Current autoencoder-based disentangled representation learning methods achieve disentanglement by penalizing the (aggregate) posterior to encourage statistical independence of the latent factors. This approach introduces a trade-off between disentangled representation learning and reconstruction quality since the model does not have enough capacity to learn correlated latent variables that capture detail information present in most image data. To overcome this trade-off, we present a novel multi-stage modelling approach where the disentangled factors are first learned using a preexisting disentangled representation learning method (such as $\beta$-TCVAE); then, the low-quality reconstruction is improved with another deep generative model that is trained to model the missing correlated latent variables, adding detail information while maintaining conditioning on the previously learned disentangled factors. Taken together, our multi-stage modelling approach results in a single, coherent probabilistic model that is theoretically justified by the principal of D-separation and can be realized with a variety of model classes including likelihood-based models such as variational autoencoders, implicit models such as generative adversarial networks, and tractable models like normalizing flows or mixtures of Gaussians. We demonstrate that our multi-stage model has much higher reconstruction quality than current state-of-the-art methods with equivalent disentanglement performance across multiple standard benchmarks.

The ability to accurately estimate uncertainties in neural network predictions is of great importance in many critical tasks. In this paper, we first analyze the intrinsic relation between two main use cases of uncertainty estimation, i.e., selective prediction and confidence calibration. We then reveal the potential issues with the existing quality metrics for uncertainty estimation and propose new metrics to mitigate them. Finally, we apply these new metrics to resource-constrained platforms such as autonomous driver assistance systems where the quality of uncertainty estimation is critical. By exploring the trade-off between the model size and the estimation quality, a missing piece in the literature, some interesting trends are observed.