Bayesian Network

Recent work in supervised learning has shown that a surprisingly simple Bayesian classifier with strong assumptions of independence among features, called naive Bayes, is competitive with state-of-the-art classifiers such as C4.5. This fact raises the question of whether a classifier with less restrictive assumptions can perform even better. In this paper we evaluate approaches for inducing classifiers from data, based on the theory of learning Bayesian networks. These networks are factored representations of probability distributions that generalize the naive Bayesian classifier and explicitly represent statements about independence. Among these approaches we single out a method we call Tree Augmented Naive Bayes (TAN), which outperforms naive Bayes, yet at the same time maintains the computational simplicity (no search involved) and robustness that characterize naive Bayes. We experimentally tested these approaches, using problems from the University of California at Irvine repository, and compared them to C4.5, naive Bayes, and wrapper methods for feature selection.

Background: Elucidating gene regulatory networks is crucial for understanding normal cell physiology and complex pathologic phenotypes. Existing computational methods for the genomewide "reverse engineering" of such networks have been successful only for lower eukaryotes with simple genomes. Here we present ARACNE, a novel algorithm, using microarray expression profiles, specifically designed to scale up to the complexity of regulatory networks in mammalian cells, yet general enough to address a wider range of network deconvolution problems. This method uses an information theoretic approach to eliminate the majority of indirect interactions inferred by coexpression methods.

Table of contents 1. Introduction 11. Drop-loser and add-arm design 2. Classic design 12. Biomarker-adaptive design 3. Theory of adaptive design 13. Adaptive treatment switching and crossover 4. Method with direct combination of P-values 14. Response-adaptive allocation design 5. Method with inverse-Normal P-values 15. Adaptive dose finding design 6. Implementation of K-stage adaptive designs 16. Bayesian adaptive design 7. Conditional error function method 17. Planning, execution, analysis, and reporting 8. Recursive adaptive design 18. Paradox-debates in adaptive designs 9. Sample-size re-estimation design A. Random number generation 10. Multiple-endpoint adaptive design B. Implementing adaptive designs in R Readership: Biostatisticians, medical researchers, and those engaged in areas of pharmaceutical research and development. This easy-to-read book provides the reader with a unified and concise presentation of adaptive design theories; together with computer programs written in SAS and R for the design and simulation of adaptive trials. Compared to a classic trial design with static features, an adaptive design allows for changing or modifying the characteristics of a trial based on accumulated information gathered during an ongoing trial. Such adaptations are made because they can improve the efficiency of the trial design, provide earlier remedies, and reduce the time and cost of drug development-clearly, in addition to their ethical importance! Practical examples are provided throughout the text that are motivated by real issues in aspects of clinical trialsparticularly, stopping a trial early if either the risk to subjects outweighs the benefit or there is evidence of efficacy for a safe drug. The last chapter in the book presents a discussion of controversial issues surrounding statistical theories, and highlights future research and the application of adaptive designs. The text, computer programs and data sets will be of value to both practitioners and students alike.

This paper provides algorithms that use an information-theoretic analysis to learn Bayesian network structures from data. Based on our three-phase learning framework, we develop efficient algorithms that can effectively learn Bayesian networks, requiring only polynomial numbers of conditional independence (CI) tests in typical cases. We provide precise conditions that specify when these algorithms are guaranteed to be correct as well as empirical evidence (from real world applications and simulation tests) that demonstrates that these systems work efficiently and reliably in practice. 

Supervised classification is one of the tasks most frequently carried out by so-called Intelligent Systems. Thus, a large number of techniques have been developed based on Artificial Intelligence (Logic-based techniques, Perceptron-based techniques) and Statistics (Bayesian Networks, Instance-based techniques). The goal of supervised learning is to build a concise model of the distribution of class labels in terms of predictor features.

Bayesian networks provide a language for qualitatively representing the conditional independence properties of a distribution. This allows a natural and compact representation of the distribution, eases knowledge acquisition, and supports effective inference algorithms. It is well-known, however, that there are certain independencies that we cannot capture qualitatively within the Bayesian network structure: independencies that hold only in certain contexts, i.e., given a specific assignment of values to certain variables. In this paper, we propose a formal notion of context-specific independence (CSI), based on regularities in the conditional probability tables (CPTs) at a node. We present a technique, analogous to (and based on) d-separation, for determining when such independence holds in a given network. We then focus on a particular qualitative representation scheme---tree-structured CPTs---for capturing CSI. We suggest ways in which this representation can be used to support effective inference algorithms. In particular, we present a structural decomposition of the resulting network which can improve the performance of clustering algorithms, and an alternative algorithm based on cutset conditioning.

Bayesian Networks (BN) provide a robust probabilistic method of reasoning under uncertainty. They have been successfully applied in a variety of real-world tasks but they have received little attention in the area of dependability. The present paper is aimed at exploring the capabilities of the BN formalism in the analysis of dependable systems. To this end, the paper compares BN with one of the most popular techniques for dependability analysis of large, safety critical systems, namely Fault Trees (FT). The paper shows that any FT can be directly mapped into a BN and that basic inference techniques on the latter may be used to obtain classical parameters computed from the former (i.e. reliability of the Top Event or of any sub-system, criticality of components, etc). Moreover, by using BN, some additional power can be obtained, both at the modeling and at the analysis level. At the modeling level, several restrictive assumptions implicit in the FT methodology can be removed and various kinds of dependencies among components can be accommodated. At the analysis level, a general diagnostic analysis can be performed. The comparison of the two methodologies is carried out by means of a running example, taken from the literature, that consists of a redundant multiprocessor system. ᭧

Two Bayesian-network structures are said to be equivalent if the set of distributions that can be represented with one of those structures is identical to the set of distributions that can be represented with the other. Many scoring criteria that are used to learn Bayesiannetwork structures from data are score equivalent; that is, these criteria do not distinguish among networks that are equivalent. In this paper, we consider using a score equivalent criterion in conjunction with a heuristic search algorithm to perform model selection or model averaging. We argue that it is often appropriate to search among equivalence classes of network structures as opposed to the more common approach of searching among individual Bayesian-network structures. We describe a convenient graphical representation for an equivalence class of structures, and introduce a set of operators that can be applied to that representation by a search algorithm to move among equivalence classes. We show that our equivalence-class operators can be scored locally, and thus share the computational efficiency of traditional operators defined for individual structures. We show experimentally that a greedy model-selection algorithm using our representation yields slightly higherscoring structures than the traditional approach without any additional time overhead, and we argue that more sophisticated search algorithms are likely to benefit much more.

Motivation: Network inference algorithms are powerful computational tools for identifying putative causal interactions among variables from observational data. Bayesian network inference algorithms hold particular promise in that they can capture linear, non-linear, combinatorial, stochastic and other types of relationships among variables across multiple levels of biological organization. However, challenges remain when applying these algorithms to limited quantities of experimental data collected from biological systems. Here, we use a simulation approach to make advances in our dynamic Bayesian network (DBN) inference algorithm, especially in the context of limited quantities of biological data. Results: We test a range of scoring metrics and search heuristics to find an effective algorithm configuration for evaluating our methodological advances. We also identify sampling intervals and levels of data discretization that allow the best recovery of the simulated networks. We develop a novel influence score for DBNs that attempts to estimate both the sign (activation or repression) and relative magnitude of interactions among variables. When faced with limited quantities of observational data, combining our influence score with moderate data interpolation reduces a significant portion of false positive interactions in the recovered networks. Together, our advances allow DBN inference algorithms to be more effective in recovering biological networks from experimentally collected data. Availability: Source code and simulated data are available upon request. Contact:

We introduce a compact graph-theoretic representation for multi-party game theory. Our main result is a provably correct and efficient algorithm for computing approximate Nash equilibria in one-stage games represented by trees or sparse graphs.

Learning Bayesian networks is often cast as an optimization problem, where the computational task is to find a structure that maximizes a statistically motivated score. By and large, existing learning tools address this optimization problem using standard heuristic search techniques. Since the search space is extremely large, such search procedures can spend most of the time examining candidates that are extremely unreasonable. This problem becomes critical when we deal with data sets that are large either in the number of instances, or the number of attributes.

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 modeling. 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.

The popularity of wireless networks has increased in recent years and is becoming a common addition to LANs. In this paper we investigate a novel use for a wireless network based on the IEEE 802.11 standard: inferring the location of a wireless client from signal quality measures. Similar work has been limited to prototype systems that rely on nearest-neighbor techniques to infer location. In this paper, we describe Nibble, a Wi-Fi location service that uses Bayesian networks to infer the location of a device. We explain the general theory behind the system and how to use the system, along with describing our experiences at a university campus building and at a research lab. We also discuss how probabilistic modeling can be applied to a diverse range of applications that use sensor data.

In this paper, we provide new complexity results for algorithms that learn discrete-variable Bayesian networks from data. Our results apply whenever the learning algorithm uses a scoring criterion that favors the simplest structure for which the model is able to represent the ...

In this paper, a bibliographical review over the last decade is presented on the application of Bayesian networks to dependability, risk analysis and maintenance. It is shown an increasing trend of the literature related to these domains. This trend is due to the benefits that Bayesian networks provide in contrast with other classical methods of dependability analysis such as Markov Chains, Fault Trees and Petri Nets. Some of these benefits are the capability to model complex systems, to make predictions as well as diagnostics, to compute exactly the occurrence probability of an event, to update the calculations according to evidences, to represent multimodal variables and to help modeling user-friendly by a graphical and compact approach. This review is based on an extraction of 200 specific references in dependability, risk analysis and maintenance applications among a data base with 7000 Bayesian Network references. The most representatives are presented, then discussed and some perspectives of work are provided.

A Bayesian network formulation for relational shape matching is presented. The main advantage of the relational shape matching approach is the obviation of the non-rigid spatial mappings used by recent non-rigid matching approaches. The basic variables that need to be estimated in the relational shape matching objective function are the global rotation and scale and the local displacements and correspondences. The new Bethe free energy approach is used to estimate the pairwise correspondences between links of the template graphs and the data. The resulting framework is useful in both registration and recognition contexts. Results are shown on hand-drawn templates and on 2D transverse T1-weighted MR images.

The design and implementation of effective environmental policies need to be informed by a holistic understanding of the system processes (biophysical, social and economic), their complex interactions, and how they respond to various changes. Models, integrating different system processes into a unified framework, are seen as useful tools to help analyse alternatives with stakeholders, assess their outcomes, and communicate results in a transparent way. This paper reviews five common approaches or model types that have the capacity to integrate knowledge by developing models that can accommodate multiple issues, values, scales and uncertainty considerations, as well as facilitate stakeholder engagement. The approaches considered are: systems dynamics, Bayesian networks, coupled component models, agent-based models and knowledge-based models (also referred to as expert systems). We start by discussing several considerations in model development, such as the purpose of model building, the availability of qualitative versus quantitative data for model specification, the level of spatio-temporal detail required, and treatment of uncertainty. These considerations and a review of applications are then used to develop a framework that aims to assist modellers and model users in the choice of an appropriate modelling approach for their integrated assessment applications and that enables more effective learning in interdisciplinary settings.

When a tutoring system aims to provide students with interactive help, it needs to know what knowledge the student has and what goals the student is currently trying to achieve. That is, it must do both assessment and plan recognition. These modeling tasks involve a high level of uncertainty when students are allowed to follow various lines of reasoning and are not required to show all their reasoning explicitly. We use Bayesian networks as a comprehensive, sound formalism to handle this uncertainty. Using Bayesian networks, we have devised the probabilistic student models for Andes, a tutoring system for Newtonian physics whose philosophy is to maximize student initiative and freedom during the pedagogical interaction. Andes' models provide long-term knowledge assessment, plan recognition, and prediction of students' actions during problem solving, as well as assessment of students' knowledge and understanding as students read and explain worked out examples. In this paper, we describe the basic mechanisms that allow Andes' student models to soundly perform assessment and plan recognition, as well as the Bayesian network solutions to issues that arose in scaling up the model to a full-scale, ¢eld evaluated application. We also summarize the results of several evaluations of Andes which provide evidence on the accuracy of its student models.

A new method is proposed for exploiting causal independencies in exact Bayesian network inference. A Bayesian network can be viewed as representing a factorization of a joint probability into the multiplication of a set of conditional probabilities. We present a notion of causal independence that enables one to further factorize the conditional probabilities into a combination of even smaller factors and consequently obtain a finer-grain factorization of the joint probability. The new formulation of causal independence lets us specify the conditional probability of a variable given its parents in terms of an associative and commutative operator, such as "or", "sum" or "max", on the contribution of each parent. We start with a simple algorithm VE for Bayesian network inference that, given evidence and a query variable, uses the factorization to find the posterior distribution of the query. We show how this algorithm can be extended to exploit causal independence. Empirical studies, based on the CPCS networks for medical diagnosis, show that this method is more efficient than previous methods and allows for inference in larger networks than previous algorithms.

A Bayesian network consists of a graphical structure and a probabilistic description of the relationships among variables in a system. The graphical structure explicitly represents cause-and-effect assumptions that allow a complex causal chain linking actions to outcomes to be factored into an articulated series of conditional relationships. Each of these relationships can then be independently quantified using a submodel suitable for the type and scale of information available. This approach is particularly useful for ecological modelling because predictable patterns may emerge at a variety of scales, necessitating a multiplicity of model forms. As an example, we describe a Bayesian network integrating models of the various processes involved in eutrophication in the Neuse River estuary, North Carolina. These models were developed using a range of methods, including: process-based models statistically fit to long-term monitoring data, Bayesian hierarchical modelling of cross-system data gathered from the literature, multivariate regression modelling of mesocosm experiments, and judgements elicited from scientific experts. The ability of the network to accommodate such a diversity of methods allowed for the prediction of policy-relevant ecosystem attributes not normally included in models of eutrophication. All of the submodels in the network include estimates of predictive uncertainty in the form of probability distributions which are propagated to model endpoints. Predictions expressed as probabilities give stakeholders and decision-makers a realistic appraisal of the chances of achieving desired outcomes under alternative nutrient management strategies. In general, the further down the causal chain a variable was, the greater the predictive uncertainty. This suggests that a compromise is necessary between policy relevance and predictive precision, and that, to select defensible environmental management strategies, public officials must adopt decision-making methods that deal explicitly with scientific uncertainty.

Markov decision processes (MDPs) have recently been applied to the problem of modeling decision-theoretic planning. While such traditional methods for solving MDPs are often practical for small states spaces, their effectiveness for large AI planning problems is questionable. We present an algorithm, called structured policy iteration (SPI), that constructs optimal policies without explicit enumeration of the state space. The algorithm retains the fundamental computational steps of the commonly used modified policy iteration algorithm, but exploits the variable and propositional independencies in reflected in a temporal Bayesian network representation of MDPs. The principles behind SPI can be applied to any structured representation of stochastic actions, and the algorithm itself can be used in conjunction with recent approximation methods.

This paper presents a number of new algorithms for discovering the Markov Blanket of a target variable T from training data. The Markov Blanket can be used for variable selection for classification, for causal discovery, and for Bayesian Network learning. We ...

Bayesian networks (BNs), also known as Bayesian belief networks or Bayes nets, are a kind of probabilistic graphical model that has become very popular to practitioners mainly due to the powerful probability theory involved, which makes them able to deal with a wide range of problems. The goal of this review is to show how BNs are being used in environmental modelling. We are interested in the application of BNs, from January 1990 to December 2010, in the areas of the ISI Web of Knowledge related to Environmental Sciences. It is noted that only the 4.2% of the papers have been published under this item. The different steps that configure modelling via BNs have been revised: aim of the model, data pre-processing, model learning, validation and software. Our literature review indicates that BNs have barely been used for Environmental Science and their potential is, as yet, largely unexploited.

Markov decision processes (MDPs) have proven to be popular models for decision-theoretic planning, but standard dynamic programming algorithms for solving MDPs rely on explicit, state-based specifications and computations. To alleviate the combinatorial problems associated with such methods, we propose new representational and computational techniques for MDPs that exploit certain types of problem structure. We use dynamic Bayesian networks (with decision trees representing the local families of conditional probability distributions) to represent stochastic actions in an MDP, together with a decision-tree representation of rewards. Based on this representation, we develop versions of standard dynamic programming algorithms that directly manipulate decision-tree representations of policies and value functions. This generally obviates the need for state-by-state computation, aggregating states at the leaves of these trees and requiring computations only for each aggregate state. The key to these algorithms is a decision-theoretic generalization of classic regression analysis, in which we determine the features relevant to predicting expected value. We demonstrate the method empirically on several planning problems, showing significant savings for certain types of problems. We also identify certain classes of problems for which this technique fails to perform well and suggest extensions and related ideas that may prove useful for such problems. We also briefly describe an approximation scheme based on this approach.

Students are characterized by different learning styles, focusing on different types of information and processing this information in different ways. One of the desirable characteristics of a Web-based education system is that all the students can learn despite their different learning styles. To achieve this goal we have to detect how students learn: reflecting or acting; steadily or in fits and starts; intuitively or sensitively. In this work, we evaluate Bayesian networks at detecting the learning style of a student in a Web-based education system. The Bayesian network models different aspects of a student behavior while he/she works with this system. Then, it infers his/her learning styles according to the modeled behaviors. The proposed Bayesian model was evaluated in the context of an Artificial Intelligence Web-based course. The results obtained are promising as regards the detection of studentsÕ learning styles. Different levels of precision were found for the different dimensions or aspects of a learning style.

Catchment managers face considerable challenges in managing ecological assets. This task is made difficult by the variable and complex nature of ecological assets, and the considerable uncertainty involved in quantifying how various threats and hazards impact upon them. Bayesian approaches have the potential to address the modelling needs of environmental management. However, to date many Bayesian networks (Bn) developed for environmental management have been parameterised using knowledge elicitation only. Not only are these models highly qualitative, but the time and effort involved in elicitation of a complex Bn can often be overwhelming. Unfortunately in environmental applications, data alone are often too limited for parameterising a Bn. Consequently, there is growing interest in how to parameterise Bns using both data and elicited information. At present, there is little formal guidance on how to combine what can be learned from the data with what can be elicited. In a previous publication we proposed a detailed methodology for this process, focussing on parameterising and evaluating a Bn. In this paper, we further develop this methodology using a risk assessment case study, with the focus being on native fish communities in the Goulburn Catchment (Victoria, Australia).

Endocytosis is a complex process fulfilling many cellular and developmental functions. Understanding how it is regulated and integrated with other cellular processes requires a comprehensive analysis of its molecular constituents and general design principles. Here, we developed a new strategy to phenotypically profile the human genome with respect to transferrin (TF) and epidermal growth factor (EGF) endocytosis by combining RNA interference, automated high-resolution confocal microscopy, quantitative multiparametric image analysis and high-performance computing. We identified several novel components of endocytic trafficking, including genes implicated in human diseases. We found that signalling pathways such as Wnt, integrin/cell adhesion, transforming growth factor (TGF)-b and Notch regulate the endocytic system, and identified new genes involved in cargo sorting to a subset of signalling endosomes. A systems analysis by Bayesian networks further showed that the number, size, concentration of cargo and intracellular position of endosomes are not determined randomly but are subject to specific regulation, thus uncovering novel properties of the endocytic system.

Affordances encode relationships between actions, objects and effects. They play an important role on basic cognitive capabilities such as prediction and planning. We address the problem of learning affordances through the interaction of a robot with the environment, a key step to understand the world properties and develop social skills. We present a general model for learning object affordances using Bayesian networks integrated within a general developmental architecture for social robots. Since learning is based on a probabilistic model, the approach is able to deal with uncertainty, redundancy and irrelevant information. We demonstrate successful learning in the real world by having an humanoid robot interacting with objects. We demonstrate the benefits of the acquired knowledge in imitation games.

We present a new approach to structure learning in the field of Bayesian networks: We tackle the problem of the search for the best Bayesian network structure, given a database of cases, using the genetic algorithm philosophy for searching among alternative structures. We start by assuming an ordering between the nodes of the network structures. This assumption is necessary to guarantee that the networks that are created by the genetic algorithms are legal Bayesian network structures. Next, we release the ordering assumption by using a "repair operator" which converts illegal structures into legal ones. We present empirical results and analyze them statistically. The best results are obtained with an elitist genetic algorithm that contains a local optimizer.

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Recently several researchers have investi- gated techniques for using data to learn Bayesian networks containing compact rep- resentations for the conditional probability distributions (CPDs) stored at each node. The majority of this work has concentrated on using decision-tree representations for the CPDs. In addition, researchers typi- cally apply non-Bayesian (or asymptotically Bayesian) scoring functions such as MDL to evaluate the

We present an integrated system for automatic acquisition of the human body model and motion tracking using input from multiple synchronized video streams. The video frames are segmented and the 3D voxel reconstructions of the human body shape in each frame are computed from the foreground silhouettes. These reconstructions are then used as input to the model acquisition and tracking algorithms. The human body model consists of ellipsoids and cylinders and is described using the twists framework resulting in a non-redundant set of model parameters. Model acquisition starts with a simple body part localization procedure based on template fitting and growing, which uses prior knowledge of average body part shapes and dimensions. The initial model is then refined using a Bayesian network that imposes human body proportions onto the body part size estimates.

Systems biology approaches are extensively used to model and reverse engineer gene regulatory networks from experimental data. Conversely, synthetic biology allows ''de novo'' construction of a regulatory network to seed new functions in the cell. At present, the usefulness and predictive ability of modeling and reverse engineering cannot be assessed and compared rigorously. We built in the yeast Saccharomyces cerevisiae a synthetic network, IRMA, for in vivo ''benchmarking'' of reverse-engineering and modeling approaches. The network is composed of five genes regulating each other through a variety of regulatory interactions; it is negligibly affected by endogenous genes, and it is responsive to small molecules. We measured time series and steady-state expression data after multiple perturbations. These data were used to assess state-of-the-art modeling and reverse-engineering techniques. A semiquantitative model was able to capture and predict the behavior of the network. Reverse engineering based on differential equations and Bayesian networks correctly inferred regulatory interactions from the experimental data.

Many tracking problems involve several distinct objects interacting with each other. We develop a framework that takes into account interactions between objects allowing the recognition of complex activities. In contrast to classic approaches that consider distinct phases of tracking and activity recognition, our framework performs these two tasks simultaneously. In particular, we adopt a Bayesian standpoint where the system maintains a joint distribution of the positions, the interactions and the possible activities. This turns out to be advantegeous, as information about the ongoing activities can be used to improve the prediction step of the tracking, while, at the same time, tracking information can be used for online activity recognition. Experimental results in two different settings show that our approach 1) decreases the error rate and improves the identity maintenance of the positional tracking and 2) identifies the correct activity with higher accuracy than standard approaches.

We study the problem of learning the best Bayesian network structure with respect to a decomposable score such as BDe, BIC or AIC. This problem is known to be NP-hard, which means that solving it becomes quickly infeasible as the number of variables increases.

In operating today's complex systems, the lack of a systematic way to capture and query the essential system state characterizing an incident of performance failure or unavailability makes it difficult for operators to distinguish recurring problems from new ones, to leverage previous diagnostic efforts, or to establish whether problems seen at different installations of the same site are similar or distinct. We present a method for automatically extracting from a running system an indexable signature that distills the essential system state associated with a problem and can be subjected to clustering and similarity-based retrieval to identify when an observed system state is similar to a previously-observed state. This allows operators to identify and quantify the frequency of recurrent problems, or to leverage problem observations at one site in diagnosing problems at another site. We show that the naive approach to constructing these signatures is ineffective, leading us to a more sophisticated approach based on statistical modeling and inference. Our method requires only that the system's metric of merit as well as a collection of lower-level operational metrics be collected, as is done by existing commercial monitoring tools. Even if the traces have no annotations of prior diagnoses of observed incidents (as is typical), our technique successfully clusters system states corresponding to similar problems, allowing diagnosticians to identify recurring problems or to name the "syndrome" of a group of problems later. We validate our approach on both synthetic traces and several weeks of production traces from a customer-facing geoplexed 24 × 7 system; in the latter case, our approach identified a recurring problem that had required extensive manual diagnosis, and also aided the operators in correcting a previous misdiagnosis of a different problem.

Abstract. We discuss Bayesian methods for model averaging and model selection among Bayesian-network models with hidden variables. In particular, we examine large-sample approximations for the marginal likelihood of naive-Bayes models in which the root node is hidden. Such ...

The human figure exhibits complex and rich dynamic behavior that is both nonlinear and time-varying. However, most work on tracking and synthesizing figure motion has employed either simple, generic dynamic models or highly specific hand-tailored ones.