Using graphical structure to develop an optimizing compiler for the Turing probabilistic language

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Complex statistical modelling has provided important tools in the medical and social response to the COVID-19 pandemic. The use of Bayesian or probabilistic approaches has allowed synthesising information from multiple data sources and propagating prediction uncertainty within the data analysis and decision-making pipelines. However, this type of modelling is a difficult undertaking, requiring expertise in several technical areas. As a result, advances in medical research are hindered by the shortage of people able to carry out modelling, which limits the number of research questions of importance that could be investigated. One way to increase capacity in complex statistical modelling is by developing tools to make the modelling easier to carry out. Particularly attractive tools for this purpose are probabilistic programming languages (PPL). They are designed to allow non-experts to specify complex generic models using a formal computer language. Software tools can be used to compile inference algorithms for the specified model from its PPL description. The inference algorithms can then be run to fit the model efficiently in an automated manner. One of the oldest and most popular PPL is the BUGS language. This language and its supporting software were designed to exploit graphical models and their conditional independence properties. More recently, many new PPLs have been developed that are able to use differentiable programming and apply more powerful inference algorithms than the BUGS software could. One particularly promising new PPL is Turing, which uses the Julia language as its computational core. We propose combining the ease of use of the BUGS software with the Julia based core of Turing to give statisticians and data scientists a new powerful tool for complex modelling. The conditional independence arguments from the BUGS software will be used to increase the efficiency of the Turing software and allow its inference algorithm to run on multicore computers in a provably correct way. More concretely, the grammar for the BUGS language would be formalized using BNF. A type system would be used to restrict programs written in the BUGS language to statistically meaningful models. An intermediate level representation of the model would be built to allow optimized inference algorithms to be compiled. BUGS and Turing are two research projects initially developed by the MRC Biostatistics Unit within the School of Clinical Medicine and the Machine Learning Group within the School of Technology, respectively. The proposed collaborative project allows bringing together the best expertise from both sides (MRC Biostatistics Unit and Machine Learning Group) and applying state-of-the-art engineering approaches to advance medical research.