Name
Abstract | ||
|---|---|---|
The standard implementation of the Maximum Entropy Method (MEM) follows Bryan [1] and deploys a Singular Value Decomposition (SVD) to limit the dimensionality of the underlying solution space apriori. Here we present arguments based on the shape of the SVD basis functions and numerical evidence from a mock data analysis, which show that the correct Bayesian solution is not in general recovered with this approach. As a remedy we propose to extend the search basis systematically, which will eventually recover the full solution space and the correct solution. In order to adequately approach problems where an exponentially damped kernel is used, we provide an open-source implementation, using the C/C++ language that utilizes high precision arithmetic adjustable at run-time [2]. The LBFGS algorithm is included in the code in order to attack problems without the need to resort to a particular search space restriction. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1016/j.jcp.2012.12.023 | J. Comput. Physics |
Keywords | Field | DocType |
svd basis function,improved maximum entropy analysis,lbfgs algorithm,particular search space restriction,standard implementation,correct bayesian solution,open-source implementation,extended search space,full solution space,search basis systematically,underlying solution space apriori,correct solution,high energy physics,data analysis,lattice qcd,search space,basis functions,maximum entropy | Kernel (linear algebra),Information theory,Singular value decomposition,Monte Carlo method,Mathematical optimization,A priori and a posteriori,Algorithm,Curse of dimensionality,Basis function,Principle of maximum entropy,Mathematics | Journal |
Volume | ISSN | Citations |
238, | 0021-9991 | 0 |
PageRank | References | Authors |
0.34 | 0 | 1 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Alexander Rothkopf | 1 | 0 | 1.01 |