By Topic

Learning Geometric Concepts via Gaussian Surface Area

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

3 Author(s)
Klivans, A.R. ; Univ. of Texas, Austin, TX ; O'Donnell, R. ; Servedio, R.A.

We study the learnability of sets in Ropfn under the Gaussian distribution, taking Gaussian surface area as the "complexity measure" of the sets being learned. Let CS denote the class of all (measurable) sets with surface area at most S. We first show that the class CS is learnable to any constant accuracy in time nO(S 2 ), even in the arbitrary noise ("agnostic'') model. Complementing this, we also show that any learning algorithm for CS information-theoretically requires 2Omega(S 2 ) examples for learning to constant accuracy. These results together show that Gaussian surface area essentially characterizes the computational complexity of learning under the Gaussian distribution. Our approach yields several new learning results, including the following (all bounds are for learning to any constant accuracy): The class of all convex sets can be agnostically learned in time 2O ~ (radicn) (and we prove a 2Omega(radicn) lower bound for noise-free learning). This is the first subexponential time algorithm for learning general convex sets even in the noise-free (PAC) model. Intersections of k halfspaces can be agnostically learned in time nO(log k) (cf. Vempala's nO(k) time algorithm for learning in the noise-free model).Cones (with apex centered at the origin), and spheres witharbitrary radius and center, can be agnostically learned in time poly(n).

Published in:

Foundations of Computer Science, 2008. FOCS '08. IEEE 49th Annual IEEE Symposium on

Date of Conference:

25-28 Oct. 2008