Causal Discovery and Prediction: Methods and Algorithms

Abstract

We are not only observers but also actors of reality. Our capability to intervene and alter the course of some events in the space and time surrounding us is an essential component of how we build our model of the world. In this doctoral thesis we introduce a generic a-priori assessment of each possible intervention, in order to select the most cost-effective interventions only, and avoid unnecessary systematic experimentation on the real world. Based on this a-priori assessment, we propose an active learning algorithm that identifies the causal relations in any given causal model, using a least cost sequence of interventions. There are several novel aspects introduced by our algorithm. It is, in most case scenarios, able to discard many causal model candidates using relatively inexpensive interventions that only test one value of the intervened variables. Also, the number of interventions performed by the algorithm can be bounded by the number of causal model candidates. Hence, fewer initial candidates (or equivalently, more prior knowledge) lead to fewer interventions for causal discovery. Causality is intimately related to time, as causes appear to precede their effects. Cyclical causal processes are a very interesting case of causality in relation to time. In this doctoral thesis we introduce a formal analysis of time cyclical causal settings by defining a causal analog to the purely observational Dynamic Bayesian Networks, and provide a sound and complete algorithm for the identification of causal effects in the cyclic setting. We introduce the existence of two types of hidden confounder variables in this framework, which affect in substantially different ways the identification procedures, a distinction with no analog in either Dynamic Bayesian Networks or standard causal graphs.