Causal inference for cloud computing

Cloud computing involves complex technical and economical systems and interactions. This brings about various challenges, two of which are: (1) debugging and control of computing systems with the help of sandbox experiments, and (2) prediction of the cost of "spot" resources for decision making of cloud clients. In this paper, we formalize debugging by counterfactual probabilities and control by post-(soft-)interventional probabilities. We prove that counterfactuals can approximately be calculated from a "stochastic" graphical causal model (while they are originally defined only for "deterministic" functional causal models), and based on this sketch an approach to address problem (1). To address problem (2), we formalize bidding by post-(soft-)interventional probabilities and present a simple mathematical result on approximate integration of "incomplete" conditional probability distributions. We show how this can be used by cloud clients to trade off privacy against predictability of the outcome of their bidding actions in a toy scenario. We report experiments on simulated and real data.