Tsallis Regularized Optimal Transport and Ecological Inference
Why this work is in the frame
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Bibliographic record
Abstract
Optimal transport is a powerful framework for computing distances between probability distributions. We unify the two main approaches to optimal transport, namely Monge-Kantorovitch and Sinkhorn-Cuturi, into what we define as Tsallis regularized optimal transport (TROT). TROT interpolates a rich family of distortions from Wasserstein to Kullback-Leibler, encompassing as well Pearson, Neyman and Hellinger divergences, to name a few. We show that metric properties known for Sinkhorn-Cuturi generalize to TROT, and provide efficient algorithms for finding the optimal transportation plan with formal convergence proofs. We also present the first application of optimal transport to the problem of ecological inference, that is, the reconstruction of joint distributions from their marginals, a problem of large interest in the social sciences. TROT provides a convenient framework for ecological inference by allowing to compute the joint distribution -— that is, the optimal transportation plan itself — when side information is available, which is e.g. typically what census represents in political science. Experiments on data from the 2012 US presidential elections display the potential of TROT in delivering a faithful reconstruction of the joint distribution of ethnic groups and voter preferences.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it