Estimating Unknown Population Sizes Using the Hypergeometric Distribution
<|reference_start|>Estimating Unknown Population Sizes Using the Hypergeometric Distribution: The multivariate hypergeometric distribution describes sampling without replacement from a discrete population of elements divided into multiple categories. Addressing a gap in the literature, we tackle the challenge of estimating discrete distributions when both the total population size and the sizes of its constituent categories are unknown. Here, we propose a novel solution using the hypergeometric likelihood to solve this estimation challenge, even in the presence of severe under-sampling. We develop our approach to account for a data generating process where the ground-truth is a mixture of distributions conditional on a continuous latent variable, such as with collaborative filtering, using the variational autoencoder framework. Empirical data simulation demonstrates that our method outperforms other likelihood functions used to model count data, both in terms of accuracy of population size estimate and in its ability to learn an informative latent space. We demonstrate our method's versatility through applications in NLP, by inferring and estimating the complexity of latent vocabularies in text excerpts, and in biology, by accurately recovering the true number of gene transcripts from sparse single-cell genomics data.<|reference_end|>
@article{hodgson2024estimating,
    title={Estimating Unknown Population Sizes Using the Hypergeometric
  Distribution},
    author={Liam Hodgson and Danilo Bzdok},
    journal={arXiv preprint arXiv:2402.14220},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.14220},
    primaryClass={cs.LG stat.ME stat.ML}
}