns, we first present a detailed analysis of the e-DSUD algorithm and then develop an improved framework for the DSUD query, namely IDSUD. Based on the new framework, we propose an adaptive algorithm, called ADSUD, for the DSUD query. In the algorithm, we redefine the approximate global skyline probability and choose local representative tuples due to minimum probabilistic bounding rectangle adaptively. Furthermore, we design a progressive pruning method and apply the reuse mechanism to improve its efficiency. The results of extensive experiments verify the better overall performance of our algorithm than the e-DSUD algorithm.

A Bayesian network is a graphical model that encodes probabilistic relationships among variables of interest. When used in conjunction with statistical techniques, the graphical model has several advantages for data analysis. One, because the model encodes dependencies among all variables, it readily handles situations where some data entries are missing. Two, a Bayesian network can be used to learn causal relationships, and hence can be used to gain understanding about a problem domain and to predict the consequences of intervention. Three, because the model has both a causal and probabilistic semantics, it is an ideal representation for combining prior knowledge (which often comes in causal form) and data. Four, Bayesian statistical methods in conjunction with Bayesian networks offer an efficient and principled approach for avoiding the overfitting of data. In this paper, we discuss methods for constructing Bayesian networks from prior knowledge and summarize Bayesian statistical methods for using data to improve these models. With regard to the latter task, we describe methods for learning both the parameters and structure of a Bayesian network, including techniques for learning with incomplete data. In addition, we relate Bayesian-network methods for learning to techniques for supervised and unsupervised learning. We illustrate the graphical-modeling approach using a real-world case study.

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.

Cyberbullying (CB) has emerged as a growing concern among adolescents, with nearly 10% of European children affected monthly and almost half experiencing it at least once. Unlike traditional bullying, CB thrives in digital environments where anonymity and impunity are prevalent. Despite its increasing prevalence, understanding the causal mechanisms behind CB remains challenging due to the limitations of conventional statistical methods, which often rely on correlations and are prone to spurious associations. In this paper, we introduce a novel human–machine consensus framework for causal discovery, aimed at supporting social scientists in unraveling the complex dynamics of CB. We leverage recent advances in data-driven causal inference, particularly the use of Directed Acyclic Graphs (DAGs), to identify and interpret causal relationships from observational data. Our approach integrates automatic causal discovery algorithms with expert knowledge, addressing the limitations of both purely algorithmic and purely expert-driven methods, and allows for the creation of a model ensemble estimation of the causal effects. To enhance interpretability and usability, we advocate for the use of Probabilistic Graphical Causal Models (PGCMs), or Bayesian Networks, which combine probabilistic reasoning with graphical representation. This hybrid methodology not only mitigates cognitive biases and inconsistencies in expert input but also fosters transparency and critical reflection in model construction. Cyberbullying serves as a compelling case study where ethical constraints preclude experimental designs, highlighting the value of interpretable, expert-informed causal models for guiding policy and intervention strategies.

Adjusting for Selection Effects in Epidemiologic Studies

This research evaluates the impact of the Online Collaborative Information System for strengthening tourism capacities in the local communities of the Sacred Lake, southern Puno–Peru. Using a predictive quantitative research approach, conditional relationships between sociodemographic variables are modeled based on a causality analysis with graphical and probabilistic representation, conditional probability tables, estimation of the Directed Acyclic Graph (DAG) structure, and conditional independence tests and scores of Bayesian Networks (BN). A survey was conducted with 608 residents from the rural communities of Luquina, Titilaca, Socca, and Thunuhuaya regarding the use of an Online Collaborative Information System to strengthen community-based rural tourism. The results show that the design of a probabilistic Bayesian network accurately describes conditional dependency interrelations among sociodemographic variables associated with the Collaborative Information System. The educational level variable directly influences tourism strengthening, with technological interaction—device use, software applications, internet access, and social networks—acting as key elements for supporting service quality and equitable distribution of benefits among community members. The study provides empirical evidence on the role of Information and Communication Technologies (ICT) in Community-Based Rural Tourism (CBRT), generating inputs to guide public policies and intervention plans that promote local self-determination, equity, and cultural-environmental conservation in high Andean contexts.

Directed acyclic graphs (DAGs) play a large role in the modern approach to causal inference. DAGs describe the relationship between measurements taken at various discrete times including the effect of interventions. The causal mechanisms, on the other hand, would naturally be assumed to be a continuous process operating over time in a cause–effect fashion. How does such immediate causation, that is causation occurring over very short time intervals, relate to DAGs constructed from discrete observations? We introduce a time-continuous model and simulate discrete observations in order to judge the relationship between the DAG and the immediate causal model. We find that there is no clear relationship; indeed the Bayesian network described by the DAG may not relate to the causal model. Typically, discrete observations of a process will obscure the conditional dependencies that are represented in the underlying mechanistic model of the process. It is therefore doubtful whether DAGs are always suited to describe causal relationships unless time is explicitly considered in the model. We relate the issues to mechanistic modeling by using the concept of local (in)dependence. An example using data from the Swiss HIV Cohort Study is presented.

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.

Causal manipulation theorems proposed by Spirtes et al. and Pearl in the context of directed probabilistic graphs, such as Bayesian networks, offer a simple and theoretically sound formalism for predicting the effect of manipulation of a system from its causal model. While the theorems are applicable to a wide variety of equilibrium causal models, they do not address the issue of reversible causal mechanisms, i.e. mechanisms that are capable of working in several directions, depending on which of their variables are manipulated exogenously. An example involving reversible causal mechanisms is the power train of a car: normally the engine moves the transmission which, in turn, moves the wheels; when the car goes down the hill, however, the driver may want to use the power train to slow down the car, i.e. let the wheels move the transmission, which then moves the engine. Some probabilistic systems can also be symmetric and reversible. For example, the noise introduced by a noisy communication channel does not usually depend on the direction of data transmission. In this paper, we investigate whether Bayesian networks are capable of representing reversible causal mechanisms. Building on the result of Druzdzel and Simon (1993), which shows that conditional probability tables in Bayesian networks can be viewed as descriptions of causal mechanisms, we study the conditions under which a conditional probability table can represent a reversible causal mechanism. Our analysis shows that conditional probability tables are capable of modelling reversible causal mechanisms but only when they fulfill the condition of soundness, which is equivalent to injectivity in equations. While this is a rather strong condition, there exist systems where our finding and the resulting framework are directly applicable.