Learning and Designing Stochastic Processes from Logical Constraints

Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics must be known exactly. As this is seldom the case, many methods have been devised over the last decade to infer (learn) such parameters from observations of the state of the system. In this paper, we depart from this approach by assuming that our observations are {\it qualitative} properties encoded as satisfaction of linear temporal logic formulae, as opposed to quantitative observations of the state of the system. An important feature of this approach is that it unifies naturally the system identification and the system design problems, where the properties, instead of observations, represent requirements to be satisfied. We develop a principled statistical estimation procedure based on maximising the likelihood of the system's parameters, using recent ideas from statistical machine learning. We demonstrate the efficacy and broad applicability of our method on a range of simple but non-trivial examples, including rumour spreading in social networks and hybrid models of gene regulation

Learning Adjustment Sets from Observational and Limited Experimental Data

Estimating causal effects from observational data is not always possible due to confounding. Identifying a set of appropriate covariates (adjustment set) and adjusting for their influence can remove confounding bias; however, such a set is typically not identifiable from observational data alone. Experimental data do not have confounding bias, but are typically limited in sample size and can therefore yield imprecise estimates. Furthermore, experimental data often include a limited set of covariates, and therefore provide limited insight into the causal structure of the underlying system. In this work we introduce a method that combines large observational and limited experimental data to identify adjustment sets and improve the estimation of causal effects. The method identifies an adjustment set (if possible) by calculating the marginal likelihood for the experimental data given observationally-derived prior probabilities of potential adjustmen sets. In this way, the method can make inferences that are not possible using only the conditional dependencies and independencies in all the observational and experimental data. We show that the method successfully identifies adjustment sets and improves causal effect estimation in simulated data, and it can sometimes make additional inferences when compared to state-of-the-art methods for combining experimental and observational data.Comment: 10 pages, 5 figure

bayesvl: Visually Learning the Graphical Structure of Bayesian Networks and Performing MCMC with 'Stan'

The 'bayesvl' R Packag