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Newton’s Method and Scoring

  • Kenneth Lange
Chapter
Part of the Statistics and Computing book series (SCO)

Abstract

The MM and EM algorithms are hardly the only methods of optimization. Newton’s method is better known and more widely applied. We encountered Newton’s method in Section 5.4 of Chapter 5. Here we focus on the multidimensional version. Despite its defects, Newton’s method is the gold standard for speed of convergence and forms the basis of many modern optimization algorithms. Its variants seek to retain its fast convergence while taming its defects. The variants all revolve around the core idea of locally approximating the objective function by a strictly convex quadratic function. At each iteration the quadratic approximation is optimized. Safeguards are introduced to keep the iterates from veering toward irrelevant stationary points.

Keywords

Exponential Family Secant Condition Dirichlet Distribution Multinomial Family Ascent Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer New York 2010

Authors and Affiliations

  1. 1.Departments of Biomathematics, Human Genetics, and Statistics David Geffen School of MedicineUniversity of California, Los AngelesLos AngelesUSA

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