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).

Calidad de la información, un desafío para todos.

El proceso de construcción de una cultura de la información y la producción de documentación educativa, así como el análisis y la toma de decisiones con base en estas, es largo y complejo. Los sistemas educativos en América Latina, y en El Salvador particularmente, se diseñan e implementan con una visión poco clara sobre la necesidad de producir y utilizar sistemas de información educativa de calidad con participación social. Esto permitiría a los grupos con poder de decisión, enmarcar sus acciones en un contexto muy cercano a los problemas reales de las comunidades educativas. El compromiso por la mejora de índices de desarrollo humano pasa por la mejora de la investigación y documentación sobre la realidad propia de los pueblos.

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