Causal structure learning in directed, possibly cyclic, graphical models
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Bibliographic record
Abstract
Abstract We consider the problem of learning a directed graph <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mrow> <m:mi>G</m:mi> </m:mrow> <m:mrow> <m:mo>⋆</m:mo> </m:mrow> </m:msup> </m:math> {G}^{\star } from observational data. We assume that the distribution that gives rise to the samples is Markov and faithful to the graph <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mrow> <m:mi>G</m:mi> </m:mrow> <m:mrow> <m:mo>⋆</m:mo> </m:mrow> </m:msup> </m:math> {G}^{\star } and that there are no unobserved variables. We do not rely on any further assumptions regarding the graph or the distribution of the variables. Particularly, we allow for directed cycles in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mrow> <m:mi>G</m:mi> </m:mrow> <m:mrow> <m:mo>⋆</m:mo> </m:mrow> </m:msup> </m:math> {G}^{\star } and work in the fully nonparametric setting. Given the set of conditional independence statements satisfied by the distribution, we aim to find a directed graph, which satisfies the same <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>d</m:mi> </m:math> d -separation statements as <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mrow> <m:mi>G</m:mi> </m:mrow> <m:mrow> <m:mo>⋆</m:mo> </m:mrow> </m:msup> </m:math> {G}^{\star } . We propose a hybrid approach consisting of two steps. We first find a partially ordered partition of the vertices of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mrow> <m:mi>G</m:mi> </m:mrow> <m:mrow> <m:mo>⋆</m:mo> </m:mrow> </m:msup> </m:math> {G}^{\star } by optimizing a certain score in a greedy fashion. We prove that any optimal partition uniquely characterizes the Markov equivalence class of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mrow> <m:mi>G</m:mi> </m:mrow> <m:mrow> <m:mo>⋆</m:mo> </m:mrow> </m:msup> </m:math> {G}^{\star } . Given an optimal partition, we propose an algorithm for constructing a graph in the Markov equivalence class of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mrow> <m:mi>G</m:mi> </m:mrow> <m:mrow> <m:mo>⋆</m:mo> </m:mrow> </m:msup> </m:math> {G}^{\star } whose strongly connected components correspond to the elements of the partition, and which are partially ordered according to the partial order of the partition. Our algorithm comes in two versions – one that is provably correct and another one that performs fast in practice.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.002 |
| Insufficient payload (model declined to judge) | 0.000 | 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