Probabilistic Programming (Vermont Code Camp 2016)

The world is full of uncertainty. But most software handles computation deterministically. Probabilistic Programming is a bridge between general-purpose programming languages and the statistical methods of machine learning and artificial intelligence.

In this introduction, we cover some basics of probability theory, provide a conceptual framework for understanding probabilistic programming systems, compare probabilistic inference with logical inference and its use in making decisions, and survey some of the current efforts to bring probabilistic programming to industrial settings.

Transcript

1. Probabilis)c Programming 2016 Vermont Code Camp Eric Smith @eric_s_smith
2. Probabilis)c Programming System •  Probabilis)c program “Usual programs with two added constructs: (1) the ability the draw values at random from distribu)ons (2) the ability to condi)on values of variables in a program via observe statements. ” •  Probabilis)c inference “Compu)ng an explicit representa)on of the probability distribu)on implicitly specified by a probabilis)c program" Probabilis+c Programming (2014), Gordon et al
3. Possible worlds x + y = 4 When is this true?
4. Logical inference
5. h8p://www.sdsc.edu/~tbailey/teaching/cse151
6. Sample space Ω = { HHH, HHT, HTH, THH, HTT, THT, TTH, TTT } Flipping a fair coin 3 +mes
7. Event A = { HHH, HHT, HTH, HTT } A = Get Heads on the first flip B = {HHH, HHT, THH, THT } B = Get Heads on the second flip
8. Probability Degree of belief of some event being true expressed as number from 0 to 1.
9. Probability Distribu)on Discrete values Con)nuous values
10. Distribu)ons
11. Draw values at random from distribu)ons Anglican Demo webppl Demo
14. Prior vs Posterior Probability A prior probability is your understanding before making an observa)on. A posterior (or condi+onal) probability is using an observa)on to revise a prior.
15. A = { 3 } 3 dots B = { 3, 4, 5, 6 } at least 3 dots Condi)onal Probability P(A|B) is 1/4
16. Condi)on value of variables Anglican Demo
18. Joint Distribu)on Toothache No Toothache Catch No Catch Catch No Catch Cavity 0.108 0.012 0.072 0.008 No Cavity 0.016 0.064 0.144 0.576 P(cavity | toothache) = P(cavity ∧ toothache) P(toothache) = 0.108 + 0.012 0.108 + 0.012 + 0.016 + 0.064 = 0.6
19. Bayes Rule P(cause | effect) = P(effect | cause) P(cause) P(effect) Meningi)s can cause s)ff neck 70% of the )me. Incidence of meningi)s is 1/50,000. Probability that any pa)ent has a s)ff neck is 1%. P(s | m) = 0.7 P(m) = 1/50,000 P(s) = 0.01 P(m | s) = P(s | m) P(m) P(s) = 0.7 x 1/50,000 0.01 = 0.0014
20. Bayes Net What is the probability that it is raining, given that the sprinkler Is on and the grass is wet?
21. Compute an explicit representa)on of the probability distribu)on implicitly specified by a probabilis)c program Anglican Demo