2013/04/06 by Olivier Bodini, Jérémie Lumbroso, Bodini, Olivier +3
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Combinatorics (math.CO) #Data Structures and Algorithms (cs.DS) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Topological and Geometric Data Analysis #cs.DM #cs.DS #math.CO #math.PR
paper · pdf · doi:10.48550/arxiv.1304.1881
accepted at ANALCO 2015, 11 pages, 7 figures
openalex publication_date 2013/04/06 · arxiv created 2014/11/13 · arxiv updated 2014/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Boltzmann samplers, introduced by Duchon et al. in 2001, make it possible to uniformly draw approximate size objects from any class which can be specified through the symbolic method. This, through by evaluating the associated generating functions to obtain the correct branching probabilities. But these samplers require generating functions, in particular in the neighborhood of their sunglarity, which is a complex problem; they also require picking an appropriate tuning value to best control the size of generated objects. Although Pivoteau~\etal have brought a sweeping question to the first question, with the introduction of their Newton oracle, questions remain. By adapting the rejection method, a classical tool from the random, we show how to obtain a variant of the Boltzmann sampler framework, which is tolerant of approximation, even large ones. Our goal for this is twofold: this allows for exact sampling with approximate values; but this also allows much more flexibility in tuning samplers. For the class of simple trees, we will try to show how this could be used to more easily calibrate samplers.