This tutorial gives a concise overview of existing PAC-Bayesian theory focusing on three generalization bounds. The first is an Occam bound which handles rules with finite precision parameters and which states that generalization loss is near training loss when the number of bits needed to write the rule is small compared to the sample size. The second is a PAC-Bayesian bound providing a genera...

In this chapter I review Bayesian statistics as used for induction and relate it to logic based abduction Much reasoning under un certainty including induction is based on Bayes rule Bayes rule is interesting precisely because it provides a mechanism for abduc tion I review work of Buntine that argues that much of the work on Bayesian learning can be best viewed in terms of graphical models suc...

In this chapter I review Bayesian statistics as used for induction and relate it to logic-based abduction. Much reasoning under uncertainty , including induction, is based on Bayes' rule. Bayes' rule is interesting precisely because it provides a mechanism for abduction. I review work of Buntine that argues that much of the work on Bayesian learning can be best viewed in terms of graphical mode...

In Bayesian inference tasks, information about base rates as well as hit rate and false-alarm rate needs to be integrated according to Bayes' rule after the result of a diagnostic test became known. Numerous studies have found that presenting information in a Bayesian inference task in terms of natural frequencies leads to better performance compared to variants with information presented in te...

We use Bayesian methods to design cellular neural networks for signal processing tasks and the Boltzmann Machine learning rule for parameter estimation. The learning rule can be used for models with uhidden" units, or for compietely unsupervised learning. The latter is exemplified by unsupervised adaptation of an image segmentation cellular network, in particular we apply the learning rule to a...

The authors present and test a new method of teaching Bayesian reasoning, something about which previous teaching studies reported little success. Based on G. Gigerenzer and U. Hoffrage's (1995) ecological framework, the authors wrote a computerized tutorial program to train people to construct frequency representations (representation training) rather than to insert probabilities into Bayes's ...

Based on an earlier study on lazy Bayesian rule learning, this paper introduces a general lazy learning framework, called LazyRule, that begins to learn a rule only when classifying a test case. The objective of the framework is to improve the performance of a base learning algorithm. It has the potential to be used for diierent types of base learning algorithms. LazyRule performs attribute eli...

Based on an earlier study on lazy Bayesian rule learning, this paper introduces a general lazy learning framework, called LazyRule, that begins to learn a rule only when classifying a test case. The objective of the framework is to improve the performance of a base learning algorithm. It has the potential to be used for diierent types of base learning algorithms. LazyRule performs attribute eli...

Optional stopping refers to the practice of peeking at data and then, based on the results, deciding whether or not to continue an experiment. In the context of ordinary significance-testing analysis, optional stopping is discouraged, because it necessarily leads to increased type I error rates over nominal values. This article addresses whether optional stopping is problematic for Bayesian inf...

MOTIVATION Disease state prediction from biomarker profiling studies is an important problem because more accurate classification models will potentially lead to the discovery of better, more discriminative markers. Data mining methods are routinely applied to such analyses of biomedical datasets generated from high-throughput 'omic' technologies applied to clinical samples from tissues or bodi...