Using Singular Value Decomposition to Understand Variation Across Mortality Schedules from Multiple Populations
Bibliographic record
Abstract
Understanding variation in mortality age schedules across populations is a key objective of demographic and epidemiological research. Commonly used decomposi- tion methods partition differences in demographic summary indicators—such as life expectancy at birth—into age-specific contributions for only two populations. Here, we demonstrate how singular value decomposition—an existing mathematical decomposition technique—can be used to summarize and understand variation among mortality schedules from multiple populations. We explain how singular value decomposition can be used to (a) extract key mortality age patterns from a set of mortality schedules; and (b) quantify the relative importance of these age patterns for the various mortality schedules included in the set. We demonstrate this method by decomposing variation in the mortality schedules of US states, showing that (1) most of the variation in 2019 was due to differences in young-adult mortality, and that (2) different US states achieved the same high level of life expectancy at birth with fundamentally different mortality profiles. The singular value decomposition approach complements existing pairwise decomposition methods for describing and summarizing mortality differences across populations, and we discuss further potential areas of application.
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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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.003 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".