Extension of the state-of-the-art causal discovery method PCMCI augmented with a feature-selection method based on Transfer Entropy. The algorithm, starting from a prefixed set of variables, identifies the correct subset of features and possible links between them which describe the observed process. Then, from the selected features and links, a causal model is built.

• Documentation
• Tutorials

Current state-of-the-art causal discovery approaches suffer in terms of speed and accuracy of the causal analysis when the process to be analysed is composed by a large number of features. F-PCMCI is able to select the most meaningful features from a set of variables and build a causal model from such selection. To this end, the causal analysis results faster and more accurate.

In the following it is presented an example showing a comparison between causal models obtained by PCMCI and F-PCMCI causal discovery algorithms on the same data. The latter have been created by defining a 6-variables system defined as follows:

min_lag = 1
max_lag = 1
np.random.seed(1)
nsample = 1500
nfeature = 6

d = np.random.random(size = (nsample, feature))
for t in range(max_lag, nsample):
  d[t, 0] += 2 * d[t-1, 1] + 3 * d[t-1, 3]
  d[t, 2] += 1.1 * d[t-1, 1]**2
  d[t, 3] += d[t-1, 3] * d[t-1, 2]
  d[t, 4] += d[t-1, 4] + d[t-1, 5] * d[t-1, 0]

Causal Model by PCMCI	Causal Model by F-PCMCI
Execution time ~ 6min 50sec	Execution time ~ 2min 45sec

The causal analysis performed by the F-PCMCI results not only faster but also more accurate. Indeed, the causal model derived by the F-PCMCI agrees with the structure of the system of equations, instead the one derived by the PCMCI presents spurious links:

• $X_2$ → $X_4$
• $X_2$ → $X_5$

Note that, since all the 6 variables were involved in the evolution of the system, the F-PCMCI did not remove any of them. In the following example instead, we added a new variable in the system which is defined just by the noise component (as $X_1$ and $X_5$) and does not appear in any other equation, defined as follows: $X_6(t) = \eta_6(t)$. In the following the comparison between PCMCI and F-PCMCI with this new system configuration:

Causal Model by PCMCI	Causal Model by F-PCMCI
Execution time ~ 8min 40sec	Execution time ~ 3min 00sec

In this case the F-PCMCI removes the $X_6$ variable from the causal graph leading to generate exactly the same causal model as in the previous example, with comparable executional time. Instead, the PCMCI suffers the presence of $X_6$ in terms of time and accuracy of the causal structure. Indeed, a spurious link $X_6$ → $X_5$ appears in the causal graph derived by the PCMCI.

If you found this useful for your work, please cite this papers:

@inproceedings{castri2023fpcmci,
    title={Enhancing Causal Discovery from Robot Sensor Data in Dynamic Scenarios},
    author={Castri, Luca and Mghames, Sariah and Hanheide, Marc and Bellotto, Nicola},
    booktitle={Conference on Causal Learning and Reasoning (CLeaR)},
    year={2023},
}

• tigramite>=5.1.0.3
• pandas>=1.5.2
• netgraph>=4.10.2
• networkx>=2.8.6
• ruptures>=1.1.7
• scikit_learn>=1.1.3
• torch>=1.11.0
• gpytorch>=1.4
• dcor>=0.5.3
• h5py>=3.7.0
• jpype1>=1.5.0
• mpmath>=1.3.0

Before installing the F-PCMCI package, you need to install Java and the IDTxl package used for the feature-selection process, following the guide described here. Once complete, you can install the current release of F-PCMCI with:

pip install fpcmci

For a complete installation Java - IDTxl - F-PCMCI, follow the following procedure.

Verify that you have not already installed Java:

java -version

if the latter returns Command 'java' not found, ..., you can install Java by the following commands, otherwise you can jump to IDTxl installation.

# Java
sudo apt-get update
sudo apt install default-jdk

Then, you need to add JAVA_HOME to the environment

sudo nano /etc/environment
JAVA_HOME="/lib/jvm/java-11-openjdk-amd64/bin/java" # Paste the JAVA_HOME assignment at the bottom of the file
source /etc/environment

# IDTxl
git clone https://github.com/pwollstadt/IDTxl.git
cd IDTxl
pip install -e .

pip install fpcmci