A brief introduction to tinygp

軽量なガウス過程モデリングライブラリ tinygp の紹介と numpyro を用いたハイパーパラメータの推定について．

Jupyter notebook
https://gist.github.com/kzak/f963e182e6e947b5dcfd0de372d0ec9d

Transcript

1. A brief introduction to tinygp _zak3 2022/10
2. Agenda • tinygp ͱ͸ • Πϯετʔϧ • جຊతͳ࢖͍ํ • Χʔωϧͷఆٛ • Ψ΢εաఔͷఆٛʢࣄલ෼෍ɼ৚݅෇͖෼෍ʣ • ϋΠύϥͷ࠷దԽʢnumpyroʣ 2
3. tinygp ͱ͸ • ܰྔͳΨ΢εաఔϞσϦϯάϥΠϒϥϦɽ • jax ϕʔεɽࣗಈඍ෼΍ GPU ߴ଎ԽʹରԠɽ 3 Github: https://github.com/dfm/tinygp Doc : https://tinygp.readthedocs.io/en/stable/
4. Πϯετʔϧ • pip install --upgrade pip • pip install tinygp 4 GPU Λ׆༻ͷͨΊͷखॱ͢Δʹ͸΋͏গ͠खॱ͕͋Δɽ https://github.com/google/jax/#installation
5. ४උ • ਺஋ܭࢉͷਫ਼౓Λ 64bit ʹ͓ͯ͘͠ɽ 5
6. Χʔωϧͷఆٛ • tinygp.kernels ʹ͋ΔΫϥεΛར༻͢Δɽ 6 Custom Kernels https://tinygp.readthedocs.io/en/stable/tutorials/kernels.html#kernels
7. ʢิ଍ʣExpSquared Χʔωϧͷ࣮૷Λ֬ೝ • த਎͸͜Μͳײ͡ʹͳ͍ͬͯΔɽ 7
8. Ψ΢εաఔͷఆٛ • GaussianProcess ΫϥεΛར༻ɽ • Χʔωϧ kernel ͱೖྗ఺ X ΛࢦఆɽάϥϜߦྻͷର֯੒෼ʹՃ͑Β ΕΔ diag ͸ optional ɽ؍ଌϊΠζΛද͠਺஋ܭࢉͷ҆ఆੑʹد༩ɽ 8
9. ʢิ଍ʣαϯϓϦϯά • gp ʹࢦఆͨ͠ diag ͕େ͖͘ͳΔʹͭΕ noisy ͳαϯϓϧʹͳΔɽ 9
10. ৚݅෇͖෼෍ʢor पลԽ෼෍ʣ • gp.condition() ϝιουΛ༻͍Δɽ 10
11. ʢิ଍ʣgp.condition ͷ࣮૷Λ֬ೝ 11 σʔλͰ৚݅෇͚ͨ GP Λ৽ͨʹੜ੒ɽ ର਺໬౓ͱGP Λ return ɽ
12. ϋΠύϥͷ࠷దԽʢnumpyroʣ Notebook: https://gist.github.com/kzak/f963e182e6e947b5dcfd0de372d0ec9d
13. αϯϓϧσʔλ 13 ؍ଌσʔλ ͔Βਅͷؔ਺ Λ෮ݩ͍ͨ͠ɽ 㱺 GP Ͱۙࣅʢ= ʣɽ (X, y) f ̂ f ఺ : ؍ଌσʔλɼۂ໘ : ਅͷؔ਺
14. GP ϞσϧʢϋΠύϥखಈઃఆʣ 14 ͱൺ΂Δͱෳࡶ͗͢Δɽ 㱺 ϋΠύϥΛௐ੔͍ͨ͠ɽ f Լઢ෦͕ϋΠύϥ
15. numpyro ͰϋΠύϥΛਪఆ 15
16. GP Ϟσϧʢਪఆͨ͠ϋΠύϥʣ 16 㱺 ʢͦΕͳΓʹʣ Λ࠶ݱɽ f
17. ۂ໘ͷൺֱ 17 True ϋΠύϥखಈઃఆ ਪఆͨ͠ϋΠύϥ
18. ײ૝ / ·ͱΊ • tiny ͱ͍͏͚ͩ͋ͬͯશ๴Λ೺Ѳ͠΍͍͢ɽ • GaussianProcess Ϋϥεͱ kernels Ϟδϡʔϧ Λཧղ͢Ε͹࢖͑Δɽ • ύϥϝʔλͷਪఆ͸ଞͷϥΠϒϥϦʹҠৡ͢Δઃܭʹͳ͍ͬͯΔɽ • numpyro, jaxopt ͳͲ͕࢖͑Δɽ • sklearn.gaussian_process, GPy, GPyTorch ͳͲɼطଘϥΠϒϥϦͷ࿮૊ΈΛ֎Εͨ ϞσϦϯάʹ༗༻ɽ • ࣗ෼ͱͯ͠͸ॊೈੑ͕ߴ͘࢖͍΍͘͢ײͨ͡ɽ 18