On the number of modes of Gaussian kernel density estimators
Abstract
We consider the Gaussian kernel density estimator with bandwidth β-12 of n iid Gaussian samples. Using the Kac-Rice formula and an Edgeworth expansion, we prove that the expected number of modes on the real line scales as (ββ) as β,n∞ provided nc β n2-c for some constant c>0. An impetus behind this investigation is to determine the number of clusters to which Transformers are drawn in a metastable state.
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