Online Learning of a Dirichlet Process Mixture of Beta-Liouville Distributions Via Variational Inference
Bibliographic record
Abstract
A large class of problems can be formulated in terms of the clustering process. Mixture models are an increasingly important tool in statistical pattern recognition and for analyzing and clustering complex data. Two challenging aspects that should be addressed when considering mixture models are how to choose between a set of plausible models and how to estimate the model's parameters. In this paper, we address both problems simultaneously within a unified online nonparametric Bayesian framework that we develop to learn a Dirichlet process mixture of Beta-Liouville distributions (i.e., an infinite Beta-Liouville mixture model). The proposed infinite model is used for the online modeling and clustering of proportional data for which the Beta-Liouville mixture has been shown to be effective. We propose a principled approach for approximating the intractable model's posterior distribution by a tractable one-which we develop-such that all the involved mixture's parameters can be estimated simultaneously and effectively in a closed form. This is done through variational inference that enjoys important advantages, such as handling of unobserved attributes and preventing under or overfitting; we explain that in detail. The effectiveness of the proposed work is evaluated on three challenging real applications, namely facial expression recognition, behavior modeling and recognition, and dynamic textures clustering.
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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 | 0.015 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.003 | 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".