Constructive approaches to Program Induction

Search is a key technique in artificial intelligence, machine learning and Program Induction. No matter how efficient a search procedure, there exist spaces that are too large to search effectively and they include the search space of programs. In this dissertation we show that in the context of logic-program induction (Inductive Logic Programming, or ILP) it is not necessary to search for a correct program, because if one exists, there also exists a unique object that is the most general correct program, and that can be constructed directly, without a search, in polynomial time and from a polynomial number of examples. The existence of this unique object, that we term the Top Program because of its maximal generality, does not so much solve the problem of searching a large program search space, as it completely sidesteps it, thus improving the efficiency of the learning task by orders of magnitude commensurate with the complexity of a program space search. The existence of a unique Top Program and the ability to construct it given finite resources relies on the imposition, on the language of hypotheses, from which programs are constructed, of a strong inductive bias with relevance to the learning task. In common practice, in machine learning, Program Induction and ILP, such relevant inductive bias is selected, or created, manually, by the human user of a learning system, with intuition or knowledge of the problem domain, and in the form of various kinds of program templates. In this dissertation we show that by abandoning the reliance on such extra-logical devices as program templates, and instead defining inductive bias exclusively as First- and Higher-Order Logic formulae, it is possible to learn inductive bias itself from examples, automatically, and efficiently, by Higher-Order Top Program construction. In Chapter 4 we describe the Top Program in the context of the Meta-Interpretive Learning approach to ILP (MIL) and describe an algorithm for its construction, the Top Program Construction algorithm (TPC). We prove the efficiency and accuracy of TPC and describe its implementation in a new MIL system called Louise. We support theoretical results with experiments comparing Louise to the state-of-the-art, search-based MIL system, Metagol, and find that Louise improves Metagol’s efficiency and accuracy. In Chapter 5 we re-frame MIL as specialisation of metarules, Second-Order clauses used as inductive bias in MIL, and prove that problem-specific metarules can be derived by specialisation of maximally general metarules, by MIL. We describe a sub-system of Louise, called TOIL, that learns new metarules by MIL and demonstrate empirically that the metarules learned by TOIL match those selected manually, while maintaining the accuracy and efficiency of learning. iOpen Acces

Louise: A Meta-Interpretive Learner for Efficient Multi-clause Learning of Large Programs

We present Louise, a new Meta-Interpretive Learner that performs efficient multi-clause learning, implemented in Prolog. Louise is efficient enough to learn programs that are too large to be learned with the current state-of-the-art MIL system, Metagol. Louise learns by first constructing the most general program in the hypothesis space of a MIL problem and then reducing this "Top program" by Plotkin's program reduction algorithm. In this extended abstract we describe Louise's learning approach and experimentally demonstrate that Louise can learn programs that are too large to be learned by our implementation of Metagol, Thelma