Machine Discovery by Learning Algorithms

该项目旨在开发基于坚实的机器学习算法理论基础的机器发现系统。在这个项目中，我们特别关注(1)机器发现的计算逻辑，(2)机器发现的知识表示，(3)基于PAC学习的机器发现，(4)数据库中的机器发现，(5)机器发现算法的并行化。我们明确了机器发现的本质是能够用一些观察到的事实来反驳假设空间本身，并证明了在初等形式系统的框架中存在如此丰富的假设空间。由于科学数据大多是数值的，我们研究了用递归实数和区间分析表示实数和实值函数的方法，发展了一种识别微分方程的方法；我们将机器发现逻辑的结果推广到PAC学习中，可以处理可能近似正确的假设；针对数据库中的机器发现，我们开发了一个基于规则模式决策树的机器发现系统，称为盆景，使其并行化，并开发了一个氨基酸序列中某些区域的预测系统。我们还在分子生物学领域做了一些实验，并取得了非常成功的结果。

This project aimed at developing machine discovery systems based upon firm theoretical foundations of machine learning algorithms. In this project we have focused our attention specially on (1) computational logic of machine discovery, (2) knowledge representation for machine discovery, (3) machine discovery by PAC learning, (4) machine discovery in databases, and (5) making machine discovery algorithms parallel.First we have developed a logic of machine discovery compared with the logic of scientific discovery by K.Popper. We have made it clear that the essential of machine discovery is to be able to refute the hypothesis space itself by some observed facts, and showed that there are such rich hypothesis spaces in the framework of the elementary formal systems. Since scientific data are mostly numerical, we have studied representation of real numbers and real-valued functions in terms of recursive reals and interval analysis, and developed a method of identifying differential equations.We have extended our results on the logic of machine discovery to the PAC learning, which can cope with probably approximately correct hypotheses.Concerning the machine discovery in database, we have developed a machine discovery system based upon a decision trees over regular patterns called BONSAI,made it parallel, and also developed a prediction system for some domains in amino acid sequences. We have also made some experiments on the field of molecular biology, and got very successful results.