Energy-Tweedie links Gibbs noise denoising to Stein scores
Original title: Energy-Tweedie: Score meets Score, Energy meets Energy
The identity extends the Gaussian posterior-mean relation to kernel scoring rules and user-chosen noise paths.
The paper extends Tweedie’s formula from Gaussian noise to Gibbs, energy-based noise distributions, using the generalized Gaussian family as an example. It derives an Energy-Tweedie identity in which the path derivative of a kernel scoring rule recovers the Stein score of the noisy marginal. Consequences include score estimation from posterior samples, a criterion for unknown noise parameters, and diffusion-style sampling along chosen noise-parameter paths.
- The classical case ties Gaussian noise, posterior means, squared loss, and Tweedie’s formula.
- The new relation is stated for each noise potential in the Gibbs class.
- It supplies a score-based view of generative methods trained with scoring rules.
From the original article
1 min read at huggingface.co
Denoising and score estimation are classically linked through Tweedie's formula, which relates the posterior mean under Gaussian noise to the Stein score of the noisy marginal. In this work, we extend this perspective beyond Gaussian noise to a broad class of Gibbs (energy-based) noise distributions, with the generalized Gaussian family as an example.
By Andrej Leban · huggingface.co
A short excerpt; the article and its images belong to the publisher. Summary, key facts and assessment above are AI-written from the article and can be wrong.