Adriano Meligrana

Lilith Orion Hafner, Adriano Meligrana

Sampling from a dynamic discrete distribution means drawing an index with probability proportional to a mutable set of weights. Classical constant-time techniques such as the Alias Method are well suited to static distributions, but become expensive in dynamic settings because updates require rebuilding auxiliary tables. Existing dynamic approaches, including Forest of Trees and BUcket Sampling (BUS), achieve reasonable practical performance but require infinite precision real arithmetic to be correct and produce meaningfully incorrect results when implemented on real hardware. We present EBUS (Exact BUcket Sampling), a dynamic sampler for finite-precision weights that is exact by construction: every returned index has probability exactly proportional to its represented weight. Our guarantees are proved in a word RAM model with bounded exponent range. In that model, our method supports $O(1)$ worst-case expected sampling time, $O(1)$ amortized time to update a single weight, $O(n)$ space, and $O(n)$ construction. We also provide an implementation for IEEE 64-bit floating-point weights and show experimentally that it is competitive with, and often faster than, several implementations of previous inexact methods while avoiding their numerical failure modes.

Adriano Meligrana, Adriano Fazzone

In this work, we present a new random sampling method for data streams where the probability of an element's inclusion in the sample is proportional to a weight associated with that element. Our method is based on sampling with replacement, although most of the literature on this topic has focused on sampling without replacement. Our algorithm generates a weighted random sample in one pass over a population of unknown size. At any point in time, the sample is representative of the population seen so far and can be directly used by other modules without requiring any post-processing. We formally prove the correctness and efficiency of our method. An experimental analysis shows the performance of our method in practice when compared to state-of-the-art methods.

Adriano Meligrana

StreamSampling$.$jl is a Julia library designed to provide general and efficient methods for sampling from data streams in a single pass, even when the total number of items is unknown. In this paper, we describe the capabilities of the library and its advantages over traditional sampling procedures, such as maintaining a small, constant memory footprint and avoiding the need to fully materialize the stream in memory. Furthermore, we provide empirical benchmarks comparing online sampling methods against standard approaches, demonstrating performance and memory improvements.