Event
Hassan Ashtiani, University of Waterloo
Wednesday, December 6, 2017 10:00to11:00
Burnside Hall
Room 1205, 805 rue Sherbrooke Ouest, Montreal, QC, H3A 0B9, CA
Sample-Efficient Learning of Mixture Distributions.
Learning about a probability distribution from a sample generated by that distribution is a fundamental task. We consider PAC learning of probability distributions (a.k.a. density estimation), where we are given an i.i.d. sample generated from an unknown target distribution, and want to output a distribution that is close to the target. Given the target distribution can be approximated by a member of some predetermined class of distributions, we analyze how large should a sample be so that one is able to find a distribution that is close to the target in total variation distance.聽 Determining such sample complexity with respect to an arbitrary class of distributions is a fundamental open problem.
In particular, we improve the best known upper bounds for learning a variety of mixture classes, including mixtures of Gaussian distributions over R^n. Furthermore, we introduce a novel method for learning distributions via a form of compression. Using this generic framework, we provide the first tight bound (up to logarithmic factors) for learning the class of mixtures of axis-aligned Gaussians. This is joint work with Abbas Mehrabian and Shai Ben-David.Learning about a probability distribution from a sample generated by that distribution is a fundamental task. We consider PAC learning of probability distributions (a.k.a. density estimation), where we are given an i.i.d. sample generated from an unknown target distribution, and want to output a distribution that is close to the target. Given the target distribution can be approximated by a member of some predetermined class of distributions, we analyze how large should a sample be so that one is able to find a distribution that is close to the target in total variation distance.聽 Determining such sample complexity with respect to an arbitrary class of distributions is a fundamental open problem.
In particular, we improve the best known upper bounds for learning a variety of mixture classes, including mixtures of Gaussian distributions over R^n. Furthermore, we introduce a novel method for learning distributions via a form of compression. Using this generic framework, we provide the first tight bound (up to logarithmic factors) for learning the class of mixtures of axis-aligned Gaussians. This is joint work with Abbas Mehrabian and Shai Ben-David.
In particular, we improve the best known upper bounds for learning a variety of mixture classes, including mixtures of Gaussian distributions over R^n. Furthermore, we introduce a novel method for learning distributions via a form of compression. Using this generic framework, we provide the first tight bound (up to logarithmic factors) for learning the class of mixtures of axis-aligned Gaussians. This is joint work with Abbas Mehrabian and Shai Ben-David.Learning about a probability distribution from a sample generated by that distribution is a fundamental task. We consider PAC learning of probability distributions (a.k.a. density estimation), where we are given an i.i.d. sample generated from an unknown target distribution, and want to output a distribution that is close to the target. Given the target distribution can be approximated by a member of some predetermined class of distributions, we analyze how large should a sample be so that one is able to find a distribution that is close to the target in total variation distance.聽 Determining such sample complexity with respect to an arbitrary class of distributions is a fundamental open problem.
In particular, we improve the best known upper bounds for learning a variety of mixture classes, including mixtures of Gaussian distributions over R^n. Furthermore, we introduce a novel method for learning distributions via a form of compression. Using this generic framework, we provide the first tight bound (up to logarithmic factors) for learning the class of mixtures of axis-aligned Gaussians. This is joint work with Abbas Mehrabian and Shai Ben-David.