ProReGen: Progressive Residual Generation under Attribute Correlations

Attribute correlations in the training data will compromise the ability of a deep generative model (DGM) to synthesize images with under-represented attribute combinations ($\textit{i.e.,}$ minority samples). Existing approaches mitigate this by data re-sampling to remove attribute correlations seen by the DGM, using a classifier to provide $\textit{pseudo-supervision}$ for the generation of counterfactual samples, or incorporating inductive bias to explicitly decompose the generation into independent causal mechanisms. We present ProReGen, a $\textit{progressive residual generation}$ approach inspired by the classical Robinson's transformation to partial out from an image attribute $\mathbf{x}_2$ its component $m(\mathbf{x}_1)$ that is predictable by other image attributes $\mathbf{x}_1$, and the residual $\gamma = \mathbf{x}_2 - m(\mathbf{x}_1)$ that is not. This simplifies the original problem of learning a DGM $g(\mathbf{x}_1, \mathbf{x}_2)$ conditioned on correlated inputs, to learning $\tilde{g}(\mathbf{x}_1, \gamma)$ conditioned on orthogonal inputs. It further allows us to progressively learn $\tilde{g}$ by first shifting the burden to abundant majority samples to learn the generator $\tilde{g}(\mathbf{x}_1, \gamma = 0)$, and then expanding it with additional layers $g\_{\text{res}}$ to resolve its difference to $\tilde{g}(\mathbf{x}_1, \gamma)$ using residual attribute $\gamma$ on limited minority samples. On three benchmark datasets with curated varying strengths of attribute correlations, we demonstrate that ProReGen---with input orthogonalizaton and progressive residual learning---improved the correctness and quality of generations compared to existing strategies.