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We analyze the “query by committee” algorithm, a method for filtering informative queries from a random stream of inputs. We show that if the two-member committee algorithm achieves information gain with positive lower bound, then the prediction error decreases exponentially with the number of queries. We show that, in particular, this exponential decrease(More)
Expanders have many applications in Computer Science. It is known that random d-regular graphs are very efficient expanders, almost surely. However, checking whether a particular graph is a good expander is co-NP-complete. We show that the second eigenvalue of d-regular graphs, λ2, is concentrated in an interval of width O(√d) around its(More)
The problem of minimizing the depth of formulas by equivalence preserving transformations is formalized in a general algebraic setting. For a particular algebraic system ∑0 specific methods of a dynamic programming nature are developed for proving lower bounds on depth. Such lower bounds for ∑0 automatically imply the same results for the systems of (i)(More)
Generalization in most PAC learning analysis starts around O (d) examples, where d = V Cdim of the class. Nevertheless, analysis of learning curves using statistical mechanics shows much earlier generalization [7]. Here we introduce a gadget called Early Predictor, which exists if somewhat better than random prediction of the label of an arbitrary instance(More)
Recent works have shown the advantage of using Active Learning methods, such as the Query by Committee (QBC) algorithm, to various learning problems. This class of Algorithms requires an oracle with the ability to randomly select a consistent hypothesis according to some predeened distribution. When trying to implement such an oracle, for the linear(More)
This thesis is a study of automata learning. Most of the work presented here is in the framework of Computational Learning Theory and hence emphasizes the theoretical aspects of learning algorithms and their rigorous analysis. However, a substantial part of this work was directly motivated by practical applications in human-machine interactions such as the(More)