Linear and parallel learning of Markov random fields
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Bibliographic record
Abstract
In this thesis, we introduce a new class of embarrassingly parallel parameter learning algorithms for Markov random fields (MRFs) with untied parameters, which are efficient for a large class of practical models. The algorithms parallelize naturally over cliques and, for graphs of bounded degree, have complexity that is linear in the number of cliques. We refer to these algorithms with the acronym LAP, which stands for Linear And Parallel. Unlike their competitors, the marginal versions of the proposed algorithms are fully parallel and for log-linear models they are also data efficient, requiring only the local sufficient statistics of the data to estimate parameters. LAP algorithms are ideal for parameter learning in big graphs and big data applications. The correctness of the newly proposed algorithms relies heavily on the existence and uniqueness of the normalized potential representation of an MRF. We capitalize on this theoretical result to develop a new theory of correctness and consistency of LAP estimators corresponding to different local graph neighbourhoods. This theory also establishes a general condition on composite likelihood decompositions of MRFs that guarantees the global consistency of distributed estimators, provided the local estimators are consistent. We introduce a conditional variant of LAP that enables us to attack parameter estimation of fully-observed models of arbitrary connectivity, including fully connected Boltzmann distributions. Once again, we show consistency for this distributed estimator, and relate it to distributed pseudo-likelihood estimators. Finally, for linear and non-linear inverse problems with a sparse forward operator, we present a new algorithm, named iLAP, which decomposes the inverse problem into a set of smaller dimensional inverse problems that can be solved independently. This parallel estimation strategy is also memory efficient.
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 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 it