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SUMMARY:Unbiased Estimation of the Eigenvalues of Large Implicit Matrices 
 - Professor Ryan Adams\, Princeton
DTSTART:20170914T100000Z
DTEND:20170914T110000Z
UID:TALK74501@talks.cam.ac.uk
CONTACT:Pat Wilson
DESCRIPTION:\nMany important problems are characterized by the eigenvalues
  of a\nlarge matrix.  For example\, the difficulty of many optimization\np
 roblems\, such as those arising from the fitting of large models in\nstati
 stics and machine learning\, can be investigated via the spectrum\nof the 
 Hessian of the empirical loss function.  Network data can be\nunderstood v
 ia the eigenstructure of the Laplacian matrix through\nspectral graph theo
 ry.  Quantum simulations and other many-body\nproblems are often character
 ized via the eigenvalues of the solution\nspace\, as are various dynamic s
 ystems.  However\, naive eigenvalue\nestimation is computationally expensi
 ve even when the matrix can be\nrepresented\; in many of these situations 
 the matrix is so large as to\nonly be available implicitly via products wi
 th vectors.  Even worse\,\none may only have noisy estimates of such matri
 x vector products.  In\nthis talk I will discuss how several different ran
 domized techniques\ncan be combined into a single procedure for unbiased e
 stimates of the\nspectral density of large implicit matrices in the presen
 ce of noise.\n\n
LOCATION:CBL Room BE-438\, Department of Engineering
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