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VC Dimension and Distribution-Free Sample-Based Testing
Conversely, we show that two natural classes of functions, juntas and monotone functions, can be tested with a number of samples that is polynomially smaller than the number of samples required for PAC learning.
Downsampling for Testing and Learning in Product Distributions
For many important classes of functions, such as intersections of halfspaces, polynomial threshold functions, convex sets, and $k$-alternating functions, the known algorithms either have complexity that depends on the support size of the distribution, or are proven to work only for specific examples of product distributions.
Testing Halfspaces over Rotation-Invariant Distributions
We present an algorithm for testing halfspaces over arbitrary, unknown rotation-invariant distributions.
