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Fig. 2 | BMC Medical Research Methodology

Fig. 2

From: Minimizing bias in massive multi-arm observational studies with BCAUS: balancing covariates automatically using supervision

Fig. 2

Results of BCAUS on IHDP dataset. Model trained on one realization. a Number of balanced covariates (standardized difference, Δ between arms < 0.1, Eq. 5) as training progresses for different values of hyperparameter ν. When ν = 0, the network is trained with \( {\mathcal{L}}_{BCE} \) alone. b Loss curves for \( {\mathcal{L}}_{BCE} \) (green) and \( {\mathcal{L}}_{BIAS} \) (violet) for network trained with ν = 1. c Standardized differences for all 25 covariates in IHDP dataset for network trained with ν = 1. Green trace is raw unadjusted data and violet trace shows data adjusted by Inverse Propensity Weights (IPW). Dashed line represents threshold at 0.1. Inset shows normalized histograms of the distribution of propensity scores i.e. output of BCAUS, for control (green) and treatment (violet) groups

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