A TUTORIAL OF TECHNIQUES FOR IMPROVING STANDARD HIDDEN MARKOV MODEL ALGORITHMS
Bibliographic record
Abstract
In this tutorial, we discuss two main algorithms for Hidden Markov Models or HMMs: the Viterbi algorithm and the expectation phase of the Baum-Welch algorithm, and we describe ways to improve their naïve implementations. For the Baum-Welch algorithm we first present an implementation of the expectation computations using constant space. We then discuss the classical implementation of this calculation and describe ways to reduce its space usage to logarithmic and O(square root n), with their respective CPU costs. We also note where each respective algorithm can be parallelized. For the Viterbi algorithm, we describe O(square root n) and logarithmic space algorithms which increase CPU use by a factor of two and by a logarithmic factor respectively. We also present two recent heuristics for decreasing space use, which in practice lead to logarithmic space use. Classical version of Viterbi cannot be parallelized by splitting sequence in several subsequences, but we show a parallelization that works if we are willing to pay a significant extra CPU cost. Finally we show a very simple parallelization trick which enables full usage of multiple CPUs/cores under the condition that they share memory.
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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 | 0.003 | 0.017 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.003 | 0.005 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.006 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.031 | 0.024 |
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".