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[theory-seminar] Theory Lunch 12/3: Weihao Kong on Estimating the Covariance Spectrum
Dan Michael Stubbs
dstubbs at stanford.edu
Wed Dec 2 14:29:04 PST 2015
After a week off, the theory lunch makes it triumphant return tomorrow in Gates 463A, with food around 12:15pm and theory at 12:30pm, presented by Weihao Kong; details below.
Estimating the Covariance Spectrum
Suppose one wishes to accurately recover the set of eigenvalues of the
covariance matrix of a distribution, given access to samples from the
distribution. To what extent can this set be accurately approximated
given an amount of data that is sublinear in the dimension of the
space? The naive empirical estimate has poor performance when the
number of samples is linear or sub-linear in the dimension of the
data. In the "large sample, large dimension" setting, we proposed an
efficient and information theoretically near-optimal algorithm to
learn the moments of the covariance spectral distribution. Further we
show that given the first k moments of a distribution, we can pin down
the distribution in Earthmover distance up to an error of O(1/k).
These two results combined allow us to efficiently and accurately
learn the spectrum of the underlying covariance matrix from data
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