SlowGuess/NeurIPS_2023_OCR huggingface dataset:
(a) Error of the mean
Figure 11: Comparison of moments for the two-type population model.
Figure 12: Comparison of moments for the switchpoint model.
(a) Error of the mean
Figure 13: Comparison of moments for the mixture model.
(a) Error of the mean
Figure 14: Comparison of moments for the HMM.
(a) Original population model.
(d) Switchpoint model.
Figure 15: Histograms of the exact distribution and the MCMC samples with the lowest TVD and similar running time to our exact method.
(b) Modified population model.
(e) Mixture model.
(c) Two-type population model.
(f) Hidden Markov model.
1 Introduction 1
2 Bayesian Probabilistic Programming 3
3 Generating Functions 4
3.1 Translating programs to generating functions 5
4 Implementation & Optimizations 6
5 Empirical Evaluation 8
5.1 Comparison with exact inference methods 8
5.2 Comparison with approximate inference methods 8
5.3 Benchmarks with infinite-support distributions 9
A Details on the Probabilistic Programming Language SGCL 14
A.1 A minimal grammar 14
A.2 Syntactic sugar 14
A.3 Standard measure semantics 14
B Details on Generating Functions 15
B.1 Generating function semantics 17
B.2 Correctness proof 17
B.3 Possible extensions to the probabilistic programming language 22
C Details on implementation and optimizations 23
C.1 Automatic differentiation and Taylor polynomials 24
C.2 Optimizing Observations from Compound Distributions 26
C.3 Analysis of the running time 29
C.4 Numerical issues 30
D Details on the Empirical Evaluation 30
D.1 Comparison with exact inference 30
D.2 Comparison with approximate inference 31
D.3 Benchmarks with infinite support 31
D.4 Additional results 34