Implementing Hierarchical Bayesian Networks on the GPU - PowerPoint Presentation

1. Implementing Hierarchical Bayesian Networks on the GPULászló Dobos, Tamás Budavári, Carrie Filion,Rosie Wyse, Alex SzalayDept. of Physics & Astronomy, The Johns Hopkins University

2. Subaru Prime Focus SpectrographManua Kea Observatory, Hawaii2400-fiber spectrograph for the 8.2 m Japanese Subaru telescopeLow and medium resolution spectroscopy from infrared to blueUnique features: large mirror, large field of view

3. PFS on the SubaruFiber positionersPrime focus array frameNear infrared camera

4. Galactic ArcheologyObserving the oldest stars in the local UniverseIn the halos of the Milky Way and the Andromeda galaxiesIn satellite dwarf galaxies orbiting the Milky WayReconstructing the formation history of the Milky WayObserving stars of tidal streams of disrupted satellite galaxiesReconstructing the dark matter distribution around the Milky WayOnly possible through its gravitation effect on the motion of stars

5. Stellar observationsPHOTOMETRYApparent brightnessTemperatureASTROMETRY2D position on the skyProper motion (2D velocity)Parallax (distance)SPECTROSCOPYTemperatureGravityTell red giants from red dwarvesMetallicityFraction of elements heavier than HeliumRadial velocityFrom the Dopples shift of spectral linespossible only within the Milky Way

6. Blue and red stellar spectraA type young blue star (short-lived)K type red dwarf star (long-lived)

7. Red giant stars vs red dwarf starsHow they appear:How they really compare:actually, they both appear asfaint dots, slightly smearedA distant red giant looks exactly like a nearby red dwarfDespite the huge difference inradius and brightness theycan have very similar mass!

8. Red giant stars vs red dwarf starsred dwarf stars eventually becomered giants once they haveburned all Hydrogen in theircores into Helium.In a satellite dwarf galaxy, low mass starsare still in the dwarf phase whileslightly larger mass stars are red giants

9. Red giant stars vs red dwarf starsRed giant: narrow linesRed dwarf: broad lines

10. Dwarf spheroidal galaxyAppears as an overdensity of starsAt a very large distanceVery old, red starsSome of them are giantsMilky Way foregroundNearbyMany red dwarf starsWe want to find the distant red giants. How?At least we can calculate a membership probability

11. Photometric observationsWe use multiple filters to photograph stars (colors)We measure the magnitude (brightness)color = temperaturered giants in a distantsatellite galaxyeverything else:dwarf red stars ofdifferent stellarpopulationsof the Milky Way

12. Folding in the theoryGiven themetal content, mass and age of a star, we can calculate its color and brightnessResults of calculations are available in so-called isochrone tablesHow can we invert the isochone tables?Given the observed colors of a star,what are the possible physical parameters?We don’t know the distance! Is it a red dwarf or a red giant?

13. We need more assumptionsWe know quite a lot about the Milky WayIt consists of different stellar populations (disk, halo…)Detailed model of the radial distribution of the starsWe think we know the mass function of the starsThere are a lot more low mass stars than massive starsThe dwarf galaxy member stars are at the same, but large distance

14. Bayesian Mixture ModelsWe model the problem as a mixture of stellar populationsFor each population, we have priors (prescriptions) for thedistributions of the parametersWe have some rough assumptions on the population weightsEvery star belongs to exactly one population but we can’t tell whichWe aim to calculate a membership probabilityWe want to fit the population parametersMean age and variance of red giant stars of the dwarf galaxyAs a byproduct, we calculate the probability distributions of all physical parameters of every single star

15. Monte Carlo on tens of thousand of starsAlmost nothing is known analytically, we have to go full numericIsochrone tables are non-invertible, degenerate functionsThis is unfortunate, sincemany MCMC codes (pyro, tf probabilty) usually aim at analytic Bayesian problemse.g. No U-turn sampling (NUTS) where the kernel is differentiablethese problems can benefit a lot from automatic differentiation capabilities of deep learning frameworksOur problem is computationally very intensiveFast linear algebra on small but numerous matrices (SVD, Cholesky)Fast random sampling of analytic but complex distributionsIsochrone table interpolation – iterative method

16. Spectroscopic targetingWhy is population membership so important?We want toobserve member stars of satellite galaxiesbut a fair sample of all stars is not necessarily the best!Some stars carry more information than others(more precisely: some subset of stars carry more information than other subsets)trace the dark matter distribution bettermaybe because they are further out from the center of the satellite galaxy

17. Implementation detailsCode is written in eager mode TensorFlowEasy debugging but no multi-GPU supportSome function could be compiled into execution graphs for more speedAdaptive MCMC is implemented from scratchNone of the existing Bayesian libraries could handle the tricky isochrone interpolation and mixture models (sampling of categorical variables)We could still reuse a lot from tf.linalg and tf probabilityWe are running on Tesla V100 GPUs with 12 GB of RAMEnough to do 1 million isochrone interpolation in parallelBut powerful enough to run the MCMC only on about a 100k stars

18. ConclusionsEager TF and other deep learning frameworks are excellent for implementing more traditional inference algorithmsGPUs enable tackling computationally very intensive problemsAdvanced parameter inference algorithms can significantly increase spectroscopic survey efficiency