Limits on mass of missing mass

On the concentration of the missing mass ∗

A random variable is sampled from a discrete distribution. The missing mass is the probability of the set of points not observed in the sample. We sharpen and simplify McAllester and Ortiz’s results (JMLR, 2003) bounding the probability of large deviations of the missing mass. Along the way, we refine and rigorously prove a fundamental inequality of Kearns and Saul (UAI, 1998).

Upper Limits on a Possible Gluon Mass

Limits on ντ mass by DELPHI

A limit on the tau neutrino mass is obtained using all the Z → ττ data collected at LEP by the DELPHI detector between 1992 and 1995. In this analysis events in which one of the taus decays into one charged particle, while the second τ decays into five charged pions (1-5 topology) have been used. The neutrino mass is determined from a bidimensional fit on the invariant mass m∗5π and on the ener...

Photon and Graviton Mass Limits

Efforts to place limits on deviations from canonical formulations of electromagnetism and gravity have probed length scales increasing dramatically over time. Historically, these formulations have passed through three stages: (1) Testing the power in the inverse-square laws of Newton and Coulomb, (2) Seeking a nonzero value for the rest mass of photon or graviton, (3) Considering more degrees o...

On the Impossibility of Learning the Missing Mass

Abstract This paper shows that one cannot learn the probability of rare events without imposing further structural assumptions. The event of interest is that of obtaining an outcome outside the coverage of an i.i.d. sample from a discrete distribution. The probability of this event is referred to as the “missing mass”. The impossibility result can then be stated as: the missing mass is not dist...