Variational autoencoders (VAEs) have recently been used for unsupervised disentanglement learning of complex density distributions. Numerous variants exist to encourage disentanglement in latent space while improving reconstruction. However, none have simultaneously managed the trade-off between attaining extremely low reconstruction error and a high disentanglement score. We present a generalized framework to handle this challenge under constrained optimization and demonstrate that it outperforms state-of-the-art existing models as regards disentanglement while balancing reconstruction. We introduce three controllable Lagrangian hyperparameters to control reconstruction loss, KL divergence loss and correlation measure. We prove that maximizing information in the reconstruction network is equivalent to information maximization during amortized inference under reasonable assumptions and constraint relaxation.

Mountain river torrents and snow avalanches generate human and material damages with dramatic consequences. Knowledge about natural phenomenona is often lacking and expertise is required for decision and risk management purposes using multi-disciplinary quantitative or qualitative approaches. Expertise is considered as a decision process based on imperfect information coming from more or less reliable and conflicting sources. A methodology mixing the Analytic Hierarchy Process (AHP), a multi-criteria aid-decision method, and information fusion using Belief Function Theory is described. Fuzzy Sets and Possibilities theories allow to transform quantitative and qualitative criteria into a common frame of discernment for decision in Dempster-Shafer Theory (DST ) and Dezert-Smarandache Theory (DSmT) contexts. Main issues consist in basic belief assignments elicitation, conflict identification and management, fusion rule choices, results validation but also in specific needs to make a difference between importance and reliability and uncertainty in the fusion process.