Direct design of biquad filter cascades with deep learning by sampling random polynomials

1 code implementation • 7 Oct 2021 • Joseph T. Colonel, Christian J. Steinmetz, Marcus Michelen, Joshua D. Reiss

In this work, we address some of these limitations by learning a direct mapping from the target magnitude response to the filter coefficient space with a neural network trained on millions of random filters.

Anti-concentration of random variables from zero-free regions

no code implementations • 15 Feb 2021 • Marcus Michelen, Julian Sahasrabudhe

This paper provides a connection between the concentration of a random variable and the distribution of the roots of its probability generating function.

Probability Combinatorics

Asymptotic bounds on graphical partitions and partition comparability

no code implementations • 28 Mar 2020 • Stephen Melczer, Marcus Michelen, Somabha Mukherjee

Key to our argument is an asymptotic result of Pittel characterizing the joint distribution of the first rows and columns of a uniformly random partition, combined with a characterization of graphical partitions due to Erd\H{o}s and Gallai.

Combinatorics Probability 05A16, 05A17, 11P82, 60C05