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Like the ID3 algorithm, FOIL hill climbs using a metric based on information theory to construct a rule that covers the data. Unlike ID3, however, FOIL uses a separate-and-conquer method rather than divide-and-conquer, focusing on creating one rule at a time and collecting uncovered examples for the next iteration of the algorithm. [citation ...
He has contributed extensively to the development of decision tree algorithms, including inventing the canonical C4.5 and ID3 algorithms. He also contributed to early ILP literature with First Order Inductive Learner (FOIL). He is currently running the company RuleQuest Research which he founded in 1997.
Although DT algorithms was well recognized in the past few decades, CA started to attract the attention due to its direct rule induction property, as emphasized by Kurgan et al. [1]. Under this type of inductive learning approach, several families have been developed and improved.
Inductive logic programming has adopted several different learning settings, the most common of which are learning from entailment and learning from interpretations. [16] In both cases, the input is provided in the form of background knowledge B, a logical theory (commonly in the form of clauses used in logic programming), as well as positive and negative examples, denoted + and respectively.
The FOIL method is a special case of a more general method for multiplying algebraic expressions using the distributive law. The word FOIL was originally intended solely as a mnemonic for high-school students learning algebra. The term appears in William Betz's 1929 text Algebra for Today, where he states: [2]
Data mining in general and rule induction in detail are trying to create algorithms without human programming but with analyzing existing data structures. [1]: 415- In the easiest case, a rule is expressed with “if-then statements” and was created with the ID3 algorithm for decision tree learning.
The proof of this is derived from a game between the induction and the environment. Essentially, any computable induction can be tricked by a computable environment, by choosing the computable environment that negates the computable induction's prediction. This fact can be regarded as an instance of the no free lunch theorem.
Unlike the searches of Ehud Shapiro's model inference system (MIS) and J. Ross Quinlan's FOIL, Progol's search has a provable guarantee of returning a solution having the maximum compression [definition needed] in the search-space.