Causal Discovery Using Proxy Variables

Discovering causal relations is fundamental to reasoning and intelligence. In particular, observational causal discovery algorithms estimate the cause-effect relation between two random entities X and Y, given n samples from P(X,Y). In this paper, we develop a framework to estimate the cause-effect relation between two static entities x and y: for instance, an art masterpiece x and its fraudulent copy y. To this end, we introduce the notion of proxy variables, which allow the construction of a pair of random entities (A,B) from the pair of static entities (x,y). Then, estimating the cause-effect relation between A and B using an observational causal discovery algorithm leads to an estimation of the cause-effect relation between x and y. For example, our framework detects the causal relation between unprocessed photographs and their modifications, and orders in time a set of shuffled frames from a video. As our main case study, we introduce a human-elicited dataset of 10,000 pairs of casually-linked pairs of words from natural language. Our methods discover 75% of these causal relations. Finally, we discuss the role of proxy variables in machine learning, as a general tool to incorporate static knowledge into prediction tasks.