Learning Convex Concepts from Gaussian Distributions with PCA

We present a new algorithm for learning a convex set in n-dimensional space given labeled examples drawn from any Gaussian distribution. The complexity of the algorithm is bounded by a fixed polynomial in n times a function of k and where k is the dimension of the normal subspace (the span of normal vectors to supporting hyperplanes of the convex set) and the output is a hypothesis that correctly classifies at least 1- of the unknown Gaussian distribution. For the important case when the convex set is the intersection of k halfspaces, the complexity is poly(n, k, 1/ ) + n

• Type: Journal
• Year: 2010
• Where: FOCS
• Authors: Santosh Vempala
• Keywords: Algorithm, FOCS 2010, Gaussian Distributions, Theoretical Computer Science, Unknown Gaussian Distribution