Control variables are widely used in statistical modelling to account for omitted variable bias of known confounders. However, they have largely been underexplored in deep learning. This is surprising, given that deep learning models encode image-inferable covariates, such as demographic variables, into their predictions when these covariates are correlated with the outcome---a form of omitted variable bias referred to as'shortcut learning'. While many existing confound-control or fairness methods try to restrict the correlation of such covariates with model predictions, we show that this fails to correct for omitted variable bias. We therefore propose a control variable approach for deep learning models, based on generalised additive modelling of the effects of model inputs and covariates. As flexible additive models can suffer from concurvity, we introduce an estimation procedure that refits the final layer of a pre-trained network to include covariate effects, using cross-fitting with ridge penalisation. We show how these effects can be orthogonalised with respect to covariates to exclude their mediated effects and that model predictions can be marginalised over the covariate distribution to control for their effect. This yields unbiased, interpretable predictions and offers flexibility to model the desired effects depending on the scientific or fairness objective. We verify our approach using simulated images, and demonstrate consistent estimation of true effects. Existing methods either require more data or fail to recover the true effects. We apply our method to real neuroimaging data with experimentally induced confounding, where it recovers prediction performance to near the level of a model trained on unconfounded data. Code is available at https://github.com/mpff/cocodeel.
Manuel Pfeuffer, R. Rane, Kerstin Ritter et al.· 0 citations
Conditional independence tests (CITs) test for conditional dependence between two random objects $X$ and $Y$ given a third random object $Z$. Existing CITs have limited applicability to high-dimensional data, especially multimodal data like text. However, we show that such tests are of interest for large language model (LLM) outputs, where we test whether an output $X$ generated from a source text $Z$ carries information about an attribute $Y$ beyond $Z$ itself. For this purpose, we propose embedded CITs (eCITs), which embed $X$ and $Z$ and apply an existing CIT to the resulting representations and to $Y$. We show that, provided the embedding of $Z$ is sufficient, i.e. retains the information $Z$ carries about either $Y$ or the representation of $X$, the null hypothesis transfers from $X$ and $Z$ to their representations, so that a CIT valid for the embedded hypothesis is valid for the original one. We further give conditions for equivalence of the two hypotheses, and show that sufficiency weakens to mean sufficiency when the embedded test targets conditional mean independence. We propose a semi-synthetic simulation design to assess type I error (T1E) control and power of the eCITs for given embedding maps on a specific dataset and task, and use it to evaluate them on our application. Applying the eCITs to German Parliament speeches, we find for all combinations of embedding maps considered that the summaries of two LLMs contain information about the speaker's faction and gender beyond the speech they were generated from.
Marco Simnacher, Georg Keilbar, Benjamin König et al.· 0 citations
CON decomposition is introduced, which quantifies how much of a layer's variance each concept explains given all other concepts and the outcome, and how much none of them explains, yielding layer-comparable, calibrated scores that suppress false positives.
R. Rane, Marco Simnacher, Manuel Pfeuffer et al.· 0 citations
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