Weakly learning DNF and characterizing statistical query learning using Fourier analysis

We present new results on the well-studied problem of learning DNF expressions. We prove that an algorithm due to Kushilevitz and Mansour [13] can be used to weakly learn DNF formulas with membership queries with respect to the uniform distribution. This is the first positive result known for learning general DNF in polynomial time in a nontrivial model. Our results should be contrasted with those of Kharitonov [12], who proved that AC0 is not efficiently learnable in this model based on cryptographic assumptions. We also present efficient learning algorithms in various models for the read-k and SAT-k subclasses of DNF. We then turn our attention to the recently introduced statistical query model of learning [9]. This model is a restricted version of the popular Probably Approximately Correct (PAC) model, and practically every PAC learning algorithm falls into the statistical query model [9]. We prove that DNF and decision trees are not even weakly learnable in polynomial time in this...

• Type: Conference
• Year: 1994
• Where: STOC
• Authors: Avrim Blum, Merrick L. Furst, Jeffrey C. Jackson, Michael J. Kearns, Yishay Mansour, Steven Rudich
• Keywords: Algorithms, DNF Expressions, DNF Formulas, Statistical Query Model, STOC 1994