Learning Arbitrary Finite Gaussian Location Mixtures
Year: 2026
Type: preprint
Abstract: We give a sample-only improper total-variation learner for finite Gaussian location mixtures with arbitrary means and weights and known common covariance. The exact-real sample, training, real-register representation and per-output costs are fixed polynomials in dimension, component count, inverse accuracy and logarithmic inverse failure probability. The construction combines a finite full-jet randomized gate, independent Gaussian views obtained from fresh original observations, rank-k compression of the actual accepted latent measures, a square-root PSD density dictionary, directional likelihood fitting with linear omitted-mass loss, and a robust posterior mass-cover refinement. An explicit noncircular noise schedule starts from raw observations and removes the need for a supplied mean radius. Every rejection loop is capped. Standard Gaussian analysis, convex optimization and robust mean estimation are identified explicitly; the last ingredient is implemented by a fully specified finite weighted filter, with a cited high-probability statistical subset theorem.
Author: Zheng, Zhijie
Institution: Peking University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222123324
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