Open Access

The main challenge in Bayesian models is to determine the posterior for the model parameters. Already, in models with only one or few parameters, the analytical posterior can only be determined in special settings. In Bayesian neural networks, variational inference is widely used to approximate difficult-to-compute posteriors by variational distributions. Usually, Gaussians are used as variational distributions (Gaussian-VI) which limits the quality of the approximation due to their limited flexibility. Transformation models on the other hand are flexible enough to fit any distribution. Here we present transformation model-based variational inference (TM-VI) and demonstrate that it allows to accurately approximate complex posteriors in models with one parameter and also works in a mean-field fashion for multi-parameter models like neural networks.

Twenty-first century infrastructure needs to respond to changing demographics, becoming climate neutral, resilient and economically affordable, while remaining a driver for development and shared prosperity. However, the infrastructure sector remains one of the least innovative and digitalised, plagued by delays, cost overruns and benefit shortfalls (Cantarelli et al. 2008; Flyvbjerg, 2007; Flyvbjerg et al., 2003; Flyvbjerg et al., 2004). The root cause is the prevailing fragmentation of the infrastructure sector (Fellows and Liu, 2012). To help overcome these challenges, integration of the value chain is needed. This could be achieved through a use-case-based creation of federated ecosystems connecting open and trusted data spaces and advanced services applied to infrastructure projects. Such digital platforms enable full-lifecycle participation and responsible governance guided by a shared infrastructure vision. Digital federation enables secure and sovereign data exchange and thus collaboration across the silos within the infrastructure sector and between industries as well as within and between countries. Such an approach to infrastructure technology policy would not rely on technological solutionism but proposes the development of open and trusted data alliances. Federated data spaces provide access to the emerging data economy, especially for SMEs, and can foster the innovation of new digital services. Such responsible digital governance can help make the infrastructure sector more resilient, efficient and aligned with the realisation of ambitious decarbonisation and environmental protection targets. The European Union and the United States have already developed architectures for sovereign and secure data exchange.