Algorithm 1.

PSSAM-GAN: Propensity Score Synthetic Augmentation Matching using Generative Adversarial Networks.

Input: Training set X = {(x(1), t(1), y(1)),…, (x(n), t(n), y(n)) }, loss function L(., .), hyperparameter β > 0, generator network G with initial parameters θg, discriminator network D with initial parameters θd, epochs K

1. Perform neural network-based propensity score π(X) calculation and matching between the treated samples (t = 1) and control samples (t = 0) using the nearest neighbor algorithm with replacement

2. Separate out the unmatched control samples from the matched ones

3. for epochs = 1, 2, … ,Ks do

4.   Sample minibatch of m noise samples ${\left\{z^{(i)}\right\}}_{i=1}^m$ where $z~\mathcal{N}(0,1)$

5.   Sample minibatch of m unmatched control samples from the distribution pdata(xuc)

6.   Update the discriminator D by ascending its stochastic gradient: ${\nabla }_{{\theta }_d}\left({\varphi }_d(D,G)\right)$

7.   Sample minibatch of m noise samples ${\left\{z^{(i)}\right\}}_{i=1}^m$ where $z~\mathcal{N}(0,1)$

8.   Update the generator G by descending its stochastic gradient: ${\nabla }_{{\theta }_d}\left({\varphi }_d(D,G)\right)$

9. end for

10. Remove the discriminator D and get the generated samples from the generator G and assign them as treated

11. Train a multitask regression model with the original training set X to obtain outcome labels for the generated treated samples

12. Merge the original dataset with the synthetic data into an augmented balanced dataset

13. Train a multitask regression model with the augmented dataset