Algorithmic learning theory and typed pattern languages

计算学习理论（CLT）是理论计算机科学、数学和人工智能范围内的一个领域。它的研究主题是机器学习的理论基础。我提出的研究计划解决了某些正式的CLT模型与机器学习在现实世界问题中的应用之间的差距。CLT模型是机器学习场景的正式抽象，其中对现实世界、学习者、信息源和成功学习的标准进行了假设。在这样一个正式的框架内，人们可以证明特定的机器学习任务可以实现（积极的结果）或不能实现（消极的结果）。CLT和应用机器学习之间的主要差距在于，CLT的负面结果通常是由于不必要的悲观假设；积极的结果往往基于不切实际的乐观假设。我提出的研究是关于如何在正式模型中更好地表示机器学习的实际方面。随着对高效学习的新关注，我将研究(a)基于递归理论的经典形式学习模型的变体，以及(b)基于形式语言理论的机器学习场景中数据的形式模型的变体以及它们向学习者表示的方式。

Computational Learning Theory (CLT) is a field within the scope of theoretical computer science, mathematics, and artificial intelligence. Its subject of research is the theoretical foundation of machine learning. My proposed research program addresses the gaps between certain formal CLT models and applications of machine learning to real-world problems. CLT models are formal abstractions of machine learning scenarios, in which assumptions are made about the real world, the learner, the source of information, and the criteria for successful learning. Within such a formal framework, one can prove that a specific machine learning task can be achieved (positive results) or cannot be achieved (negative results). The major gap between CLT and applied machine learning is that negative results in CLT are often due to assumptions that are unnecessarily pessimistic; positive results are often based on unrealistically optimistic assumptions. My proposed research is concerned with how practical aspects of machine learning can be better represented in formal models. With a new focus on efficient learning, I will study (a) variants of classical formal learning models, built on recursion theory, and (b) variants of formal models of the data and the way they are represented to the learner in machine learning scenarios, built on formal language theory.