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Tight Simulation of a Distribution Using Conditional Samples

Author Tomer Adar

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LIPIcs.APPROX-RANDOM.2026.32.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Streaming, sublinear and near linear time algorithms
Keywords
  • Distribution learning
  • Distribution simulation
  • Probability estimation

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Abstract

We present an algorithm for simulating a distribution using prefix conditional samples (Adar, Fischer and Levi, 2024), as well as "prefix-compatible" conditional models such as the interval model (Cannone, Ron and Servedio, 2015) and the subcube model (CRS15, Bhattacharyya and Chakraborty, 2018). The sample complexity is O(log² N/ε²) prefix conditional samples per query, which improves on the previously known Õ(log³ N/ε²) (Kumar, Meel and Pote, 2025). Moreover, our simulating distribution is O(ε²)-close to the input distribution with respect to the Kullback-Leibler divergence, which is stricter than the usual guarantee of being O(ε)-close with respect to the total-variation distance.
We show that our algorithm is tight with respect to the highly-related task of estimation: every algorithm that is able to estimate the mass of individual elements within (1 ± ε)-multiplicative error must make Ω(log²N/ε²) prefix conditional samples per element.

Cite As Get BibTex

Tomer Adar. Tight Simulation of a Distribution Using Conditional Samples. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 392, pp. 32:1-32:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2026.32

Author Details

Tomer Adar
  • Technion - Israel Institute of Technology, Haifa, Israel

References

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