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math.PR2025
Gaussian universality for approximately polynomial functions of high-dimensional data
Kevin Han Huang, Morgane Austern, Peter Orbanz
Gaussian universality results assert that the properties of many estimators remain unchanged when the input data are replaced by Gaussians. Such results have gained popularity in h…
math.PR2025
Bounding Hellinger Distance with Stein's Method
Morgane Austern, Lester Mackey
This work introduces a new, explicit bound on the Hellinger distance between a continuous random variable and a Gaussian with matching mean and variance. As example applications, w…
math.PR2025
Wasserstein-p Bounds via Cumulant-Based Edgeworth Expansion for -Mixing Random Fields
Tianle Liu, Morgane Austern
Recent progress has been made in establishing normal approximation bounds in terms of the Wasserstein- distance for i.i.d. and locally dependent random variables. However, for $…