Fig. 1

Schematic of BCAUS. Structured data composed of control and treatment instances is fed to a neural network. The output of the network p⁽ⁱ⁾ for each instance i is a propensity score that optimizes a combination of two loss functions. A The binary cross entropy loss \( {\mathcal{L}}_{BCE} \) is computed by comparing p⁽ⁱ⁾ against targets t⁽ⁱ⁾ = 0 for control and t⁽ⁱ⁾ = 1 for treatment. B The bias loss \( {\mathcal{L}}_{B\mathrm{I} AS} \) is computed as follows: (i) p⁽ⁱ⁾ is used to compute an inverse probability weight (IPW, orange box) that multiplies all covariates of instance i (ii) weighted means \( {\overline{x}}_j \) are computed separately for treatment and control groups for each covariate x_j, and (iii) the mean squared error between weighted means of treatment and control covariates defines the bias loss. The sum of both losses is computed and backpropagated. μ is the scalar ratio of \( {\mathcal{L}}_{BCE} \) to \( {\mathcal{L}}_{BIAS} \) that is detached from the computation graph. The relative contribution of each loss component is tuned using hyperparameter, ν