Distribution-Independent Evolvability of Linear Threshold Functions

12 years 4 months ago
Distribution-Independent Evolvability of Linear Threshold Functions
Valiant’s (2007) model of evolvability models the evolutionary process of acquiring useful functionality as a restricted form of learning from random examples. Linear threshold functions and their various subclasses, such as conjunctions and decision lists, play a fundamental role in learning theory and hence their evolvability has been the primary focus of research on Valiant’s framework (2007). One of the main open problems regarding the model is whether conjunctions are evolvable distribution-independently (Feldman and Valiant, 2008). We show that the answer is negative. Our proof is based on a new combinatorial parameter of a concept class that lower-bounds the complexity of learning from correlations. We contrast the lower bound with a proof that linear threshold functions having a non-negligible margin on the data points are evolvable distribution-independently via a simple mutation algorithm. Our algorithm relies on a non-linear loss function being used to select the hypoth...
Vitaly Feldman
Added 13 May 2011
Updated 13 May 2011
Type Journal
Year 2011
Where CORR
Authors Vitaly Feldman
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