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Non-negative matrix factorization (NMF) is a singular statistical model whose Bayesian asymptotics are governed by the real log canonical threshold (RLCT).
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Non-negative matrix factorization (NMF) is a singular statistical model whose Bayesian asymptotics are governed by the real log canonical threshold (RLCT). We study the local geometry of the factorization map and derive an upper bound for the RLCT of NMF. Let $H$ be the model inner dimension and $H_0$ the non-negative rank of the true $M\times N$ matrix. Assuming that the true matrix admits a strictly positive factorization of inner dimension $H_0$ in the interior of the parameter domain, we prove, for smooth positive priors, that $λ\leq \{(H-H_0)\min(M,N)+H_0(M+N-H_0)\}/2$. This bound strictl...
Discovered via ArXiv
Research papers and preprints from arXiv.
Publisher: arxiv.org
ID: http://arxiv.org/abs/2609.34043v1 · Indexed 42 minutes ago