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Many efforts have been dedicated to deriving score functions based on logits, distances, or rigorous data distribution assumptions to identify low-scoring OOD samples. Nevertheless, these estimate scores may fail to accurately reflect the true data density or impose impractical constraints. To provide a unified perspective on density-based score design, we propose a novel theoretical framework grounded in Bregman divergence, which extends distribution considerations to encompass an exponential family of distributions. Leveraging the conjugation constraint revealed in our theorem, we introduce a \\textsc{ConjNorm} method, reframing density function design as a search for the optimal norm coefficient $p$ against the given dataset. In light of the computational challenges of normalization, we devise an unbiased and analytical","title":"ConjNorm: Tractable Density Estimation for Out-of-Distribution Detection","url":"https://arxiv.org/abs/2402.17888","vendor":"arxiv_cs_ai"},"summary":"arXiv:2402.17888v5 Announce Type: replace-cross \nAbstract: Post-hoc out-of-distribution (OOD) detection has garnered intensive attention in reliable machine learning. Many efforts have been dedicated to deriving score functions based on logits, distances, or rigorous data distribution assumptions to identify low-scoring OOD samples. Nevertheless, these estimate scores may fail to accurately reflect the true data density or impose impractical constraints. To provide a unified perspective on density-based score design, we propose a novel theoretical framework grounded in Bregman divergence, which extends distribution considerations to encompass an exponential family of distributions. Leveraging the conjugation constraint revealed in our theorem, we introduce a \\textsc{ConjNorm} method, reframing density function design as a search for the optimal norm coefficient $p$ against the given dataset. 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