MSE vs topology for GMRFs

Closed form expressions for the MSE for stylized topologies such as complete graph, star and cycle seem very doable.. and so are the error exponents

Keeping up with the GMRFs

Turns out the family of GMRFs is quite a motley one. Researchers have specified these models in varied fashion across the body of literature. Here are some prime examples:

1. Intrinsic (Improper)
2. Linear filters specification as in the perturb-and-MAP paper.
3. Via the covariance matrix
4. Generalized CAR
5. Besag's classical zero-mean CAR
6. AR/SAR.

The CAR vs SAR dilemma was pretty informational as Katt Williams put it. The bottom line seems to be that SAR models are sorta more well suited to ML estimation (but not so much for MCMC fitting). The
hierarchical conditional representation of CAR helps it trump here. 

*Must read more*

Some chump change MATLAB code, model comparisons

This post, I reckon is mostly for book keeping. To remind me the not-so-subtle difference in the MSE when the two seemingly cross-compatible models are switched.
Nice 'data science' lesson this ...

GMRF based imputation in Average emergency visits

Lets look at the California dataset of average emergency visits. Can we throw a GMRF+SVR regression model at it and impute missing values?
If so, how good are the results?

Bhattacharya co-efficient + GMRF

Bhattacharya co-efficient and gradient evaluation: Some hand calculations here ...

 

Spectral radius + GMRF

SPECTRAL RADIUS OF THE GRAPH: I've seen you lurking around virality and epidemiology SIR/SIS sorta papers.
Looks like we've formally met finally ...
Also, added is an idea, or rather a recipe to bring in the pseudo-control-node as external field into the GMRF.

Continuous case: GMRF + Probability of error

Main points:

1. MSE comparisons for WLS (Network aided) vs LS  for different topologies.
2. Extension to the detection problem.
3. Some more performance comparisons ...

Classification erro vs topology

An attempt at doing low SNR analysis of MSE which is UB of Probability of error via the Verdu-Estimation-marries-Info theory route.
Result: MSE in terms of the graph spectra. Or rather spectra of the covariance matrix!

Trick: Approximate the GMRF via a common Gaussian.