Earlier Applications of HiddenMarkov Chain Models
Bibliographic record
Abstract
Introduction In this appendix some earlier application methods are briefly described. Markov chain models can be used to provide probability models for sequences of symbols. This will aid in genome annotation. The types of questions that can be asked include the following: Does a particular sequence belong to a particular family and what can one say about its internal structure? How can one discriminate between two sequences? Some general reviews are given in (Durbin et al., 1998, Chapters 2 and 3), (Robin et al., 2005, Chapters 1 and 2), but a more detailed review of observed Markov chains is provided by (Koski, 2001, Chapter 9). We have added some extra details to Koski's treatment. A straightforward application of Markov chains to genome sequencing. This approach does not seem to work for the following reasons: • The four bases A, T, G, C are not uniformly distributed in a sequence and the compositions vary within and between sequences. • Various k-tuples of bases are not uniformly distributed. However, exons and introns are often separated on the basis of dinucleotide frequencies. • It seems that higher-order chains need to be used as probabilities of a base in a particular location and then can depend not only on the immediately adjacent bases. In addition, the base composition can vary from one segment to another. The segmentation techniques for decomposing DNA sequences into homogeneous segments includes hidden Markov models. Frame-dependent Markov chains. These use the GeneMark software; information can be found at http://genemark.biology.gatech.edu/GeneMark/gm_info.html Mixture transition distribution chain of order k . These are called MTD(k) models. For a Markov chain of order k with a state-space of size N, there are (N − 1)N k entries in the transition matrix A to be estimated, (the column sums of A are 1), plus the initial probabilities. With N = 4 and k = 8, we have 3 ・ 4 8 = 196, 608 which is quite large. This has a further implication that we may not have enough data to calibrate all these entries in A. We comment on estimation using sparse data below.
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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 | 0.019 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.004 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.018 | 0.004 |
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".