Summary of Limits Of Approximating the Median Treatment Effect, by Raghavendra Addanki et al.
Limits of Approximating the Median Treatment Effect
by Raghavendra Addanki, Siddharth Bhandari
First submitted to arxiv on: 15 Mar 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Artificial Intelligence (cs.AI); Data Structures and Algorithms (cs.DS); Econometrics (econ.EM); Methodology (stat.ME)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper addresses the Average Treatment Effect (ATE) estimation problem in causal inference. While ATE does not account for data heterogeneity, several approaches have been proposed to tackle this issue, including estimating Quantile Treatment Effects. In the finite population setting, prior work has focused on estimating median(a) – median(b), where a and b are potential outcome vectors. However, estimating the difference of medians is easier than the desired estimand of median(a-b), also known as the Median Treatment Effect (MTE). The paper argues that MTE is not estimable and proposes a novel notion of approximation relying on the sorted order of values in a-b. A quantity called variability exactly captures the complexity of MTE estimation, drawing connections to instance-optimality studied in theoretical computer science. The authors show that every algorithm for estimating MTE obtains an approximation error no better than an algorithm computing variability. Finally, they provide a simple linear-time algorithm for computing variability exactly. This work highlights the importance of making no assumptions about potential outcome vector generation or correlation, except that values are k-ary. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper is about how to measure the effect of something on people in a fair way. When we want to know if one thing affects another thing, we need to be careful because we can only see what happened to each person once. The paper talks about a problem where we don’t have enough information to figure out what would have happened if someone had gotten a different treatment. It argues that there’s no way to solve this problem exactly and proposes a new way to get close. This method takes into account how the data is arranged, which helps us understand the complexity of the problem better. The paper also shows a simple algorithm that can be used to compute this measure quickly. |
Keywords
* Artificial intelligence * Inference
