Multivariate Poisson lognormal distribution for modeling counts from modern biological data: An overview
Bibliographic record
Abstract
Modern biological data are often multivariate discrete counts, and there has been a dearth of statistical distributions to directly model such counts in an efficient manner. While mixed Poisson distributions, e.g., negative binomial distribution, are often the distribution of choice for univariate data, multivariate statistical distributions and their algorithmic implementations tend to have different drawbacks, e.g., non-tractable distributions, non-closed form solutions for parameter estimates, constrained correlation structures, and slow convergence during iterative parameter estimation. Herein, we provide an overview of the Poisson lognormal and multivariate Poisson lognormal distributions. These distributions can be written in an hierarchical fashion. An efficient variational approximation-based parameter estimation strategy as well as a hybrid approach for full Bayesian posterior estimation is available for such models, allowing for scaling up and modeling high-dimensional data. We provide comparisons of the univariate Poisson, the negative binomial, and the Poisson lognormal distributions in terms of the estimated mean-variance relationships using simulations and example real datasets. We also discuss the properties of the multivariate Poisson lognormal distribution, and ability to directly model count data including zero counts, over-dispersion, both positive and negative covariance elements, and the mapping from correlations in the latent space vs. the observed space. Finally, we illustrate their use through two model-based clustering examples using a mixtures of distributions approach in RNA-seq and microbiome data.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".