Poisson PCA: Poisson measurement error corrected PCA, with application to microbiome data
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
In this paper, we study the problem of computing a principal component analysis of data affected by Poisson noise. We assume samples are drawn from independent Poisson distributions. We want to estimate principal components of a fixed transformation of the latent Poisson means. Our motivating example is microbiome data, though the methods apply to many other situations. We develop a semiparametric approach to correct the bias of variance estimators, both for untransformed and transformed (with particular attention to log-transformation) Poisson means. Furthermore, we incorporate methods for correcting different exposure or sequencing depth in the data. In addition to identifying the principal components, we also address the nontrivial problem of computing the principal scores in this semiparametric framework. Most previous approaches tend to take a more parametric line: for example, fitting a log-normal Poisson (PLN) model. We compare our method with the PLN approach and find that in many cases our method is better at identifying the main principal components of the latent log-transformed Poisson means, and as a further major advantage, takes far less time to compute. Comparing methods on real and simulated data, we see that our method also appears to be more robust to outliers than the parametric method.
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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 | 0.001 | 0.008 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.006 |
| 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 it