Operations for Learning with Graphical Models

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 concludes by sketching some implications for data analysis and summarizing how some popular algorithms fall within the framework presented. The main original contributions here are the decomposition techniques and the demonstration that graphical models provide a framework for understanding and developing complex learning algorithms.Comment: See http://www.jair.org/ for any accompanying file

METHODOLOGY FOR FLEET UNCERTAINTY REDUCTION WITH UNSUPERVISED LEARNING

Operational and environmental variance can skew reliability metrics and increase uncertainty around lifetime estimates. For this reason, fleet-wide analysis is often too general for accurate predictions on heterogeneous populations. Also, modern sensor based reliability and maintainability field and test data provide a higher level of specialization and disaggregation to relevant integrity metrics (e.g., amount of damage, remaining useful life). Modern advances, like Dynamic Bayesian Networks, reduce uncertainty on a unit-by-unit basis to apply condition-based maintenance. This thesis presents a methodology for leveraging covariate information to identify sub- populations. This population segmentation based methodology reduces fleet uncertainty for more practical resource allocation and scheduled maintenance. First, the author proposes, validates, and demonstrates a clustering based methodology. Afterwards, the author proposes the application of the Student-T Mixture Model (SMM) within the methodology as a versatile tool for modeling fleets with unclear sub-population boundaries. SMM’s fully Bayesian formulation, which is approximated with Variational Bayes (VB), is motivated and discussed. The scope of this research includes a new modeling approach, a proposed algorithm, and example applications

Conjoint probabilistic subband modeling

Thesis (Ph. D.)--Massachusetts Institute of Technology, Program in Media Arts & Sciences, 1997.Includes bibliographical references (leaves 125-133).by Ashok Chhabedia Popat.Ph.D