# Causes of Effects: Learning individual responses from population data

arXiv: https://arxiv.org/abs/2104.13730 · HTML: https://mlsanity.com/paper/2104.13730/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 26 references that are in the map.
- First posted on arXiv 28 Apr 2021.

## Builds on (most cited first, 3 of 3)

- [Probabilities of Causation: Bounds and Identification](https://mlsanity.com/paper/1301.3898/) (2013)
- [Counterfactuals and Policy Analysis in Structural Models](https://mlsanity.com/paper/1302.4929/) (2013)
- [Psychological and Normative Theories of Causal Power and the Probabilities of Causes](https://mlsanity.com/paper/1301.7377/) (2013)

## Built on by (most cited first, 30 of 37)

- [Desiderata for Representation Learning: A Causal Perspective](https://mlsanity.com/paper/2109.03795/) (2021)
- [Personalized Decision Making -- A Conceptual Introduction](https://mlsanity.com/paper/2208.09558/) (2022)
- [Probabilities of Causation with Nonbinary Treatment and Effect](https://mlsanity.com/paper/2208.09568/) (2022)
- [A Review of Causality for Learning Algorithms in Medical Image Analysis](https://mlsanity.com/paper/2206.05498/) (2022)
- [Unit Selection with Causal Diagram](https://mlsanity.com/paper/2109.07556/) (2021)
- [Unit Selection with Nonbinary Treatment and Effect](https://mlsanity.com/paper/2208.09569/) (2022)
- [Counterfactual Analysis in Dynamic Latent State Models](https://mlsanity.com/paper/2205.13832/) (2022)
- [Probabilities of Causation: Adequate Size of Experimental and Observational Samples](https://mlsanity.com/paper/2210.05027/) (2022)
- [Efficient Computation of Counterfactual Bounds](https://mlsanity.com/paper/2307.08304/) (2023)
- [Probabilities of Causation for Continuous and Vector Variables](https://mlsanity.com/paper/2405.20487/) (2024)
- [On the Complexity of Counterfactual Reasoning](https://mlsanity.com/paper/2211.13447/) (2022)
- [Bounding Counterfactuals under Selection Bias](https://mlsanity.com/paper/2208.01417/) (2022)
- [Unit Selection: Learning Benefit Function from Finite Population Data](https://mlsanity.com/paper/2210.08203/) (2022)
- [Feature Attribution with Necessity and Sufficiency via Dual-stage Perturbation Test for Causal Explanation](https://mlsanity.com/paper/2402.08845/) (2024)
- [Unit Selection: Case Study and Comparison with A/B Test Heuristic](https://mlsanity.com/paper/2210.05030/) (2022)
- [Probabilities of Causation: Role of Observational Data](https://mlsanity.com/paper/2210.08874/) (2022)
- [Epsilon-Identifiability of Causal Quantities](https://mlsanity.com/paper/2301.12022/) (2023)
- [Is More Data All You Need? A Causal Exploration](https://mlsanity.com/paper/2206.02409/) (2022)
- [Partial counterfactual identification and uplift modeling: theoretical results and real-world assessment](https://mlsanity.com/paper/2211.07264/) (2022)
- [Bounding the Probabilities of Benefit and Harm Through Sensitivity Parameters and Proxies](https://mlsanity.com/paper/2303.05396/) (2023)
- [Simulation-Based Counterfactual Causal Discovery on Real World Driver Behaviour](https://mlsanity.com/paper/2306.03354/) (2023)
- [A Causal Research Pipeline and Tutorial for Psychologists and Social Scientists](https://mlsanity.com/paper/2206.05175/) (2022)
- [Unifying Invariant and Variant Features for Graph Out-of-Distribution via Probability of Necessity and Sufficiency](https://mlsanity.com/paper/2407.15273/) (2024)
- [Estimating Probabilities of Causation with Machine Learning Models](https://mlsanity.com/paper/2502.08858/) (2025)
- [An Algorithm and Complexity Results for Causal Unit Selection](https://mlsanity.com/paper/2302.14412/) (2023)
- [Identification of Probabilities of Causation: from Recursive to Closed-Form Bounds](https://mlsanity.com/paper/2505.15274/) (2025)
- [Learning Probabilities of Causation with Mask-Augmented Data](https://mlsanity.com/paper/2505.17133/) (2025)
- [Causal computations in Semi Markovian Structural Causal Models using divide and conquer](https://mlsanity.com/paper/2511.13852/) (2025)
- [Bounding Probabilities of Causation with Partial Causal Diagrams](https://mlsanity.com/paper/2602.14503/) (2026)
- [General Probabilities of Causation with Causal Knowledge](https://mlsanity.com/paper/2608.12657/) (2026)

## Abstract (arXiv)

The problem of individualization is recognized as crucial in almost every field. Identifying causes of effects in specific events is likewise essential for accurate decision making. However, such estimates invoke counterfactual relationships, and are therefore indeterminable from population data. For example, the probability of benefiting from a treatment concerns an individual having a favorable outcome if treated and an unfavorable outcome if untreated. Experiments conditioning on fine-grained features are fundamentally inadequate because we can't test both possibilities for an individual. Tian and Pearl provided bounds on this and other probabilities of causation using a combination of experimental and observational data. Even though those bounds were proven tight, narrower bounds, sometimes significantly so, can be achieved when structural information is available in the form of a causal model. This has the power to solve central problems, such as explainable AI, legal responsibility, and personalized medicine, all of which demand counterfactual logic. We analyze and expand on existing research by applying bounds to the probability of necessity and sufficiency (PNS) along with graphical criteria and practical applications.