Gibbs Sampler with Split-Merge Moves for the Infinite Hidden Markov Model (IHMM) (on top of Juergen Van Gaels IHMM toolbox http://mloss.org/software/view/205/ - see also the LICENSE file) and the Infinite Wishart Mixture Model (IWMM) implemented in MATLAB. The code was used a part of a publication "Predictive Assesment of Models for Dynamic Functional Connectivity", which as of now has been submitted. But models support calculating the predictive likelihood on a new data set, and this is showcased in the two demos demoIHMM.m and demo_wishartMM.m.
NB! The IWMM requires the test-set to have all postive-definite matrices to currently calculate the predictive likelihood. A future release will feature an option to drop the term involving the determinant of the test data, which will still allow for model comparision and paramter tuning.
If you found the code useful and use it a publication, please cite the following paper:
Nielsen, S. F. V., Schmidt, M. N., Madsen, K. H., & Mørup, M. (2018). Predictive assessment of models for dynamic functional connectivity. Neuroimage, 171, 116-134.
Infinite Hidden Markov Model
The Infinite Hidden Markov Model (IHMM) [2] is the Bayesian non-parametric extension of the hidden Markov model (HMM), in which we place a prior on the number of states and through inference (MCMC) learn the posterior distribution over state sequences. This construction is also known as a hierarchical Dirichlet Process. The implementation can be found in IHMMgibbs.m and a demonstration of how to use the code in demoIHMM.m.
To fully specify the IHMM we need an emission distribution. In software we have implemented three types of emission namely,
- ZMG : A zero-mean Gaussian in which the covariance matrix is state-specific.
- SSM : A Gaussian emission distribution with state specifc mean and covariance.
- VAR : A Gaussian emission distribution with a state specific vector-autoregressive mean and covariance
To switch between emissions use the opts structure with flags opts.emission_type = 'ZMG' for the zero-mean Gaussian. All flags and settings can be seen in the header of the code.
The infinite Wishart Mixture Model (IWMM)[4] is the Bayesian non-parametric extensin of the Wishart Mixture Model [5], in which a clustering of scatter matrices is modeled using a mixture of Wishart distribution, i.e. the model does not work on the 'raw' data excatly but for instance on windowed covariance matrices. The implementation can be found in wishart_MM.m and a demonstration of how to use the code can be found in demo_wishartMM.m
[1] Van Gael, J. (July, 2010). The Infinite Hidden Markov Model 0.5. Retrieved from http://mloss.org/software/view/205/
[2] Beal, M. J., Ghahramani, Z., & Rasmussen, C. E. (2002). The Infinite Hidden Markov Model. In T. G. Dietterich and S. Becker and Z. Ghahramani (Ed.), Advances in Neural Information Processing Systems 14 (pp. 577–584). MIT Press.
[3] Nielsen, S. F. V., Madsen, K. H., Røge, R., Schmidt, M. N., & Mørup, M. (2016, January 4). Nonparametric Modeling of Dynamic Functional Connectivity in fMRI Data. arXiv [stat.AP]. Retrieved from http://arxiv.org/abs/1601.00496
[4] Korzen, J., Madsen, K. H., & Mørup, M. (June 8-12, 2014). Quantifying Temporal States in rs-fMRI Data using Bayesian Nonparametrics. Presented at the Human Brain Mapping 2014
[5] Hidot, S., & Saint-Jean, C. (2010). An Expectation–Maximization algorithm for the Wishart mixture model: Application to movement clustering. Pattern Recognition Letters, 31(14), 2318–2324.