Unbiased Estimation of the Eigenvalues of Large Implicit Matrices
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If you have a question about this talk, please contact Pat Wilson.
Many important problems are characterized by the eigenvalues of a
large matrix. For example, the difficulty of many optimization
problems, such as those arising from the fitting of large models in
statistics and machine learning, can be investigated via the spectrum
of the Hessian of the empirical loss function. Network data can be
understood via the eigenstructure of the Laplacian matrix through
spectral graph theory. Quantum simulations and other manybody
problems are often characterized via the eigenvalues of the solution
space, as are various dynamic systems. However, naive eigenvalue
estimation is computationally expensive even when the matrix can be
represented; in many of these situations the matrix is so large as to
only be available implicitly via products with vectors. Even worse,
one may only have noisy estimates of such matrix vector products. In
this talk I will discuss how several different randomized techniques
can be combined into a single procedure for unbiased estimates of the
spectral density of large implicit matrices in the presence of noise.
This talk is part of the Machine Learning @ CUED series.
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