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Polynomial Methods in Statistical Inference - Theory and Practice (Paperback)
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Polynomial Methods in Statistical Inference - Theory and Practice (Paperback)
Series: Foundations and Trends (R) in Communications and Information Theory
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The authors of this monograph survey a suite of techniques based on
the theory of polynomials, collectively referred to as polynomial
methods. These techniques provide useful tools not only for the
design of highly practical algorithms with provable optimality, but
also for establishing the fundamental limits of inference problems
through moment matching. The authors demonstrate the effectiveness
of the polynomial method using concrete problems such as entropy
and support size estimation, distinct elements problem, and
learning Gaussian mixture models. This monograph provides a
comprehensive, yet concise, overview of the theory covering topics
such as polynomial approximation, polynomial interpolation and
majorization, moment space and positive polynomials, orthogonal
polynomials and Gaussian quadrature. The authors proceed to show
the applications of the theory in statistical inference. Polynomial
Methods in Statistical Inference provides students, and researchers
with an accessible and complete treatment of a subject that has
recently been used to solve many challenging problems in
statistical inference.
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