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abstract indexed · arXiv 2610.01088 · updated 2026-10-18

Polylogarithmic Sparsity of Randomly Reweighted NPMLEs for Gaussian Mixtures

First page of Polylogarithmic Sparsity of Randomly Reweighted NPMLEs for Gaussian Mixtures
From the original paper · arXiv 2610.01088Page 1. Select the image to read the PDF.

The method replaces the classical Gaussian location-mixture NPMLE, whose support can grow linearly with sample size, with a Gamma-reweighted likelihood estimator that has provably polylogarithmic support while nearly maximizing the ordinary likelihood. It costs a small random perturbation of the likelihood and the same convex optimization machinery as the standard NPMLE, with Hellinger risk parametric up to logarithmic factors. It can fail in that the sparsity bound is asymptotic and probabilistic, the analysis is specific to Gaussian location mixtures, and the numerical evidence is illustrative rather than benchmarked on production workloads.

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Randomly reweighted NPMLE for sparse Gaussian mixtures
published
2026-10-01

This is a nonparametric density-estimation theory result with no connection to LLM inference, training, agents, or retrieval on the reader's constrained infrastructure, so it is outside their production practice.

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    The method replaces the classical Gaussian location-mixture NPMLE, whose support can grow linearly with sample size, with a Gamma-reweighted likelihood estimator that has provably polylogarithmic support while nearly maximizing the ordinary likelihood. It costs a small random perturbation of the likelihood and the same convex optimization machinery as the standard NPMLE, with Hellinger risk parametric up to logarithmic factors. It can fail in that the sparsity bound is asymptotic and probabilistic, the analysis is specific to Gaussian location mixtures, and the numerical evidence is illustrative rather than benchmarked on production workloads.

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