Causal Explanation Under Indeterminism: A Sampling Approach Christopher A Merck and Samantha Kleinberg Stevens Institute of Technology Hoboken NJ Abstract However if we want to tell an individual why their blood sugar is low at 4 PM, we need to be able to automatically One of the key uses of causes is to explain why things happen. determine that it is due to the race they ran the day before Explanations of specific events, like an individual’s heart at- tack on Monday afternoon or a particular car accident, help plus their current insulin dosing. Runs from a week ago are assign responsibility and inform our future decisions. Com- not important here, but neither is a brief jog that morning. putational methods for causal inference make use of the vast To accurately and automatically explain events, we need amounts of data collected by individuals to better understand to handle both continuous time and state (e.g. glucose level), their behavior and improve their health. However, most meth- and go beyond only looking at whether an event happens and ods for explanation of specific events have provided theo- instead identify causes that change when and how the event retical approaches with limited applicability. In contrast we happens. Perhaps an individual had a genetic disposition to- make two main contributions: an algorithm for explanation ward lung cancer, but smoking led to diagnosis at a much that calculates the strength of token causes, and an evaluation earlier age than otherwise would have happened. It may based on simulated data that enables objective comparison be that two arsonists individually didn’t change whether a against prior methods and ground truth. We show that the approach finds the correct relationships in classic test cases fire happened (since either would have brought it about), but (causal chains, common cause, and backup causation) and in they increased the intensity of the fire and prevented it from a realistic scenario (explaining hyperglycemic episodes in a being extinguished. simulation of type 1 diabetes). In this work, we show how to compute answers to coun- terfactual queries in continuous-time systems using proba- bility trajectories. We then show how to test whether one Introduction event changes the probability, time, or intensity of another The past two decades have seen significant progress in com- event and compute quantitative strengths for these relation- putational discovery of causal relationships at the popula- ships. We first evaluate our method in a continuous-time tion level. Given a database of medical records, we can simulation of billiard ball collisions, showing that it rejects find causal relationships between variables like medications, spurious correlations when there is a common cause, finds lifestyle, and disease. Yet while causal inference can tell us hastening despite probability lowering in cases of backup what causes heart failure in general, it cannot tell us that causation, and identifies the most direct relationships in a specific patient’s heart failure is caused by their thyroid causal chains. Finally, we use it to explain a hypoglycemic disfunction rather than their uncontrolled diabetes — that is episode in a simulation of Type 1 Diabetes, demonstrating the role of causal explanation. One of the core approaches the technique’s readiness for real-world use. to explanation is based on counterfactuals, which capture that without the cause the effect would not have happened. Related Work However, this approach and other solutions have been pri- Causal explanation has been studied in philosophy, com- marily theoretical and since we only see what actually hap- puter science, and other fields including law (determining pened, it is difficult to determine what would have happened fault and culpability), medicine (diagnosing individuals to had things been different. Since the solutions to explana- identify the cause of their symptoms), and software engi- tion have been mainly theoretical, computational methods neering (finding causes of program bugs). We focus on re- for explanation have lagged behind those for inference. viewing the work in the first two areas since they provide The primary shortcoming of existing explanation meth- insight into what constitutes a causal explanation and how ods is their handling of time. Methods either ignore event we can realistically find these. timing entirely (e.g. Bayesian networks) or add time ad-hoc (e.g. dynamic Bayesian networks) at the expense of com- Philosophy putational complexity and large amounts of required input. We draw inspiration from two approaches to causal explana- Copyright c 2015, Association for the Advancement of Artificial tion, or token causality, that aim to evaluate or quantify how Intelligence (www.aaai.org). All rights reserved. much of a difference a cause made to its effect. The first approach, due to Eells (1991), looks at the prob- to provide causal explanations automatically. Consider a ability of the effect over time (its probability trajectory) and model that shows that smoking causes lung cancer. A user examines how this changes after the cause happens up un- must interpret what it means for smoking to be true for an in- til the time of the effect. For example, if the probability dividual and which instances are relevant. Some issues with of hypoglycemia is raised after a run, and remains high un- the approach can be resolved by introducing variables to til hypoglycemia actually happens, then it is because of the model time (cf. the revised rock throwing model of (Halpern run. The probability trajectory approach explicitly incorpo- 2014)), but this becomes more difficult in cases like finding rates the timing of events, but it requires selecting so-called why a person’s blood glucose is raised since people tend to background contexts to hold fixed. This requires extensive give too much credence to recent events in causal explana- background knowledge that we normally do not have, mak- tion. As a result, the approach is susceptible to the same ing it difficult to translate into a computable model. biases as human reasoning, and it has only been evaluated Counterfactual methods, such as the concept of counter- conceptually. factual dependence introduced by Lewis (1973), stipulate One of the few computational methods for explanation that a cause is something without whose presence the effect that has been implemented and evaluated on simulated data would not have occurred. An event B is said to be caused by encodes the processes underlying relationships with logical A if both A and B occur in the actual world but B does not formulas (Dash, Voortman, and De Jongh 2013), links these occur in the not-A world most similar to the actual world. with a Bayesian network (BN), and then finds the most likely Despite the intuitive appeal of this approach, it is not directly path through the structure to the effect. However, this ap- reducible to an algorithm because the similarity function is proach does not explicitly model the timing of events and not specified by the theory. Furthermore, the main coun- cannot handle cases where multiple causes are responsible terfactual methods cannot handle overdetermination (when for an effect. Rather the approach finds only the most likely multiple causes occur). If a person who smokes is exposed causal sequence. Further, it does not distinguish between to asbestos, each factor individually may be enough to bring the significance of each component of the sequence. An- about lung cancer, leading to no counterfactual dependence. other logic-based approach (Kleinberg 2012) can handle the Yet it may be that exposure to both risk factors led to a more case of multiple causes, but it aims to rank the significance aggressive case of cancer or made it happen sooner than it of causes rather than test counterfactual queries. Methods otherwise would have (thus the cause changed the way in for fault detection (Poole 1994; Lunze and Schiller 1999; which cancer occurred). Paul (1998) and Lewis (2000) later Chao, Yang, and Liu 2001) aim to find why a system is extended the counterfactual theory to capture these types of behaving incorrectly, but are computationally complex and changes, though without a way of quantifying the similarity rely on an accurate mechanistic model. Finally, the causal between events, these approaches remained incomputable. impact method of Brodersen et al. (2015) computes the ef- We take inspiration from both of these approaches, us- fect of an intervention (advertising campaign) on a contin- ing change in probability to find relations such as because uous variable (market response), but requires a specified al- of and despite (making an event that actually occurs more ternative to the intervention rather than supporting general or less likely, respectively), and changes in timing (hasten- counterfactual queries. ing, delaying) and manner (intensifying, attenuating) to cap- ture other types of difference-making. This lets us find that Motivating Example while an event may have been inevitable, and a cause made As a running example, we discuss how to explain changes in no change to whether it occurred, it can still change when blood glucose (BG) of a person with type 1 diabetes mellitus and how it happens. For example, if we have a continuous (T1DM). This is challenging, since many factors affect BG variable that assesses severity of cancer, we can test how and can do so many hours after they occur. For example, much this is changed by each exposure in the prior exam- moderate exercise can lead to heightened insulin sensitivity ple. Similarly, a genetic predisposition may make cancer for up to 22 hours (Dalla Man, Breton, and Cobelli 2009). extremely likely, but an environmental exposure may bring Being able to find this and tell an individual why they have it about much earlier. By looking at changes in probability, low blood glucose (hypoglycemia) can help them prevent timing, and intensity, we can capture these differences.