Probabilistic programming

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1. What have the authors stated for future works in "Probabilistic programming" ?

2. What are the contributions mentioned in the paper "Probabilistic programming" ?

3. What is the meaning of naive sampling?

4. What are the types of statements that are used in PROB?

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In this section the authors outline some avenues for future work.. While the goals of the communities have been different, the authors believe that cross-fertilization between the two communities is an interesting direction for future work.. This is a promising avenue since optimization techniques scale better than search techniques such as MCMC ( which were discussed in Section 6 ).

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In this paper, the authors describe connections this research area called “ Probabilistic Programming ” has with programming languages and software engineering, and this includes language design, and the static and dynamic analysis of programs.. The authors survey current state of the art and speculate on promising directions for future research.

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Naive sampling, which corresponds to running the program, can result in rejected samples leading to wasteful computation and subsequently loss in efficiency.

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Statements include primitive statements (deterministic assignment, probabilistic assignment, observe, skip ) and composite statements (sequential composition, conditionals and loops).

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CTMCs can be encoded as probabilistic programs by explicitly introducing time as a program variable, and using a technique known as uniformization [46].

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the slicing algorithm can be implemented as a source-to-source program transformation, which greatly improves the efficiency of inference by removing irrelevant statements, while providing provably equivalent answers.

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Probabilistic programs are “usual” programs (written in languages like C, Java, LISP or ML) with two added constructs: (1) the ability to draw values at random from distributions, and (2) the ability to condition values of variables in a program via observe statements (which allow data from real world observations to be incorporated into a probabilistic program).

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The pre-image of called with respect to this assignment statement is maryWakes&&phoneWorking, which is propagated back through the program.

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Probabilistic graphical models are widely used in statistics and machine learning, with diverse[Copyright notice will appear here once ’preprint’ option is removed.]application areas including information extraction, speech recognition, computer vision, coding theory, biology and reliability analysis.

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The modifications exploit the structure in the transformed programs that observe statements immediately follow probabilistic assignments, and sample from sub-distributions in order to avoid rejections.

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Bayesian Networks can be used to pose and answer conditional queries, and this can be encoded in probabilistic programs using observe statements.

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The probability of a particular state in the joint distribution can be evaluated by starting at the leaf nodes of the Bayesian Network (that is the nodes at the “top” without any inputs) and proceeding in topological order.

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A more efficient computation would exploit the structure of the factorization ofP (B,E,A, J,M) that is induced by the structure of the Bayesian network.

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For instance, if the authors want to calculate the probability that the program terminates in a particular state σ̂, the authors can return a predicate σ = σ̂, which returns 1 iff the state just before returning is σ̂ and 0 otherwise.

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A parameter β is used to decide whether to accept or reject a new sampled value for x, and is defined as follows:β = min { 1, P (xnew) ·Q(xnew → xold) P (xold) ·Q(xold → xnew) }

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In general, every Bayesian Network can be encoded as an acyclic probabilistic program in a straightforward manner, and conditioning can be modeled using observe statements in the probabilistic program.

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Another example which illustrates bounding the expected value is “the expected time for the protocol to finish transmitting one packet is less than 3 milliseconds”.

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Once again, since conditioning by permitted executions yields Pr(c1=false,c2=false) = 0, and Pr(c1=false,c2=true) = Pr(c1=true,c2=false) = Pr(c1=true,c2=true) = 1/3, the authors have that the expected return value is 0× 0 + 1/3× 1 + 1/3× 1 + 1/3× 2 = 4/3.The authors note that the statement observe(x) is very related to the statement assume(x) used in program verification literature [2, 15, 42].

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An example property illustrating bounds on probability is “the probability that an airbag fails to deploy within 0.02 seconds after a crash is less than 0.01”.

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The authors also show that while Markov Chains can be encoded as loopy probabilistic programs, the steady state probability distribution of Markov Chains can be represented as outputs of probabilistic programs (and hence computed using probabilistic inference) only for a restricted class of Markov Chains, since their semantics for probabilistic programs considers only terminating executions and Markov Chains have non-terminating executions.

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output = 0; today = 260; // the current date if ((bday>=today) && (bday<today+7)) output=1;The access control question is whether to allow the advertiser to see the output, and the policy is to allow it so long as the advertiser’s knowledge of the secret data after running the query does not exceed the knowledge thresholds stated above.

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The answer to a query Q on a probabilistic database is the set of tuples T that are possible answers to Q, along with a probability P (t) for every t ∈ T denoting the probability that t belongs the answer for queryQ.

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adding time complicates the semantics and tooling needed for probabilistic programs and hence needs to be done carefully without exploding the complexity of the entire system.

Probabilistic programming

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Most frequently asked questions

1. What have the authors stated for future works in "Probabilistic programming" ?

2. What are the contributions mentioned in the paper "Probabilistic programming" ?

3. What is the meaning of naive sampling?

4. What are the types of statements that are used in PROB?

5. How can a probabilistic database be encoded?

6. What can be done with the slicing algorithm?

7. What are the two constructs of a probabilistic program?

8. What is the pre-image of called with respect to this assignment statement?

9. What are the main uses of probabilistic graphical models?

10. What is the purpose of the modifications?

11. How can the authors encode the Bayesian Network?

12. How can the authors evaluate the probability of a particular state in the Bayesian Network?

13. What is the way to compute the probability distribution of a Bayesian network?

14. What is the probability that the program terminates in a particular state?

15. What is the simplest way to decide whether to accept or reject a new sampled value?

16. How can the authors encode the Bayesian Network as a probabilistic program?

17. How long does it take for a protocol to finish transmitting?

18. What is the expected return value of the observe statement?

19. What is the probability of an airbag failing to deploy?

20. How can the authors explain the relationship between probabilistic programs and other probabilistic models?

21. What is the policy for allowing the querier to see the output?

22. What is the answer to a query Q on a probabilistic database?

23. What is the main reason for adding time to probabilistic programs?

Figures

Citations

The frontier of simulation-based inference

A Survey of Machine Learning for Big Code and Naturalness

Kernel Mean Embedding of Distributions: A Review and Beyond

A Survey of Machine Learning for Big Code and Naturalness

Distributionally Robust Optimization: A Review

References

Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference

Markov Decision Processes: Discrete Stochastic Dynamic Programming

Markov Decision Processes

Information Theory, Inference and Learning Algorithms

Probabilistic graphical models : principles and techniques

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