Variational Bayesian Learning of Generalized Dirichlet-Based Hidden Markov Models Applied to Unusual Events Detection
Bibliographic record
Abstract
Learning a hidden Markov model (HMM) is typically based on the computation of a likelihood which is intractable due to a summation over all possible combinations of states and mixture components. This estimation is often tackled by a maximization strategy, which is known as the Baum-Welch algorithm. However, some drawbacks of this approach have led to the consideration of Bayesian methods that add a prior over the parameters in order to work with the posterior probability and the marginal likelihood. These approaches can lead to good models but to the cost of extremely long computations (e.g., Markov Chain Monte Carlo). More recently, variational Bayesian frameworks have been proposed as a Bayesian alternative that keeps the computation tractable and the approximation tight. It relies on the introduction of a prior over the parameters to be learned and on an approximation of the true posterior distribution. After proving good standing in the case of finite mixture models and discrete and Gaussian HMMs, we propose here to derive the equations of the variational learning of the Dirichlet mixture-based HMM, and to extend it to the generalized Dirichlet. The latter case presents several properties that make the estimation more accurate. We prove the validity of this approach within the context of unusual event detection in public areas using the University of California San Diego data sets. HMMs are trained over normal video sequences using the typical Baum-Welch approach versus the variational one. The variational learning leads to more accurate models for the detection and localization of anomaly, and the general HMM approach is shown to be versatile enough to handle the detection of various synthetically generated tampering events.
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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 | 0.005 | 0.018 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".