2/10/2015

Post date: Feb 21, 2015 8:05:46 PM

Speaker: Ravi Varadhan, Division of Biostatistics and Bioinformatics, SKCCC, JHU

"Part 2: Fundamentals of convergence acceleration and Some New Techniques"

[abstract]

I will discuss, with examples, the classical convergence acceleration technique for scalar sequences called Aitken's extrapolation, and a closely related iterative scheme called Steffensen's iteration for finding fixed-points of the function F(x) on the reals. I will then discuss the extension of these ideas to vector sequences and functions. Then, I will show how these ideas can be used to accelerate the convergence of EM and MM algorithms. Finally, I will present a newly developed class of acceleration techniques called SQUAREM (Varadhan and Roland 2008) and discuss their properties. SQUAREM is simple, stable, and fast. SQUAREM generally achieves superlinear convergence in problems with a large fraction of missing information. Globally convergent schemes are easily obtained by viewing SQUAREM as a continuation of EM. SQUAREM can be readily implemented as an “off-the-shelf” accelerator for any EM-type algorithm, as it only requires the EM parameter updating. It is implemented in an R package called SQUAREM, which is available on the Comprehensive R Archive Network (CRAN).

In the two talks, I will demonstrate the convergence behavior of the various algorithms with several examples using R.