A Trade-Off between Sample Complexity and Computational Complexity in Learning Boolean Networks from Time-Series Data
Bibliographic record
Abstract
A key problem in molecular biology is to infer regulatory relationships between genes from expression data. This paper studies a simplified model of such inference problems in which one or more Boolean variables, modeling, for example, the expression levels of genes, each depend deterministically on a small but unknown subset of a large number of Boolean input variables. Our model assumes that the expression data comprises a time series, in which successive samples may be correlated. We provide bounds on the expected amount of data needed to infer the correct relationships between output and input variables. These bounds improve and generalize previous results for Boolean network inference and continuous-time switching network inference. Although the computational problem is intractable in general, we describe a fixed-parameter tractable algorithm that is guaranteed to provide at least a partial solution to the problem. Most interestingly, both the sample complexity and computational complexity of the problem depend on the strength of correlations between successive samples in the time series but in opposing ways. Uncorrelated samples minimize the total number of samples needed while maximizing computational complexity; a strong correlation between successive samples has the opposite effect. This observation has implications for the design of experiments for measuring gene expression.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.017 | 0.115 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.004 | 0.013 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.003 | 0.006 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".