Kenny ZhangWhile traditional causal inference has primarily focused on population-level parameters such as the average treatment effect (ATE), the individual treatment effect (ITE) —- often considered the ideal target for personalized decision-making -— has recently garnered increasing attention. However, the ITE is generally not identifiable from the observed data, even in the context of randomized experiments.
In this talk, we consider the problem of solving ITE bounds and prediction intervals when the marginal distributions of potential outcomes are identifiable. We aim to answer the general question: what constraints exist on the joint distribution of potential outcomes, given these known marginals?
We first revisit a classical problem posed by Kolmogorov concerning the sharp upper and lower bounds for the cumulative distribution function (cdf) of the sum of two random variables with fixed marginals. We focus on the achievability of these bounds and contribute new results for the case of discrete random variables.
Second, we extend Strassen’s classical coupling theorem on finite sets to the partial‑mass setting. This result provides a unifying tool for several problems in causal inference.
Finally we return to individual treatment effects, using our new results to construct prediction intervals and bounds on the proportion of individuals whose ITE lies within a specified range. We also answer questions regarding the existence of prediction intervals for individual treatment effects for binary, ordinal and continuous outcomes.
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