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- W2276522003 abstract "In computational learning theory, concepts are subsets of a set of instances and a concept class is a set of concepts. In many computational learning models, learning algorithms have the goal to identify the target concept in a concept class from a small number of examples, i.e., labelled instances. We study graph-theoretic representations of concept classes and their connections to a particular notion of learning complexity, namely teaching complexity. Teaching complexity is a complexity measure for the number of training examples needed in teaching models in which a helpful teacher provides examples to the learner. One type of graph that we study in this thesis is the one-inclusion graph; In this graph the vertices are concepts and there is an edge between two concepts if they disagree on exactly one instance. One-inclusion graphs have proven useful in analyzing some computational learning properties, e.g., sample compression sizes and expected mistake bounds of prediction algorithms. This thesis establishes strong connections between one-inclusion graphs and teaching complexity. We show that the teaching dimension of a concept, i.e., the minimum number of examples required for teaching that concept, is lower bounded by the degree of the corresponding vertex in the one-inclusion graph. Furthermore, we prove that for concepts in shortest-path-closed classes, the lower bounds are always attained. We then prove that the average case teaching complexity of any shortest-path-closed class is linearly upper-bounded by the Vapnik-Chervonenkis (VC) dimension of the class. As the VC dimension reflects the complexity of learning from randomly chosen examples, our theorem gives the evidence that, for the shortest-path-closed concept classes, the average difficulty of learning from a helpful teacher is not higher than that" @default.
- W2276522003 created "2016-06-24" @default.
- W2276522003 creator A5055722478 @default.
- W2276522003 date "2012-07-01" @default.
- W2276522003 modified "2023-09-22" @default.
- W2276522003 title "A Graph-Theoretic View of Teaching" @default.
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