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arXiv · 2212.09391

Bounds for matrices of inclusion probabilities in rejective sampling

Simon Ruetz·Karin Schnass
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Abstract

Motivated by a desire to model n-sparse signals more realistically, we study matrices of inclusion probabilities for conditional Poisson or rejective sampling in the non-asymptotic regime. In particular, we provide bounds in the semi-definite ordering for matrices that collect first and second order inclusion probabilities as their diagonal and off-diagonal entries respectively, and operator norm bounds of their Hadamard products with other matrices. Finally, we demonstrate the usefulness on these bounds, which only involve first order inclusion probabilities, in a toy application from dictionary learning.

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Simon Ruetz, Karin Schnass. 2022-12-19. Bounds for matrices of inclusion probabilities in rejective sampling. https://arxiv.org/abs/2212.09391

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