This repository contains code to learn mixtures of continuous-time (and discrete-time) Markov chains using methods. Our method is split into three steps:

1. Discretization
2. Soft-Clustering: We use methods from learning discrete-time Markov chains
   • Discrete-Time EM
   • SVD (Gupta et al., Spaeh and Tsourakakis)
   • Spectral Clustering (Kausik et al.)
3. Recovery

Additionally, we provide code for continuous-time EM.

Methods are split into the representation of discrete and continuous-time mixtures (dtmixtures.py, ctmixtures.py) and learning of discrete and continuous-time mixtures (dtlearn.py, ctlearn.py). The code for experiments is in experiments.py.

Enter the Anaconda environment:

conda activate std_env

Compile cython:

python setup.py build_ext --inplace

We can run a small example using

python run.py

which places a figure under plots. All results are cached in the cache folder. Empty the folder to re-run experiments.

In order to experiment with the NBA data from Second Spectrum, put passes.csv and player_ssid.csv in the NBA folder and run NBA/extract.py.

The LastFM data is available under http://millionsongdataset.com/lastfm/#desc Unzip lastfm-dataset-1K.tar.gz in the folder LastFM.

Code for plots produced in the paper are in the notebook main.ipynb