LSM

Latent space model (LSM) for link prediction

This Git-repository features the Matlab code as well as the Stan models that were used in [1]. Using the Matlab-scripts requires

1. A Stan installation. Stan 2.9 was used for this project and may be found at http://mc-stan.org/.
2. The MatlabStan interface, which may be acquired at http://mc-stan.org/interfaces/matlab-stan.

Please note that Stan outputs temporary files to store the HMC samples. The way this is implemented in the MatlabStan wrapper is NOT thread-safe! If you want to have LSM samplers run in parallel, you need to modify the MatlabStan scripts to associate a unique ID which each sampling chain temp file.

Models

The following Stan models are available:

1. The core LSM (lsm.stan).
2. The LSM extended with random effects for sources and targets (lsm_directionaleffects.stan). This is the model around which [1] centers.
3. The LSM for datafusion, combining two input connectivity matrices (lsm_directionaleffects_datafusion.stan).
4. A model with only the random effects (directionaleffects.stan).
5. A model with only the random effects, combining two input connectivity matrices (directionaleffects_datafusion.stan).
6. A model with fixed instead of latent positions, with random effects (fpm_directionaleffects.stan).

Using the Matlab-wrapper

The core Matlab script is sampler.m. Examples of how to use this script are shown in DEMO.m. The sampler takes care of:

1. Collecting, thinning and storing the HMC samples.
2. Monitoring convergence using the Potential Scale Reduction Factor (PSRF) measure [2], as implemented by Simo Särkkä and Aki Vehtari (http://research.cs.aalto.fi/pml/software/mcmcdiag/). Depending on user settings, the sampler will automatically restart itself with more iterations if convergence has not been achieved. The default threshold for the PSRF is 1.1 (applied to all elements of the indicated variables). Which variables must be monitored for convergence is a user-supplied parameter.

In the DEMO.m script, a latent space model is estimated for the Felleman & van Essen macaque visual cortex data set, with latent dimensionality D=2.

References

1. Max Hinne, Annet Meijers, Rembrandt Bakker, Paul Tiesinga, Morten Mørup and Marcel van Gerven, 2017. The Missing Link: Predicting Connectomes from Noisy and Partially Observed Tract Tracing Data. PLoS Computational Biology.
2. Brooks, S.P. and Gelman, A. (1998) General methods for monitoring convergence of iterative simulations. Journal of Computational and Graphical Statistics. 7, 434-455.