A Class of Algorithms for General Instrumental Variable Models
This work addresses the need for more flexible causal inference methods in fields like personalized medicine and policy-making, offering a novel approach to handle continuous treatments and trade off assumptions for tighter bounds, though it is incremental in building on existing bounding techniques.
The paper tackles the problem of causal treatment effect estimation in general instrumental variable models, particularly for continuous treatments, by developing a bounding method that avoids strong structural assumptions and demonstrates its effectiveness on synthetic and real-world data where additive methods fail.
Causal treatment effect estimation is a key problem that arises in a variety of real-world settings, from personalized medicine to governmental policy making. There has been a flurry of recent work in machine learning on estimating causal effects when one has access to an instrument. However, to achieve identifiability, they in general require one-size-fits-all assumptions such as an additive error model for the outcome. An alternative is partial identification, which provides bounds on the causal effect. Little exists in terms of bounding methods that can deal with the most general case, where the treatment itself can be continuous. Moreover, bounding methods generally do not allow for a continuum of assumptions on the shape of the causal effect that can smoothly trade off stronger background knowledge for more informative bounds. In this work, we provide a method for causal effect bounding in continuous distributions, leveraging recent advances in gradient-based methods for the optimization of computationally intractable objective functions. We demonstrate on a set of synthetic and real-world data that our bounds capture the causal effect when additive methods fail, providing a useful range of answers compatible with observation as opposed to relying on unwarranted structural assumptions.