Variational mixture smoothing for non-linear dynamical systems
Bibliographic record
Abstract
We present an algorithm for computing joint state, smoothed, density estimates for non-linear dynamical systems in a Bayesian setting. Many visual tracking problems can be formulated as probabilistic inference over time series, but we are not aware of mixture smoothers that would apply to weakly identifiable models, where multimodality is persistent rather than transient (e.g. monocular 3D human tracking). Such processes, in principle, exclude iterated Kalman smoothers, whereas flexible MCMC methods or sample based particle smoothers encounter computational difficulties: accurately locating an exponential number of probable joint state modes representing high-dimensional trajectories, rapidly mixing between those or resampling probable configurations missed during filtering. In this paper we present an alternative, layered, mixture density smoothing algorithm that exploits the accuracy of efficient optimization within a Bayesian approximation framework. The distribution is progressively refined by combining polynomial time search over the embedded network of temporal observation likelihood peaks, MAP continuous trajectory estimates, and Bayesian variational adjustment of the resulting joint mixture approximation. Our results demonstrate the effectiveness of the method on the problem of inferring multiple plausible 3D human motion trajectories from monocular video.
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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 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".