A model-learner pattern for bayesian reasoning

Gordon, Andrew D.; Aizatulin, Mihhail; Borgström, Johannes; Claret, Guillaume; Graepel, Thore; Nori, Aditya V.; Rajamani, Sriram K.; Russo, Claudio

doi:10.1145/2429069.2429119

Cited by 25 publications

(9 citation statements)

References 36 publications

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“…Probabilistic programs are very widely studied (e.g. see [9,[17][18][19][20][21]) and have many applications in different fields, such as machine learning [22][23][24][25], randomized algorithms [26], and analyzing stochastic networks [27][28][29]. Probability vs Non-determinism.…”

Section: Preliminariesmentioning

confidence: 99%

Probabilistic Smart Contracts: Secure Randomness on the Blockchain

Chatterjee

Goharshady

Pourdamghani

2019

2019 IEEE International Conference on Blockchain and Cryptocurrency (ICBC)

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In today's programmable blockchains, smart contracts are limited to being deterministic and non-probabilistic. This lack of randomness is a consequential limitation, given that a wide variety of real-world financial contracts, such as casino games and lotteries, depend entirely on randomness. As a result, several ad-hoc random number generation approaches have been developed to be used in smart contracts. These include ideas such as using an oracle or relying on the block hash. However, these approaches are manipulatable, i.e. their output can be tampered with by parties who might not be neutral, such as the owner of the oracle or the miners.We propose a novel game-theoretic approach for generating provably unmanipulatable pseudorandom numbers on the blockchain. Our approach allows smart contracts to access a trustworthy source of randomness that does not rely on potentially compromised miners or oracles, hence enabling the creation of a new generation of smart contracts that are not limited to being non-probabilistic and can be drawn from the much more general class of probabilistic programs.

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Section: Preliminariesmentioning

confidence: 99%

Probabilistic Smart Contracts: Secure Randomness on the Blockchain

Chatterjee

Goharshady

Pourdamghani

2019

2019 IEEE International Conference on Blockchain and Cryptocurrency (ICBC)

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“…Also, we note that observe(x) is equivalent to the while-loop while(!x) skip since the semantics of probabilistic programs is concerned about the normalized distribution of outputs over terminating runs of the program, and ignores non-terminating runs. However, we use the terminology observe(x) because of its common use in probabilistic programming systems [2,12].…”

Section: Overviewmentioning

confidence: 99%

Slicing probabilistic programs

et al. 2014

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Probabilistic programs use familiar notation of programming languages to specify probabilistic models. Suppose we are interested in estimating the distribution of the return expression r of a probabilistic program P . We are interested in slicing the probabilistic program P and obtaining a simpler program SLI(P ) which retains only those parts of P that are relevant to estimating r, and elides those parts of P that are not relevant to estimating r. We desire that the SLI transformation be both correct and efficient. By correct, we mean that P and SLI(P ) have identical estimates on r. By efficient, we mean that estimation over SLI(P ) be as fast as possible.We show that the usual notion of program slicing, which traverses control and data dependencies backward from the return expression r, is unsatisfactory for probabilistic programs, since it produces incorrect slices on some programs and sub-optimal ones on others. Our key insight is that in addition to the usual notions of control dependence and data dependence that are used to slice nonprobabilistic programs, a new kind of dependence called observe dependence arises naturally due to observe statements in probabilistic programs.We propose a new definition of SLI(P ) which is both correct and efficient for probabilistic programs, by including observe dependence in addition to control and data dependences for computing slices. We prove correctness mathematically, and we demonstrate efficiency empirically. We show that by applying the SLI transformation as a pre-pass, we can improve the efficiency of probabilistic inference, not only in our own inference tool R2, but also in other systems for performing inference such as Church and Infer.NET.

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“…Open fail-free Fun expressions have a straightforward semantics (Ramsey and Pfeffer, 2002) as computations in the probability monad (Giry, 1982). In order to treat the fail primitive, we use an existing extension (Gordon et al, 2013) of the semantics of Ramsey and Pfeffer (2002) to a richer monad: the sub-probability monad (Panangaden, 1999) 3 . Compared to the operations of the probability monad, the sub-probability monad additionally admits a zero constant, yielding the zero measure.…”

Section: Syntax and Types Of Funmentioning

confidence: 99%

“…Below we recapitulate the semantics of Fun by Gordon et al (2013). Here σ is a closed value substitution whose domain contains all the free variables of M, and detOp(M) ranges over op(M), fst M, snd M, inl M and inr M. We also let either f g (inl V ) f V and either f g (inr V ) g V .…”

Section: Syntax and Types Of Funmentioning

confidence: 99%

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Deriving Probability Density Functions from Probabilistic Functional Programs

Bhat

Borgström

Gordon

et al. 2013

Tools and Algorithms for the Construction and Analysis of Systems

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The probability density function of a probability distribution is a fundamental concept in probability theory and a key ingredient in various widely used machine learning methods. However, the necessary framework for compiling probabilistic functional programs to density functions has only recently been developed. In this work, we present a density compiler for a probabilistic language with failure and both discrete and continuous distributions, and provide a proof of its soundness. The compiler greatly reduces the development effort of domain experts, which we demonstrate by solving inference problems from various scientific applications, such as modelling the global carbon cycle, using a standard Markov chain Monte Carlo framework.computing PDFs for a large class of programs written in a rich probabilistic programming language. An abridged version of this paper was published as (Bhat et al., 2013).Probability density functions. In this work, probabilistic programs correspond directly to probability distributions, which are important because they are a powerful formalism for data analysis. However, many techniques we would like to use require the probability density function of a distribution instead of the distribution itself. Unfortunately, not every distribution has a density function.Distributions. One interpretation of a probabilistic program is that it is a simulation that can be run to generate a random sample from some set Ω of possible outcomes. The corresponding probability distribution P characterizes the program by assigning probabilities to different subsets of Ω (events). The probability P(A) for a subset A of Ω corresponds to the proportion of runs that generate an outcome in A, in the limit of an infinite number of repeated runs of the simulation.Consider for example a simple mixture of Gaussians, here written in Fun (Borgström et al., 2011), a probabilistic functional language embedded within F# (Syme et al., 2007).if flip 0.7 then random(Gaussian(0.0, 1.0)) else random(Gaussian(4.0, 1.0))The program above specifies a distribution on the real line (Ω is R) and corresponds to a generative process that flips a biased coin and then generates a number from one of two Gaussian distributions, both with standard deviation 1.0 but with mean either 0.0 or 4.0 depending on the result of the coin toss. In this example, we will be more likely to produce a value near 0.0 than near 4.0 because of the bias. The probability P(A) for A = [0, 1], for instance, is the proportion of runs that generate a number between 0 and 1.Densities. A distribution P is a function that takes subsets of Ω as input, but for many purposes it turns out to be more convenient if we can find a function f that takes elements of Ω directly, while still somehow capturing the same information as P.When Ω is the real line, we are interested in a function f that satisfies P(A) = A f (x) dx for all intervals A, and we call f the probability density function (PDF) of the distribution P. In other words, f is a function where the area under its ...

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A model-learner pattern for bayesian reasoning

Cited by 25 publications

References 36 publications

Probabilistic Smart Contracts: Secure Randomness on the Blockchain

Probabilistic Smart Contracts: Secure Randomness on the Blockchain

Slicing probabilistic programs

Deriving Probability Density Functions from Probabilistic Functional Programs

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