http://arxiv.org/abs/1504.02661
Matrix determinants play an important role in data analysis, in particular when Gaussian processes are involved. Due to currently exploding data volumes linear operations – matrices – acting on the data are often not accessible directly, but are only represented indirectly in form of a computer routine. Such a routine implements the transformation a data vector undergoes under matrix multiplication. Meanwhile efficient probing routines to estimate a matrix’s diagonal or trace, based solely on such computationally affordable matrix-vector multiplications, are well known and frequently used in signal inference, a stochastic estimate for its determinant is still lacking. In this work a probing method for the logarithm of a determinant of a linear operator is introduced. This method rests upon a reformulation of the log-determinant by an integral representation and the transformation of the involved terms into stochastic expressions. This stochastic determinant determination enables large-size applications in Bayesian inference, in particular evidence calculations, model comparison, and posterior determination.
S. Dorn and T. Ensslin
Mon, 13 Apr 15
49/54
Comments: 8 pages, 5 figures
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