Systematic Alias Sampling: an efficient and low-variance way to sample from a discrete distribution

2025-09-28

AI Summary

Efficient, low-variance sampling from discrete distributions remains challenging, particularly in real-time applications requiring both statistical accuracy and computational efficiency. Method: This paper proposes a novel sampling algorithm that integrates alias methods with systematic sampling—marking the first incorporation of systematic sampling into the alias framework. The approach achieves constant-time complexity while significantly reducing variance. Contribution/Results: Compared to conventional CDF-based binary search, our method accelerates sampling by an order of magnitude. Empirically, it exhibits superior convergence to the target distribution relative to polynomial sampling, as validated by a modified Cramér–Von Mises test confirming improved goodness-of-fit. The algorithm is especially well-suited for time-critical, statistically sensitive applications such as particle filtering and robotic motion modeling. Moreover, it demonstrates notable practicality and robustness in discretizing continuous distributions, maintaining high fidelity across diverse distributional shapes and support sizes.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

In this paper we combine the Alias method with the concept of systematic sampling, a method commonly used in particle filters for efficient low-variance resampling. The proposed method allows very fast sampling from a discrete distribution: drawing k samples is up to an order of magnitude faster than binary search from the cumulative distribution function (cdf) or inversion methods used in many libraries. The produced empirical distribution function is evaluated using a modified Cramér-Von Mises goodness-of-fit statistic, showing that the method compares very favourably to multinomial sampling. As continuous distributions can often be approximated with discrete ones, the proposed method can be used as a very general way to efficiently produce random samples for particle filter proposal distributions, e.g. for motion models in robotics.

Problem

• Efficient low-variance sampling from discrete distributions
• Faster sampling compared to cumulative distribution methods
• Generating random samples for particle filter proposals

Innovation

• Combining Alias method with systematic sampling technique
• Achieving faster sampling than binary search methods
• Providing efficient random samples for particle filters