Bijan Mazaheri, Chandler Squires, Caroline Uhler
arXiv 29 May 2024 · Machine Learning
arXiv:2405.19225 · PDF · DOI · OpenAlex · Extracted main text
Heterogeneous data from multiple populations, sub-groups, or sources is often represented as a “mixture model” with a single latent class influencing all of the observed covariates. Heterogeneity can be resolved at multiple levels by grouping populations according to different notions of similarity. This paper proposes grouping with respect to the causal response of an intervention or perturbation on the system. This definition is distinct from previous notions, such as similar covariate values (e.g. clustering) or similar correlations between covariates (e.g. Gaussian mixture models). To solve the problem, we “synthetically sample” from a counterfactual distribution using higher-order multi-linear moments of the observable data. To understand how these “causal mixtures” fit in with more classical notions, we develop a hierarchy of mixture identifiability.
appendix boundary found by appendix_command · 67% of the source is main text. Read the extracted text to check this.
The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Allman, E. S., Matias, C., and Rhodes, J. A (2009) Identifiability of parameters in latent structure models with many observed variables | 0.737 | 3 | 3 | 67% |
| 2 | Pearl, J (2009) Causality | 0.644 | 4 | 1 | 100% |
| 3 | Gordon, S., Mazaheri, B., Schulman, L. J., and Rabani, Y (2020) The sparse hausdorff moment problem, with application to topic models self | 0.511 | 2 | 2 | 50% |
| 4 | Kim, Y., Koehler, F., Moitra, A., Mossel, E., and Ramnarayan, G (2019) How many subpopulations is too many? exponential lower bounds for inferring population histories | 0.511 | 2 | 2 | 50% |
| 5 | Imbens, G. W. and Rubin, D. B (2015) Causal inference in statistics, social, and biomedical sciences | 0.511 | 2 | 1 | 100% |
| 6 | Miao, W., Shi, X., Li, Y., and Tchetgen Tchetgen, E. J (2024) A confounding bridge approach for double negative control inference on causal effects | 0.511 | 2 | 1 | 100% |
| 7 | Suk, Y., Kim, J.-S., and Kang, H (2021) Hybridizing machine learning methods and finite mixture models for estimating heterogeneous treatment effects in latent classes | 0.511 | 2 | 1 | 100% |
| 8 | Tchetgen, E. J. T., Ying, A., Cui, Y., Shi, X., and Miao, W (2020) An introduction to proximal causal learning | 0.511 | 2 | 1 | 100% |
| 9 | Kossaifi, J., Panagakis, Y., Anandkumar, A., and Pantic, M (2019) Tensorly: Tensor learning in python | 0.511 | 2 | 1 | 100% |
| 10 | Abadie, A., Diamond, A., and Hainmueller, J (2010) Synthetic control methods for comparative case studies: Estimating the effect of california’s tobacco control program | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 45 scored citations.