Localising Dropout Variance in Twin Networks

Abstract

Accurate individual treatment-effect estimation demands not only reliable point predictions but also uncertainty measures that help practitioners \emph{locate} the source of model failure. We introduce a layer-wise variance decomposition for deep twin-network models: by toggling Monte Carlo Dropout independently in the shared encoder and the outcome heads, we split total predictive variance into an \emph{encoder component} ($\ddot{I}{ƒ}_{\mathrm{enc}}^2$) and a \emph{head component} ($\ddot{I}{ƒ}_{\mathrm{head}}^2$), with $\ddot{I}{ƒ}_{\mathrm{enc}}^2+\ddot{I}{ƒ}_{\mathrm{head}}^2\approx \ddot{I}{ƒ}_{\mathrm{tot}}^2$ by the law of total variance. Across three synthetic covariate-shift regimes, the encoder component dominates under distributional shift ($\ddot{I}{}_{\mathrm{enc}}=0.53$) while the head component becomes informative only once encoder uncertainty is controlled. On a real-world twins cohort with induced multivariate shift, only $\ddot{I}{ƒ}_{\mathrm{enc}}^2$ spikes on out-of-distribution samples and becomes the primary error predictor ($\ddot{I}{}_{\mathrm{enc}}\approx 0.89$), while $\ddot{I}{ƒ}_{\mathrm{head}}^2$ remains flat. The decomposition adds negligible cost over standard MC Dropout and provides a practical diagnostic for deciding whether to collect more diverse covariates or more outcome data.

14 pages, 5 figures, 3 tables