Dirichlet-process probability tree

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Jamie Oaks

An "animation" of a probability tree to provide some intuition about how the Dirichlet process works.

Dados e análise

α = 0.1
A
A B
A B C
α
α+2 = 0.048
AC B
1
α+2 = 0.476
A BC
1
α+2 = 0.476
α
α+1 = 0.091
AB
AB C
α
α+2 = 0.048
ABC2
α+2 = 0.952
1
α+1 = 0.909

α = 0.1
A
A B
A B C α
α+1
α
α+2 = 0.004
α
α+2 = 0.048
AC B α
α+1
1
α+2 = 0.043
1
α+2 = 0.476
A BC α
α+1
1
α+2 = 0.043
1
α+2 = 0.476
α
α+1 = 0.091
AB
AB C 1
α+1
α
α+2 = 0.043
α
α+2 = 0.048
ABC 1
α+1
2
α+2 = 0.8662
α+2 = 0.952
1
α+1 = 0.909

α = 1.5
A
A B
A B C α
α+1
α
α+2 = 0.257
α
α+2 = 0.429
AC B α
α+1
1
α+2 = 0.171
1
α+2 = 0.286
A BC α
α+1
1
α+2 = 0.171
1
α+2 = 0.286
α
α+1 = 0.600
AB
AB C 1
α+1
α
α+2 = 0.171
α
α+2 = 0.429
ABC 1
α+1
2
α+2 = 0.2292
α+2 = 0.571
1
α+1 = 0.400

α = 50.0
A
A B
A B C α
α+1
α
α+2 = 0.943
α
α+2 = 0.962
AC B α
α+1
1
α+2 = 0.019
1
α+2 = 0.019
A BC α
α+1
1
α+2 = 0.019
1
α+2 = 0.019
α
α+1 = 0.980
AB
AB C 1
α+1
α
α+2 = 0.019
α
α+2 = 0.962
ABC 1
α+1
2
α+2 = 0.0012
α+2 = 0.038
1
α+1 = 0.020

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Dirichlet-process probability tree

1. α = 0.1 A A B A B C α α+2 = 0.048 AC B 1 α+2 = 0.476 A BC 1 α+2 = 0.476 α α+1 = 0.091 AB AB C α α+2 = 0.048 ABC2 α+2 = 0.952 1 α+1 = 0.909

2. α = 0.1 A A B A B C α α+2 = 0.048 AC B 1 α+2 = 0.476 A BC 1 α+2 = 0.476 α α+1 = 0.091 AB AB C α α+2 = 0.048 ABC2 α+2 = 0.952 1 α+1 = 0.909

3. α = 0.1 A A B A B C α α+2 = 0.048 AC B 1 α+2 = 0.476 A BC 1 α+2 = 0.476 α α+1 = 0.091 AB AB C α α+2 = 0.048 ABC2 α+2 = 0.952 1 α+1 = 0.909

4. α = 0.1 A A B A B C α α+2 = 0.048 AC B 1 α+2 = 0.476 A BC 1 α+2 = 0.476 α α+1 = 0.091 AB AB C α α+2 = 0.048 ABC2 α+2 = 0.952 1 α+1 = 0.909

5. α = 0.1 A A B A B C α α+2 = 0.048 AC B 1 α+2 = 0.476 A BC 1 α+2 = 0.476 α α+1 = 0.091 AB AB C α α+2 = 0.048 ABC2 α+2 = 0.952 1 α+1 = 0.909

6. α = 0.1 A A B A B C α α+2 = 0.048 AC B 1 α+2 = 0.476 A BC 1 α+2 = 0.476 α α+1 = 0.091 AB AB C α α+2 = 0.048 ABC2 α+2 = 0.952 1 α+1 = 0.909

7. α = 0.1 A A B A B C α α+2 = 0.048 AC B 1 α+2 = 0.476 A BC 1 α+2 = 0.476 α α+1 = 0.091 AB AB C α α+2 = 0.048 ABC2 α+2 = 0.952 1 α+1 = 0.909

8. α = 0.1 A A B A B C α α+2 = 0.048 AC B 1 α+2 = 0.476 A BC 1 α+2 = 0.476 α α+1 = 0.091 AB AB C α α+2 = 0.048 ABC2 α+2 = 0.952 1 α+1 = 0.909

9. α = 0.1 A A B A B C α α+2 = 0.048 AC B 1 α+2 = 0.476 A BC 1 α+2 = 0.476 α α+1 = 0.091 AB AB C α α+2 = 0.048 ABC2 α+2 = 0.952 1 α+1 = 0.909

10. α = 0.1 A A B A B C α α+2 = 0.048 AC B 1 α+2 = 0.476 A BC 1 α+2 = 0.476 α α+1 = 0.091 AB AB C α α+2 = 0.048 ABC2 α+2 = 0.952 1 α+1 = 0.909

11. α = 0.1 A A B A B C α α+2 = 0.048 AC B 1 α+2 = 0.476 A BC 1 α+2 = 0.476 α α+1 = 0.091 AB AB C α α+2 = 0.048 ABC2 α+2 = 0.952 1 α+1 = 0.909

12. α = 0.1 A A B A B C α α+2 = 0.048 AC B 1 α+2 = 0.476 A BC 1 α+2 = 0.476 α α+1 = 0.091 AB AB C α α+2 = 0.048 ABC2 α+2 = 0.952 1 α+1 = 0.909

13. α = 0.1 A A B A B C α α+2 = 0.048 AC B 1 α+2 = 0.476 A BC 1 α+2 = 0.476 α α+1 = 0.091 AB AB C α α+2 = 0.048 ABC2 α+2 = 0.952 1 α+1 = 0.909

14. α = 0.1 A A B A B C α α+2 = 0.048 AC B 1 α+2 = 0.476 A BC 1 α+2 = 0.476 α α+1 = 0.091 AB AB C α α+2 = 0.048 ABC2 α+2 = 0.952 1 α+1 = 0.909

15. α = 0.1 A A B A B C α α+2 = 0.048 AC B 1 α+2 = 0.476 A BC 1 α+2 = 0.476 α α+1 = 0.091 AB AB C α α+2 = 0.048 ABC2 α+2 = 0.952 1 α+1 = 0.909

16. α = 0.1 A A B A B C α α+1 α α+2 = 0.004 α α+2 = 0.048 AC B α α+1 1 α+2 = 0.043 1 α+2 = 0.476 A BC α α+1 1 α+2 = 0.043 1 α+2 = 0.476 α α+1 = 0.091 AB AB C 1 α+1 α α+2 = 0.043 α α+2 = 0.048 ABC 1 α+1 2 α+2 = 0.8662 α+2 = 0.952 1 α+1 = 0.909

17. α = 1.5 A A B A B C α α+1 α α+2 = 0.257 α α+2 = 0.429 AC B α α+1 1 α+2 = 0.171 1 α+2 = 0.286 A BC α α+1 1 α+2 = 0.171 1 α+2 = 0.286 α α+1 = 0.600 AB AB C 1 α+1 α α+2 = 0.171 α α+2 = 0.429 ABC 1 α+1 2 α+2 = 0.2292 α+2 = 0.571 1 α+1 = 0.400

18. α = 50.0 A A B A B C α α+1 α α+2 = 0.943 α α+2 = 0.962 AC B α α+1 1 α+2 = 0.019 1 α+2 = 0.019 A BC α α+1 1 α+2 = 0.019 1 α+2 = 0.019 α α+1 = 0.980 AB AB C 1 α+1 α α+2 = 0.019 α α+2 = 0.962 ABC 1 α+1 2 α+2 = 0.0012 α+2 = 0.038 1 α+1 = 0.020

Dirichlet-process probability tree

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