Sequential Optimal Recovery: A Paradigm for Active Learning

In most classical frameworks for learning from examples, it is assumed that examples are randomly drawn and presented to the learner. In this paper, we consider the possibility of a more active learner who is allowed to choose his/her own examples. Our investigations are carried out in a function approximation setting. In particular, using arguments from optimal recovery (Micchelli and Rivlin, 1976), we develop an adaptive sampling strategy (equivalent to adaptive approximation) for arbitrary approximation schemes. We provide a general formulation of the problem and show how it can be regarded as sequential optimal recovery. We demonstrate the application of this general formulation to two special cases of functions on the real line 1) monotonically increasing functions and 2) functions with bounded derivative. An extensive investigation of the sample complexity of approximating these functions is conducted yielding both theoretical and empirical results on test functions. Our theoretical results (stated insPAC-style), along with the simulations demonstrate the superiority of our active scheme over both passive learning as well as classical optimal recovery. The analysis of active function approximation is conducted in a worst-case setting, in contrast with other Bayesian paradigms obtained from optimal design (Mackay, 1992).

Stimulus Familiarity Determines Recognition Strategy for Novel 3-D Objects

We describe a psychophysical investigation of the effects of object complexity and familiarity on the variation of recognition time and recognition accuracy over different views of novel 3D objects. Our findings indicate that with practice the response times for different views become more uniform and the initially orderly dependency of the response time on the distance to a "good" view disappears. One possible interpretation of our results is in terms of a tradeoff between memory needed for storing specific-view representations of objects and time spent in recognizing the objects.