Linear causal filtering: definition and theory
Bibliographic record
Abstract
1. Abstract This work provides a framework based on multivariate autoregressive modeling for linear causal filtering in the sense of Granger. In its bivariate form, the linear causal filter defined here takes as input signals A and B, and it filters out the causal effect of B on A, thus yielding two new signals only containing the Granger-causal effect of A on B. In its general multivariate form for more than two signals, the effect of all indirect causal connections between A and B, mediated by all other signals, are accounted for, partialled out, and filtered out also. The importance of this filter is that it enables the estimation of directional measures of causal information flow from any non-causal, non-directional measure of association. For instance, based on the classic coherence, a directional measure of strength of information flow from A to B is obtained when applied to the linear causal filtered pair containing only A to B connectivity information. This particular case is equivalent to the isolated effective coherence (doi.org/10.3389/fnhum.2014.00448). Of more recent interest are the large family of phase-phase, phase-amplitude, and amplitude-amplitude cross-frequency coupling measures which are non-directional. The linear causal filter makes it now possible to estimate the directional causal versions these measures of association. One important field of application is in brain connectivity analysis based on cortical signals of electric neuronal activity (e.g. estimated sources of EEG and MEG, and invasive intracranial ECoG recordings). The linear causal filter introduced here provides a novel solution to the problem of estimating the direction of information flow from any non-directional measure of association. This work provides definitions, non-ambiguous equations, and clear prescriptions for implementing the linear causal filter in diverse settings.
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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 | 0.001 | 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 | 0.001 | 0.000 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| 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".