New Results for Random Walk Learning
Jeffrey C. Jackson, Karl Wimmer; 15(112):3815−3846, 2014.
In a very strong positive result for passive learning algorithms, Bshouty et al. showed that DNF expressions are efficiently learnable in the uniform random walk model. It is natural to ask whether the more expressive class of thresholds of parities (TOP) can also be learned efficiently in this model, since both DNF and TOP are efficiently uniform-learnable from queries. However, the time bounds of the algorithms of Bshouty et al. are exponential for TOP. We present a new approach to weak parity learning that leads to quasi-efficient uniform random walk learnability of TOP. We also introduce a more general random walk model and give two positive results in this new model: DNF is efficiently learnable and juntas are efficiently agnostically learnable.
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