Additions and corrections to “Terminal coalgebras in well-founded set theory”

This note is to correct certain mistaken impressions of the author's that were in the original paper, “Terminal coalgebras in well-founded set theory”, which appeared in Theoretical Computer Science 114 (1993) 299–315.

Well-founded orderings for proving termination of systems of rewrite rules /

Bibliography: p. 34.

Adequate Compacta which are Gul’ko or Talagrand

2000 Mathematics Subject Classification: 54H05, 03E15, 46B26

Extended Tree Augmented Naive Classifier

This work proposes an extended version of the well-known tree-augmented naive Bayes (TAN) classifier where the structure learning step is performed without requiring features to be connected to the class. Based on a modification of Edmonds’ algorithm, our structure learning procedure explores a superset of the structures that are considered by TAN, yet achieves global optimality of the learning score function in a very efficient way (quadratic in the number of features, the same complexity as learning TANs). A range of experiments show that we obtain models with better accuracy than TAN and comparable to the accuracy of the state-of-the-art classifier averaged one-dependence estimator.

Learning Extended Tree Augmented Naive Structures

This work proposes an extended version of the well-known tree-augmented naive Bayes (TAN) classifier where the structure learning step is performed without requiring features to be connected to the class. Based on a modification of Edmonds' algorithm, our structure learning procedure explores a superset of the structures that are considered by TAN, yet achieves global optimality of the learning score function in a very efficient way (quadratic in the number of features, the same complexity as learning TANs). We enhance our procedure with a new score function that only takes into account arcs that are relevant to predict the class, as well as an optimization over the equivalent sample size during learning. These ideas may be useful for structure learning of Bayesian networks in general. A range of experiments shows that we obtain models with better prediction accuracy than naive Bayes and TAN, and comparable to the accuracy of the state-of-the-art classifier averaged one-dependence estimator (AODE). We release our implementation of ETAN so that it can be easily installed and run within Weka.

Perspectives on periodontal risk factors

The development of a clinical decision tree based on knowledge about risks and reported outcomes of therapy is a necessity for successful planning and outcome of periodontal therapy. This requires a well-founded knowledge of the disease entity and a broad knowledge of how different risk conditions attribute to periodontitis. The infectious etiology, a complex immune response, and influence from a large number of co-factors are challenging conditions in clinical periodontal risk assessment. The difficult relationship between independent and dependent risk conditions paired with limited information on periodontitis prevalence adds to difficulties in periodontal risk assessment. The current information on periodontitis risk attributed to smoking habits, socio-economic conditions, general health and subjects' self-perception of health, is not comprehensive, and this contributes to limited success in periodontal risk assessment. New models for risk analysis have been advocated. Their utility for the estimation of periodontal risk assessment and prognosis should be tested. The present review addresses several of these issues associated with periodontal risk assessment.