BIDA

Code for causal effect discovery and linear causal effect estimation using Bayesian IDA (BIDA). The code package contains an C++ implementation (APS) for exact computation of parent set and ancestor relation posterior probabilities using dynamic programming (see Algorithm 1 in Pensar et al. [1]). The computationally less demanding part of the effect estimation method has been implemented in R.

The repo also contains the supplementary material for the accepted paper.

APS

The APS tool can be used for two related but separate problems:

• For each variable and parent set, compute the total weight of all DAGs where a node has a particular parent set.

• For each pair (i, j) of variables, compute the total weight of DAGs where j is an ancestor of i.

To compile the program, go to the aps subdirectory and run make.

After compilation, use aps help for more details about the tool.

Calculating BIDA posteriors

After compiling the APS program, BIDA can be run from R. As an example case, we will use the included data, which contains 200 observations from a Gaussian DAG model over 10 variables. The data has been zero-centered and standardized.

Assuming the BIDA folder is set as the current working directory in R, we read in the data and true causal effect matrix.

data <- read.csv(file = 'example_data/data_d10.txt', header = FALSE)
true_effects <- as.matrix(read.csv(file = 'example_data/tce_d10.txt', header = FALSE))

In the true effect matrix, a value at row i and column j will correspond to the causal effect of i on j.

We then source the R-files.

file_paths <- list.files(pattern = "[.]R$", path = "R/", full.names = TRUE)
invisible(sapply(file_paths, source))

We compute the BIDA posteriors, setting the maximum parent set size to 5.

bida_post <- bida(data, max_parent_size = 5)

Finally, we evaluate our estimates by calculating the mean squared error (MSE) between the posterior means and true causal effects.

# Calculate mean of BIDA posteriors
bida_mean <- calc_bida_post_mean(bida_post)

# Calculate mean squared error for the mean posterior point estimates 
mse <- mean((bida_mean-true_effects)[diag(ncol(data)) == 0]^2)

This should give an MSE around 0.0655.

Alternatively, if one is interested in ranking the causal effect by their magnitude, one can calculate (numerically) the posterior absolute mean.

bida_mean_abs <- calc_bida_post_mean_abs(bida_post)

Calculating Ancestor Relation Probabilities (ARPs)

Continuing with our example above, we compute the ARPs which is a more direct Bayesian approach for estimating if there exists a causal relation or not. Again, the maximum parent set size is set to 5.

arp <- calc_arp(data, max_parent_size = 5)

In the resulting matrix, the value at row i and column j is the posterior probability of there existing an ancestral path from i to j.

Reference

BIDA was developed as part of an academic project:

[1] Pensar, J., Talvitie, T., Hyttinen, A., Koivisto, M. A Bayesian Approach for Estimating Causal Effects from Observational Data. Accepted to AAAI-20.

Please cite the above paper when using the method or parts of it (modified or as is).