Learning to be Bayesian without Supervision

By Martin Raphan, Eero P. Simoncelli. 2006

74 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability, Probabilistic & Bayesian Methods

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Citations in the corpus

Generative Modeling by Estimating Gradients of the Data Distribution (2019, methodology): “The method of denoising score matching can also be derived from the perspective of Bayes least squares [43, 44], using techniques of Stein’s Unbiased Risk Estimator [35, 56].”
Interpretation and Generalization of Score Matching (2009, background): “In [ RS07 ], score matching was interpreted as searching parameters of q so that when a Bayes least square estimator is constructed based on it, the overall mean square error with the optimal estimator based on p(~x) is minimal (see Section 4 for more details).”
On Maximum Likelihood Training of Score-Based Generative Models (2021, methodology): “(1) so that samples from p t p x q are available in closed form, and using techniques like Denoising Score Matching [Vincent, 2011; Raphan and Simoncelli, 2007, 2011] or Sliced Score Matching [Song et al., 2019] to sidestep the need for explicit ground-truth scores.”
SDEdit: Image Synthesis and Editing with Stochastic Differential Equations (2021, background): “The training objective for s θ ( x , t ) is a mixture of de-noising score matching losses [58, 44, 43] over randomly sampled time steps.”
How to Train Your Energy-Based Models (2021, background): “Similar formulations are also explored by Raphan and Simoncelli (2007, 2011) and can be traced back to Tweedie’s formula (1956) and Stein’s Unbiased Risk Estimation (Stein, 1981).”
The SURE-LET Approach to Image Denoising (2007, result): “Similarly to what was observed empirically in other settings [5], [17], adding more thresholding functions only bring marginal ( 0.”
Image Denoising in Mixed Poisson–Gaussian Noise (2011, methodology): “Similarly to what has been proposed for SURE-based denoising [2], [3], [33], [37], we describe the denoising function as the linear expansion of thresholds (LET) defined as”
Least Squares Estimation Without Priors or Supervision (2011, methodology): “, 2008), as well as linear families of estimators (Pesquet and Leporini, 1997; Luisier et al., 2006; Raphan and Simoncelli, 2007b; Blu and Luisier, 2007; Raphan and Simoncelli, 2008), which we discuss in Sec.”
Diffusion Models: A Comprehensive Survey of Methods and Applications (2022, methodology): “, score estimate) has established techniques such as score matching [101], denoising score matching [188, 189, 238], and sliced score matching [222], so we can directly employ one of them to train our noise-conditional score networks from perturbed data points.”