Higher-order interactions in statistical physics and machine learning: A model-independent solution to the inverse problem at equilibrium
Bibliographic record
Abstract
The problem of inferring pairwise and higher-order interactions in complex systems involving large numbers of interacting variables, from observational data, is fundamental to many fields. Known to the statistical physics community as the inverse problem, it has become accessible in recent years due to real and simulated big data being generated. Current approaches to the inverse problem rely on parametric assumptions, physical approximations, e.g., mean-field theory, and ignoring higher-order interactions which may lead to biased or incorrect estimates. We bypass these shortcomings using a cross-disciplinary approach and demonstrate that none of these assumptions and approximations are necessary: We introduce a universal, model-independent, and fundamentally unbiased estimator of all-order symmetric interactions, via the nonparametric framework of targeted learning, a subfield of mathematical statistics. Due to its universality, our definition is readily applicable to any system at equilibrium with binary and categorical variables, be it magnetic spins, nodes in a neural network, or protein networks in biology. Our approach is targeted, not requiring fitting unnecessary parameters. Instead, it expends all data on estimating interactions, hence substantially increasing accuracy. We demonstrate the generality of our technique both analytically and numerically on (i) the two-dimensional Ising model, (ii) an Ising-type model with four-point interactions, (iii) the restricted Boltzmann machine, and (iv) simulated individual-level human DNA variants and representative traits. The latter demonstrates the applicability of this approach to discover epistatic interactions causal of disease in population biomedicine.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
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) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".