Fisher Information Lower Bounds with Applications in Hardware-Aware
Nonlinear Signal Processing
release_fyj5wh6vjzgh7g3lzxu7l5sedm
by
Manuel Stein, Josef A. Nossek, Kurt Barbé
2018
Abstract
We discuss the problem of deriving compact and tractable lower bounds for the
Fisher information matrix. To motivate our particular approach towards such
expressions, we first examine the structure of the exact Fisher information
matrix in the context of exponential family models. Then, by replacing an
arbitrary data model by an equivalent distribution within the exponential
family of distributions, we derive a lower bound for the Fisher information
measure of probabilistic models with multivariate output and multiple
parameters. The pessimistic information matrix allows a tractable quantitative
analysis of the parameter-specific information flow through nonlinear random
systems. Therefore, the technique is exploited for the performance analysis
concerning direction-of-arrival estimation of wireless source signals with a
binary radio sensor array. Further, by the example of a sensing device
exhibiting amplifier saturation, we outline how the information bound can be
used to learn compression schemes which preserve the parameter-specific
information within the data while the probabilistic model is unknown. We also
show that the conservative estimation performance characterized by the
pessimistic Fisher information matrix is asymptotically achieved by a
consistent estimator operating on compressed data. A reformulation of the
estimation algorithm turns out to be reminiscent of Hansen's generalized method
of moments while the pessimistic Fisher information matrix shows a vivid
interpretation within a particular Gaussian modeling framework.
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