Classification using information

Abstract

Smith and Wiehagen [9] introduced a model of classification that is similar to the Gold model of learning [2]. In this model the learner is limited in both computing power and access to information. samples. In particular the learner is limited to Turing computability and initial segments of the function to be classified. When a function cannot be classified with respect to some desired property, it may be for either computational or information-theoretic reasons.

We would like to separate the computational limitations from the information-theoretic ones. To this end we study a model of learning originally due to Kelly that has no computational limits; however, the objects that we will be concerned with are rather complex. Fix a set $\mathcal{A} \subseteq \left\{ {0,1} \right\}^\omega$We will examine if a classifier (without computational limits) can classify a string x∈{0,1}^ω with respect to $\mathcal{A}$.

We will be varying the amount of information the learner can access. To increase the models ability to access information, we will give it the ability to ask more powerful questions. To decrease the models ability to access information, we will bound the number of mindchanges it may make.

Supported by NSF grants CCR-880-3641 and CCR 9020079