### Exact Exponent in Optimal Rates for Crowdsourcing

In many machine learning applications, crowdsourcing has become the primary means for label collection. In this paper, we study the optimal error rate for aggregating labels provided by a set of non-expert workers. Under the classic Dawid-Skene model, we establish matching upper and lower bounds with an exact exponent $mI(\pi)$ in which $m$ is the number of workers and $I(\pi)$ the average Chernoff information that characterizes the workers' collective ability. Such an exact characterization of the error exponent allows us to state a precise sample size requirement $m>\frac{1}{I(\pi)}\log\frac{1}{\epsilon}$ in order to achieve an $\epsilon$ misclassification error. In addition, our results imply the optimality of various EM algorithms for crowdsourcing initialized by consistent estimators.

### Extensions of a Theory of Networks for Approximation and Learning: Outliers and Negative Examples

Bruno Caprile I.R.S.T. Povo, Italy, 38050 Learning an input-output mapping from a set of examples can be regarded as synthesizing an approximation of a multidimensional function.

### Framework and Schema for Semantic Web Knowledge Bases

There is a growing need for scalable semantic web repositories which support inference and provide efficient queries. There is also a growing interest in representing uncertain knowledge in semantic web datasets and ontologies. In this paper, I present a bit vector schema specifically designed for RDF (Resource Description Framework) datasets. I propose a system for materializing and storing inferred knowledge using this schema. I show experimental results that demonstrate that this solution simplifies inference queries and drastically improves results. I also propose and describe a solution for materializing and persisting uncertain information and probabilities. Thresholds and bit vectors are used to provide efficient query access to this uncertain knowledge. My goal is to provide a semantic web repository that supports knowledge inference, uncertainty reasoning, and Bayesian networks, without sacrificing performance or scalability.

### WS06-05-006.pdf

This paper describes an effort to measure the effectiveness of tutor help in an intelligent tutoring system. Although conventional pre-and post-test experiments can determine whether tutor help is effective, they are expensive to conduct. Furthermore, pre-and post-test experiments often do not model student knowledge explicitly and thus are ignoring a source of information: students often request help about words they do not know. Therefore, we construct a dynamic Bayes net (which we call the Help model) that models tutor help and student knowledge in one coherent framework. The Help model distinguishes two different effects of help: scaffolding immediate performance vs. teaching persistent knowledge that improves long term performance. We train the Help model to fit student performance data gathered from usage of the Reading Tutor (Mostow & Aist, 2001). The parameters of the trained model suggest that students benefit from both the scaffolding and teaching effects of help. That is, students are more likely to perform correctly on the current attempt and learn persistent knowledge if tutor help is provided. Thus, our framework is able to distinguish two types of influence that tutor help has on the student, and can determine whether help helps learning without an explicit controlled study.

### A tree augmented naive Bayesian network experiment for breast cancer prediction

In order to investigate the breast cancer prediction problem on the aging population with the grades of DCIS, we conduct a tree augmented naive Bayesian network experiment trained and tested on a large clinical dataset including consecutive diagnostic mammography examinations, consequent biopsy outcomes and related cancer registry records in the population of women across all ages. The aggregated results of our ten-fold cross validation method recommend a biopsy threshold higher than 2% for the aging population.