Gaussian Process Methods for Very Large Astrometric Data Sets
Why this work is in the frame
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Bibliographic record
Abstract
Abstract We present a novel nonparametric method for inferring smooth models of the mean velocity field and velocity dispersion tensor of the Milky Way from astrometric data. Our approach is based on stochastic variational Gaussian process regression (SVGPR) and provides an attractive alternative to binning procedures. SVGPR is an approximation to standard Gaussian process regression (GPR), the latter of which suffers severe computational scaling with N and assumes independently distributed Gaussian noise. In the Galaxy, however, velocity measurements exhibit scatter from both observational uncertainty and the intrinsic velocity dispersion of the distribution function. We exploit the factorization property of the objective function in SVGPR to simultaneously model both the mean velocity field and velocity dispersion tensor as separate Gaussian processes. This achieves a computational complexity of O ( M 3 ) versus GPR’s O ( N 3 ), where M < < N is a subset of points chosen in a principled way to summarize the data. Applied to a sample of ∼8 × 10 5 stars from the Gaia DR3 Radial Velocity Survey catalog, we construct differentiable profiles of the mean velocity and velocity dispersion as functions of height above the Galactic midplane. We find asymmetric features in all three diagonal components of the velocity dispersion tensor, providing evidence that the vertical dynamics of the Milky Way are in a state of disequilibrium. Furthermore, our dispersion profiles exhibit correlated structures at several locations in ∣ z ∣, which we interpret as signatures of the Gaia phase spiral. Our method also has interdisciplinary applicability for any data set requiring simultaneous modeling of both latent functions and input-dependent noise.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.005 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| 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