[AI Seminar] AI Seminar Sponsored by Apple -- Chris Liaw, Near-optimal sample complexity bounds for learning mixtures of Gaussians

[Han Zhao]

Dear faculty and students:

We look forward to seeing you on Tuesday, Nov. 19th, at noon in *NSH 3305 *for
our AI Seminar sponsored by Apple. To learn more about the seminar series,
please visit the website <http://www.cs.cmu.edu/~aiseminar/>.
On Tuesday, Chris Liaw will give the following talk:
*Title: *Near-optimal sample complexity bounds for learning mixtures of
Gaussians

*Abstract:* Estimating distributions from observed data is a fundamental
task in statistics that has been studied for over a century. We consider
such a problem where the distribution is a mixture of k Gaussians in R^d.
The objective is density estimation: given i.i.d. samples from the
(unknown) distribution, produce a distribution whose total variation
distance from the unknown distribution is at most epsilon. We prove that
Theta(kd^2/epsilon^2) samples are necessary and sufficient for this task,
suppressing logarithmic factors. This improves both the known upper bound
and lower bound for this problem.
-- 

*Han ZhaoMachine Learning Department*


*School of Computer ScienceCarnegie Mellon UniversityMobile: +1-*
*412-652-4404*
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