Efficient Statistics, in High Dimensions, from Truncated Samples
Name
1809.03986.pdf
Description
Submitted version
Size
502.68 KB
Format
Adobe PDF
Checksum (MD5)
bb459ffa764c3268a45c94f8ed70c025
Author(s)
Daskalakis, Constantinos
Gouleakis, Themis
Tzamos, Chistos
Zampetakis, Manolis
Date Issued
October 2018
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Daskalakis, Constantinos, Gouleakis, Themis, Tzamos, Chistos and Zampetakis, Manolis. 2018. "Efficient Statistics, in High Dimensions, from Truncated Samples."
Version
Original manuscript
Abstract
We provide an efficient algorithm for the classical problem, going back to Galton, Pearson,and Fisher, of estimating, with arbitrary accuracy the parameters of a multivariate normal distribution from truncated samples. Truncated samples from ad-variate normal N(μ,Σ) means a samples is only revealed if it falls in some subset S⊆Rd; otherwise the samples are hidden and their count in proportion to the revealed samples is also hidden. We show that the meanμand covariance matrixΣcan be estimated with arbitrary accuracy in polynomial-time, as long as we have oracle access to S, and S has non-trivial measure under the unknown d-variate normal distribution. Additionally we show that without oracle access to S, any non-trivial estimation is impossible.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1109/focs.2018.00067
