### Learning From What You Don't Observe

The process of diagnosis involves learning about the state of a system from various observations of symptoms or findings about the system. Sophisticated Bayesian (and other) algorithms have been developed to revise and maintain beliefs about the system as observations are made. Nonetheless, diagnostic models have tended to ignore some common sense reasoning exploited by human diagnosticians; In particular, one can learn from which observations have not been made, in the spirit of conversational implicature. There are two concepts that we describe to extract information from the observations not made. First, some symptoms, if present, are more likely to be reported before others. Second, most human diagnosticians and expert systems are economical in their data-gathering, searching first where they are more likely to find symptoms present. Thus, there is a desirable bias toward reporting symptoms that are present. We develop a simple model for these concepts that can significantly improve diagnostic inference.

### SS99-01-023.pdf

Rule induction methods axe classified into two categories, induction of deterministic rules and probabilistic ones(Michalski 1986; Pawlak 1991; Tsumoto and Tanaka 1996). While deterministic rules are supported by positive examples, probabilistic ones are supported by large positive examples and small negative samples. That is, both kinds of rules select positively one decision if a case satisfies their conditional parts. However, domain experts do not use only positive reasoning but also negative reasoning, since a domain is not always deterministic. For example, when a patient does not have a headache, migraine should not be suspected: negative reasoning plays an important role in cutting the search space of a differential diagnosis(Tsumoto and Tanaka 1996). 1 Therefore, negative rules should be induced from databases in order to induce rules which will be easier for domain experts to 1The essential point is that if extracted patterns do not reflect experts' reasoning process, domain experts have difficulties in interpreting them. Without interpretation of domain experts, a discovery procedure would not proceed, which also means that the interaction between human experts and computers is indispensable to computer-assisted discovery.

### Evidence and Belief

We discuss the representation of knowledge and of belief from the viewpoint of decision theory. While the Bayesian approach enjoys general-purpose applicability and axiomatic foundations, it suffers from several drawbacks. In particular, it does not model the belief formation process, and does not relate beliefs to evidence. We survey alternative approaches, and focus on formal model of casebased prediction and case-based decisions. A formal model of belief and knowledge representation needs to address several questions. The most basic ones are: (i) how do we represent knowledge?

### Bayesian Sample Size Determination of Vibration Signals in Machine Learning Approach to Fault Diagnosis of Roller Bearings

Sample size determination for a data set is an important statistical process for analyzing the data to an optimum level of accuracy and using minimum computational work. The applications of this process are credible in every domain which deals with large data sets and high computational work. This study uses Bayesian analysis for determination of minimum sample size of vibration signals to be considered for fault diagnosis of a bearing using pre-defined parameters such as the inverse standard probability and the acceptable margin of error. Thus an analytical formula for sample size determination is introduced. The fault diagnosis of the bearing is done using a machine learning approach using an entropy-based J48 algorithm. The following method will help researchers involved in fault diagnosis to determine minimum sample size of data for analysis for a good statistical stability and precision.

### Gaussian Process bandits with adaptive discretization

In this paper, the problem of maximizing a black-box function $f:\mathcal{X} \to \mathbb{R}$ is studied in the Bayesian framework with a Gaussian Process (GP) prior. In particular, a new algorithm for this problem is proposed, and high probability bounds on its simple and cumulative regret are established. The query point selection rule in most existing methods involves an exhaustive search over an increasingly fine sequence of uniform discretizations of $\mathcal{X}$. The proposed algorithm, in contrast, adaptively refines $\mathcal{X}$ which leads to a lower computational complexity, particularly when $\mathcal{X}$ is a subset of a high dimensional Euclidean space. In addition to the computational gains, sufficient conditions are identified under which the regret bounds of the new algorithm improve upon the known results. Finally an extension of the algorithm to the case of contextual bandits is proposed, and high probability bounds on the contextual regret are presented.