This paper is a multidisciplinary review of empirical, statistical learning from a graphical model perspective. Well-known examples of graphical models include Bayesian networks, directed graphs representing a Markov chain, and undirected networks representing a Markov field. These graphical models are extended to model data analysis and empirical learning using the notation of plates. Graphical operations for simplifying and manipulating a problem are provided including decomposition, differentiation, and the manipulation of probability models from the exponential family. Two standard algorithm schemas for learning are reviewed in a graphical framework: Gibbs sampling and the expectation maximization algorithm. Using these operations and schemas, some popular algorithms can be synthesized from their graphical specification. This includes versions of linear regression, techniques for feed-forward networks, and learning Gaussian and discrete Bayesian networks from data. The paper conclu...

This literature review discusses different methods under the general rubric of learning Bayesian networks from data, and includes some overlapping work on more general probabilistic networks. Connections are drawn between the statistical, neural network, and uncertainty communities, and between the different methodological communities, such as Bayesian, description length, and classical statistics. Basic concepts for learning and Bayesian networks are introduced and methods are then reviewed. Methods are discussed for learning parameters of a probabilistic network, for learning the structure, and for learning hidden variables. The presentation avoids formal definitions and theorems, as these are plentiful in the literature, and instead illustrates key concepts with simplified examples. Keywords--- Bayesian networks, graphical models, hidden variables, learning, learning structure, probabilistic networks, knowledge discovery. I. Introduction Probabilistic networks or probabilistic gra...

This article discusses the history underlying the new literature, describes some of what has been learned thus far, and looks ahead towards making further progress

We have collected data on the one-year-ahead income expectations of members of American households in our Survey of Economic Expectations (SEE), a module of a national continuous telephone survey conducted at the University of Wisconsin. The income-expectations questions take this form: "What do you think is the percent chance (or what are the chances out of 100) that your total household income, before taxes, will be less than Y over the next 12 months? " We use the responses to a sequence of such questions posed for different income thresholds Y to estimate each respondent's subjective probability distribution for next year's household income. We use the estimates to study the cross-sectional variation in income expectations one year into the future

With the help of two experts in gastrointestinal oncology from the Netherlands Cancer Institute, Antoni van Leeuwenhoekhuis, a decision-support system is being developed for patient-specific therapy selection for oesophageal carcinoma. The kernel of the system is a probabilistic network that describes the characteristics of oesophageal carcinoma and the pathophysiological processes of invasion and metastasis. While the construction of the graphical structure of the network was relatively straightforward, probability elicitation with existing methods proved to be a major obstacle. We designed

How much security is enough? No one today can satisfactorily answer this question for computer-related risks. The first generation of computer security risk modelers struggled with issues arising out of their binary view of security, ensnaring them in an endless web of assessment, disagreement, and gridlock. Even as professional risk managers wrest responsibility away from the first-generation technologists, they are still unable to answer the question with sufficient quantitative rigor. Their efforts are handicapped by a reliance on non-quantitative methodologies originally developed to address the deployment and organizational acceptance issues that plagued first-generation tools.

It is difficult for organizations introducing and using software inspections to evaluate how efficient they are. However, it is of practical importance to determine whether they have been effectively implemented or whether corrective actions are necessary to bring them up to standard. We present in this paper a procedure for building inspection efficiency benchmarks based on simulation and typical inspection data. Based on most of the data published in the literature, we build an industry-wide benchmark which intends to capture the current practice regarding inspection efficiency. Moreover, we discuss how this benchmark construction procedure can be used to build enterprise specific benchmarks. Last, we assess how robust we can expect them to be in varying conditions by distorting their input distributions.

Simulation models are becoming increasingly common in the analysis of critical scientific, policy, and management issues. Such models provide a way to analyze complex systems characterized by both large parameter spaces and nonlinear interactions. Unfortunately, these same characteristics make understanding such models using traditional testing techniques extremely difficult. Here we show how a model's structure and robustness can be tested via a simple, automatic, nonlinear search algorithm designed to actively "break" the model's implications. Using the active nonlinear tests (ANTs) developed here, one can easily probe for key weaknesses in a simulation's structure, and thereby begin to improve and refine the model's design. We demonstrate ANTs by testing a well-known model of global dynamics (World3), and show how this technique can be used to uncover small, but powerful, nonlinear effects that may highlight vulnerabilities in the original model. This paper has benefited from disc...

In building Bayesian belief networks, the elicitation of all probabilities required can be a major obstacle. We learned the extent of this often-cited observation in the construction of the probabilistic part of a complex influence diagram in the field of cancer treatment. Based upon our negative experiences with existing methods, we designed a new method for probability elicitation from domain experts. The method combines various ideas, among which are the ideas of transcribing probabilities and of using a scale with both numerical and verbal anchors for marking assessments. In the construction of the probabilistic part of our influence diagram, the method proved to allow for the elicitation of many probabilities in little time.

Developing a large belief network, like any large system, requires systems engineering to manage the design and construction process. We propose that network engineering follow a rapid prototyping approach to network construction. We describe criteria for identifying network modules and the use of `stubs' within a belief network. We propose an object oriented representation for belief networks which captures the semantic as well as representational knowledge embedded in the variables, their values and their parameters. Methods for evaluating complex networks are described. Throughout the discussion, tools which support the engineering of large belief networks are identified. 1. Introduction As belief networks become more popular and well understood as a tool for modeling uncertainty and as the computational power of belief network inference engines increases, belief networks are being applied to problems of increasing size and complexity. In the early 1990's, Pathfinder, at 109 nodes...