Causal models for data-driven debugging and decision making in 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 to optimize the performance 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 a data-driven 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.