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Revision #1 to TR10-018 | 21st February 2012 01:29

A Complete Characterization of Statistical Query Learning with Applications to Evolvability

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Revision #1
Authors: Vitaly Feldman
Accepted on: 21st February 2012 01:30
Downloads: 928
Keywords: 


Abstract:

Statistical query (SQ) learning model of Kearns (1993) is a natural restriction of the PAC learning model in which a learning algorithm is allowed to obtain estimates of statistical properties of the examples but cannot see the examples themselves. We describe a new and simple characterization of the query complexity of learning in the SQ learning model. Unlike the previously known bounds on SQ learning our characterization preserves the accuracy and the efficiency of learning. The preservation of accuracy implies that that our characterization gives the first characterization of SQ learning in the agnostic learning framework of Haussler (1992) and Kearns, Schapire and Sellie (1992). The preservation of efficiency is achieved using a new boosting technique and allows us to derive a new approach to the design of evolutionary algorithms in Valiant's (2006) model of evolvability. We use this approach to demonstrate the existence of a large class of monotone evolutionary learning algorithms based on square loss performance estimation. These results differ significantly from the few known evolutionary algorithms and give evidence that evolvability in Valiant's model is a more versatile phenomenon than there had been previous reason to suspect.



Changes to previous version:

General revision based on reviews


Paper:

TR10-018 | 15th February 2010 09:58

A Complete Characterization of Statistical Query Learning with Applications to Evolvability





TR10-018
Authors: Vitaly Feldman
Publication: 19th February 2010 07:29
Downloads: 1368
Keywords: 


Abstract:

Statistical query (SQ) learning model of Kearns (1993) is a natural restriction of the PAC learning model in which a learning algorithm is allowed to obtain estimates of statistical properties of the examples but cannot see the examples themselves. We describe a new and simple characterization of the query complexity of learning in the SQ learning model. Unlike the previously known bounds on SQ learning our characterization preserves the accuracy and the efficiency of learning. The preservation of accuracy implies that that our characterization gives the first characterization of SQ learning in the agnostic learning framework of Haussler (1992) and Kearns, Schapire and Sellie (1992). The preservation of efficiency is achieved using a new boosting technique and allows us to derive a new approach to the design of evolutionary algorithms in Valiant's (2006) model of evolvability. We use this approach to demonstrate the existence of a large class of monotone evolutionary learning algorithms based on square loss fitness estimation. These results differ significantly from the few known evolutionary algorithms and give evidence that evolvability in Valiant's model is a more versatile phenomenon than there had been previous reason to suspect.



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