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SUMMARY:Sequential complexities and uniform martingale LLN - Alexander Rak
 hlin\, University of Pennsylvania\, The Wharton School
DTSTART:20140623T103000Z
DTEND:20140623T110000Z
UID:TALK53094@talks.cam.ac.uk
CONTACT:37296
DESCRIPTION:Uniform laws of large numbers play a key role in statistics an
 d learning theory. In this talk\, we describe martingale analogues of the 
 uniform laws and introduce new notions of ``sequential complexities''. Ext
 ending the symmetrization technique to sequences of dependent random varia
 bles leads us to a notion of a tree. We then\nintroduce a definition of a 
 tree covering number\, extend the chaining analysis\, introduce an analogu
 e of the VC dimension\, and prove a counterpart to the classical combinato
 rial result of Vapnik-Chervonenkis-Sauer-Shelah. Our definitions and resul
 ts can be seen as non-i.i.d. extensions of some of the key notions in empi
 rical\nprocess theory.\n
LOCATION:Centre for Mathematical Sciences\, Meeting Room 2
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