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Causal discovery for time series from multiple datasets with latent contexts

This repository is the official implementation to reproduce the experiments described in "Causal Discovery for time series from multiple datasets with latent contexts" by W. Günther, U. Ninad, and J. Runge (accepted at UAI 2023).

Requirements

To install the requirements run:

pip install -r requirements.txt

Running the presented Experiments

In this section, we describe how to run the whole experimental pipeline (data generation, method evaluation, metric calculation, plotting) to generate the results and plots presented in the paper.

In the config.py file you can specify the paths in which the output of these experiments should be stored.

To run the main experiments, execute this command:

python run_experiments.py --experiment 0

This generates toy-data from the SCM

$$X^{i,m}_t = a_i X^{i,m}_{t-1} + \sum_{j} b_j X^{j,m}_{t-\tau_j} + \sum_{j} c_jC^{\text{time},j}_{t-\tau_j} + \sum_{j} d_jC^{j, m}_\text{space} + \eta^{i,m}_t,$$

where $i \in \mathcal{I}$, $t= 1, \ldots, T$, and $m=1, \ldots, M$, $C^{\text{time},k} \sim \mathcal{N}(0,1)$, $C^{\text{space}} \sim \mathcal{N}(0,1)$. Furthermore, $\eta^i \sim \mathcal{N}(0,1)$ i.i.d., $a_i$ autocorrelation parameter uniformly drawn from $[0.3, 0.8]$, coefficients $b_j,c_j, d_j$ are uniformly drawn from $[0.5, 0.9]$, $50%$ of the links are contemporaneous, the remaining lags are drawn uniformly from $[1,3]$. See the paper for further details.

It then computes the output of the J-PCMCI+, PCMCI+ with observed context variables, PCMCI+ with dummy variables and original PCMCI+ on system variables.

Using the ground truth graphs and output graphs of these methods, it calculates the metrics which are described in more detail in the paper, and plots the results.

The results are as follows: time_conv space_conv

To run a simpler (and quicker) linear version of the experiments, run this command:

python run_experiments.py --experiment 1

This generates toy-data from a simplified version of the SCM above, namel 7225 y from

$$\begin{split} X^0_t &:= 0.5X^1_{t}+0.5C_\text{space}^0 + 0.5C_\text{space}^1 +0.5C_{\text{time}, t-1}^0 + 0.5C_{\text{time}, t-1}^1+ \eta^0\\\ X^1_t &:= 0.5X^1_{t-1}+ 0.5C_\text{space}^0 + 0.5C_\text{space}^1 +0.5C_{\text{time}, t-1}^0 +0.5C_{\text{time}, t-1}^1 + \eta^1\\\ C_\text{space}^0 &:= \eta^0_\text{space}\\\ C_\text{space}^1 &:= \eta^1_\text{space}\\\ C_{\text{time},t}^0 &:= \eta^0_\text{time}\\\ C_{\text{time},t}^1 &:= \eta^1_\text{time} \end{split}$$

And then proceeds as described above.

The results of this experimental setup are inset

To run a nonlinear variant of the simplified experiments, run this command:

python run_experiments.py --experiment 2

This generates toy-data from the following SCM

$$\begin{split} X^0_t &:= 0.5(X^1_{t})^2+0.5C_\text{space}^0 + 0.5C_\text{space}^1 +0.5C_{\text{time}, t-1}^0 + 0.5C_{\text{time}, t-1}^1+ \eta^0\\\ X^1_t &:= 0.5X^1_{t-1}+ 0.5C_\text{space}^0 + 0.5C_\text{space}^1 +0.5C_{\text{time}, t-1}^0 +0.5C_{\text{time}, t-1}^1 + \eta^1\\\ C_\text{space}^0 &:= \eta^0_\text{space}\\\ C_\text{space}^1 &:= \eta^1_\text{space}\\\ C_{\text{time},t}^0 &:= \eta^0_\text{time}\\\ C_{\text{time},t}^1 &:= \eta^1_\text{time} \end{split}$$

And then proceeds as described above. The results of this experimental setup are time_conv space_conv

Generating Data and Evaluating the Algorithm

You can also only generate data for specific parameter settings and compare the algorithms on these. This is done by running this command:

python compute.py --experiment 1

Using the parameters you can specify:

  • c float, dependence factor between $X$ and $Y$
  • affected_vars list[str], list of the affected nodes, default is ['x', 'y']
  • hs_types list[str], functional form and dependence of heteroskedasticity, either 'linear_z', 'periodic_z', or 'quadratic_z' or 'linear_time', 'periodic_time', or 'quadratic_time' , default is ['linear_time']
  • strength float, the strength of heteroskedasticity, default is 5.
  • sample_size int, sample size
  • random_seed int or None, random seed to be used for the experiment

-e -ss <sample_size> -d <nb_domains> -n <nb_nodes> -l <nb_links> -kt <k_time> "
"-ks <k_space> -o <frac_observed> -f <functional_form> -t <ci_test> -a <pc_alpha> -tm <tau_max> "
"-nr <nb_realisations>

Calculating the Metrics

To calculate the metrics on pre-computed outputs of the methods, run:

python methods.py --experiment 0

Using the parameters you can specify:

  • experiment {0, 1, 2}, experiment type

Plotting

python plot.py --experiment 0

Again, using the parameters you can specify:

  • experiment {0, 1, 2}, experiment type

License

You can redistribute and/or modify the code under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version.

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Code for reproducing the experimental results of the paper "Causal discovery for time series from multiple datasets with latent contexts" by W. Günther, U. Ninad, and J. Runge (accepted at UAI 2023).

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