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UID:1651759200@ist.ac.at
DTSTART:20220505T160000
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DESCRIPTION:Speaker: Yuri Polyanskiy\nhosted by Marco Mondelli\nAbstract: C
 onsider the following classical (unsupervised learning) problem of estimat
 ing the mean of an n-dimensional normally (with identity covariance matri
 x) or Poisson distributed vector under the squared loss.  The framework o
 f empirical Bayes (EB)\, put forth by Robbins'1956\, combines Bayesian and
  frequentist mindsets by postulating that the mean's coordinates are samp
 led iid from an unknown prior and aims to use a fully data-driven estimat
 or to compete with the Bayesian oracle that knows the true prior. The fig
 ure of merit is the total excess risk (regret) over the Bayes risk in the
  worst case (over the class of\, e.g.\, priors with a given support).  Al
 though this paradigm was introduced more than 60 years ago\, little was k
 nown about the asymptotic scaling of the optimal regret before our work e
 stablished it to be $\\Theta((\\log n/\\log \\log n)^2)$ for the Poisson c
 ase. The same  rate is shown to be a lower bound for the normal case\, ve
 rifying and strengthening upon an old conjecture of $\\omega(1)$ due to S
 ingh'1979. We will discuss practical implementation of EB estimators. The
  most performant of those are obtained by first running a non-parametric m
 aximum likelihood (NPMLE) to estimate the unknown prior\, and then comput
 ing (via Bayes) the posterior mean with respect to the estimated prior. W
 e will discuss empirical results on sports data and  short-term time seri
 es forecasting. Based on joint works with Yihong Wu\, Soham Jana and Anzo
  Teh.
LOCATION:Zoom Link: https://istaustria.zoom.us/j/69561558364?pwd=UGNVRDNSMH
 RKcjQvVFQySzQ3NGkyQT09  Meeting ID: 695 6155 8364 Passcode: 497872\, ISTA
ORGANIZER:
SUMMARY:Yuri Polyanskiy: Empirical Bayes estimators for Poisson and normal 
 means 
URL:https://talks-calendar.ista.ac.at/events/3722
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