Probabilistic causes in Markov chains

Abstract

The paper studies a probabilistic notion of causes in Markov chains that relies on the counterfactuality principle and the probabilityraising property. This notion is motivated by the use of causes for monitoring purposes where the aim is to detect faulty or undesired behaviours before they actually occur. A cause is a set of finite executions of the system after which the probability of the effect exceeds a given threshold. We introduce multiple types of costs that capture the consumption of resources from different perspectives, and study the complexity of computing cost-minimal causes

From Verification to Causality-Based Explications (Invited Talk)

“…In terms of formal models, Pearl's early notion of actual causality in terms of causal beams [96,97] entailed probabilistic flavor, and the causal probabilistic logic of [115,14] describes a language for reasoning about probabilistic causation. Nonetheless, we are aware of only a few works that study a probabilistic version of causality in operational models (see, e.g., [75,2,37,9]). Along these lines, we point out open directions for research that focus on the operational point of view.…”

“…Such a reference to a specific threshold value p has also been incorporated into a notion of p-causes in [9]. Motivated by monitoring applications (see, e.g., [87]), the underlying idea is that notions of causality could be used to foresee undesirable behavior.…”

“…Choosing the shortest of such prefixes in accordance with condition PAC2 yields a 1-cause and hence a p-cause for any p. For p < 1, there are multiple p-causes in general. In [9], the problem to find cost-optimal p-causes with respect to a variety of cost measures is addressed.…”

“…The probabilistic notions of causality discussed in this section naturally constitute forwardlooking notions: the probability-raising principle inherently addresses the behavior of a system across multiple executions, and causes are prone to exhibiting a predictive character. These notions can be useful in inferring causal dependencies in data series [75,74,66] and predicting undesirable behavior of reactive systems through runtime monitoring [9]. Nevertheless, as far as formal probabilistic models are concerned, a comprehensive study of cause-effect relationships is still at the beginning.…”