In this work, we describe a framework that unifies many different interactive learning tasks. We present a generalization of the query-by-committee active learning algorithm for this setting, and we study its consistency and rate of convergence, both theoretically and empirically, with and without noise.
This paper investigates the problem of determining a binary-valued function through a sequence of strategically selected queries. The focus is an algorithm called Generalized Binary Search (GBS). GBS is a well-known greedy algorithm for determining a binary-valued function through a sequence of strategically selected queries. At each step, a query is selected that most evenly splits the hypotheses under consideration into two disjoint subsets, a natural generalization of the idea underlying classic binary search. This paper develops novel incoherence and geometric conditions under which GBS achieves the information-theoretically optimal query complexity; i.e., given a collection of N hypotheses, GBS terminates with the correct function after no more than a constant times logN queries. Furthermore, a noise-tolerant version of GBS is developed that also achieves the optimal query complexity. These results are applied to learning halfspaces, a problem arising routinely in image processing and machine learning. A process for continously annealing a fused cast refractory body, in order to obtain a crack-free product, in which the fused cast refractory body is placed on a suitable preheated carrier which has been previously heated to a temperature of greater than 500 DEG C in a preheat chamber, and is charged into an annealing tunnel which is divided into a hot zone and a cooling zone having at least one cooling section.