Related papers: Generating Functions for Probabilistic Programs
We examine two different ways of encoding a counting function, as a rational generating function and explicitly as a function (defined piecewise using the greatest integer function). We prove that, if the degree and number of input…
GP 2 is a non-deterministic programming language for computing by graph transformation. One of the design goals for GP 2 is syntactic and semantic simplicity, to facilitate formal reasoning about programs. In this paper, we demonstrate with…
This paper introduces a unified theoretical perspective that views deep generative models as probability transformation functions. Despite the apparent differences in architecture and training methodologies among various types of generative…
The asymptotic study of the conjugacy classes of a random element of the finite affine group leads one to define a probability measure on the set of all partitions of all positive integers. Four different probabilistic understandings of…
It is natural for probabilistic programs to use conditionals to express alternative substructures in models, and loops (recursion) to express repeated substructures in models. Thus, probabilistic programs with conditionals and recursion…
The state-of-the-art error correcting codes are based on large random constructions (random graphs, random permutations, ...) and are decoded by linear-time iterative algorithms. Because of these features, they are remarkable examples of…
This is a collection of examples showing how the GAP system can be used to compute information about the probabilistic generation of finite almost simple groups. It includes all examples that were needed for the computational results in the…
Probabilistic programming languages rely fundamentally on some notion of sampling, and this is doubly true for probabilistic programming languages which perform Bayesian inference using Monte Carlo techniques. Verifying samplers - proving…
We present an overview of the role of generating functions in quantum mechanical contexts, mainly in the modern theory of polarization and in the study of quantum phase transitions. Generating functions enable the derivation of moments and…
We introduce stochastic and quantum finite-state transducers as computation-theoretic models of classical stochastic and quantum finitary processes. Formal process languages, representing the distribution over a process's behaviors, are…
Many practical techniques for probabilistic inference require a sequence of distributions that interpolate between a tractable distribution and an intractable distribution of interest. Usually, the sequences used are simple, e.g., based on…
Probabilistic programming provides a convenient lingua franca for writing succinct and rigorous descriptions of probabilistic models and inference tasks. Several probabilistic programming languages, including Anglican, Church or Hakaru,…
The generating functionals (GF) method in Bogolyubov's formulation and its application for particle physics is considered. Effectiveness of the method is illustrated by two examples. So, GF method can be used as the technical trick solving…
In a recent article a generalization of the binomial distribution associated with a sequence of positive numbers was examined. The analysis of the nonnegativeness of the formal expressions was a key-point to allow to give them a statistical…
Probabilistic programs provide an expressive representation language for generative models. Given a probabilistic program, we are interested in the task of posterior inference: estimating a latent variable given a set of observed variables.…
We describe a method to perform functional operations on probability distributions of random variables. The method uses reproducing kernel Hilbert space representations of probability distributions, and it is applicable to all operations…
Probabilistic inference procedures are usually coded painstakingly from scratch, for each target model and each inference algorithm. We reduce this effort by generating inference procedures from models automatically. We make this code…
The idea of using unfolding as a way of computing a program semantics has been applied successfully to logic programs and has shown itself a powerful tool that provides concrete, implementable results, as its outcome is actually source…
We study a syntax for specifying quantitative "assertions" - functions mapping program states to numbers - for probabilistic program verification. We prove that our syntax is expressive in the following sense: Given any probabilistic…
Deep generative models (DGMs) have recently demonstrated remarkable success in capturing complex probability distributions over graphs. Although their excellent performance is attributed to powerful and scalable deep neural networks, it is,…