<t>As far as a beginners introduction, I have been using 'Computational Topology' by Edelsbrunner and Harer at Duke. We have spoken with John Harer about the application of persistent homology type things for other (non finance) problem sets. I think there is the possibility to, just as you say, use...

<t>There seems to be more developing interest, for example topological data analysis topology of financial modeling and algebraic geometry and topology mention this kind of thing.I'm more familiar with applications in other areas (for example, gene expression data analysis), but would like to know h...

Can anyone say if they have used ideas of computational topology as a means of predictive analytics in quantitative finance? It seems that may be an under-represented technology area.

<t>The nice thing about Expectation Maximization is that it is guaranteed to converge, which is a huge plus, even though it is slow. Gradient methods, or Square Root Scoring methods, are useful to maximize the likelihoods and are faster, but may diverge. What many people do is start with EM, then wh...

<r>Would this be of help?<URL url="http://dl.acm.org/citation.cfm?doid=1870085.1870087found"><LINK_TEXT text="http://dl.acm.org/citation.cfm?doid=187 ... 70087found">http://dl.acm.org/citation.cfm?doid=1870085.1870087found</LINK_TEXT></URL> inhttp://<URL url="http://www.jhuapl.edu/spsa/Pages/Referen...

<t>If the covariance matrix is merely non-diagonal, that's not much of a problem. The determinant can still be computed (although it won't be as simple as for a diagonal matrix), any good reference on linear algebra should have methods for you to use. The real challenge is when the covariance matrix...