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.
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.
Explains how Hilbert space techniques cross the boundaries into the foundations of probability and statistics. Focuses on the theory of martingales stochastic integration, interpolation and density...
Monte Carlo methods, in particular those based on Markov chains and on interacting particle systems, are by now tools that are routinely used in machine learning. These methods have had a profound...
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