fpcmci 4.1.0

A causal discovery Python package

FPCMCI - Filtered PCMCI

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.

Useful links

• Documentation
• Tutorials

Why FPCMCI?

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. FPCMCI 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 FPCMCI 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 FPCMCI
Execution time ~ 6min 50sec	Execution time ~ 2min 45sec

The causal analysis performed by the FPCMCI results not only faster but also more accurate. Indeed, the causal model derived by the FPCMCI 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 FPCMCI 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 FPCMCI with this new system configuration:

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

In this case the FPCMCI 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.

Citation

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

@article{ghidoni2022human,
  title={From Human Perception and Action Recognition to Causal Understanding of Human-Robot Interaction in Industrial Environments},
  author={Ghidoni, Stefano and Terreran, Matteo and Evangelista, Daniele and Menegatti, Emanuele and Eitzinger, Christian and Villagrossi, Enrico and Pedrocchi, Nicola and Castaman, Nicola and Malecha, Marcin and Mghames, Sariah and others},
  year={2022}
}

@inproceedings{castri2022causal,
    title={Causal Discovery of Dynamic Models for Predicting Human Spatial Interactions},
    author={Castri, Luca and Mghames, Sariah and Hanheide, Marc and Bellotto, Nicola},
    booktitle={International Conference on Social Robotics (ICSR)},
    year={2022},
}

Requirements

• numpy==1.21.5
• scipy==1.8.0
• tigramite==5.1.0.3
• matplotlib==3.6.2
• netgraph==4.10.2
• networkx==2.8.8
• pandas==1.5.2
• ruptures==1.1.7
• scikit_learn==1.1.3
• torch==1.13.0
• gpytorch==1.9.0
• dcor==0.5.7
• h5py==3.7.0

Installation

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

pip install fpcmci

Recent changes

• 4.1.0 FSelector and FValidator turned into FPCMCI and PCMCI, show_edge_label removed and dag optimized, new package included in the setup.py, added tutorials, and new example in README.md.
• 4.0.1 online documentation and paths fixes.
• 4.0.0 package published.