Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
MAP Estimation with Denoisers: Convergence Rates and Guarantees
Authors: Scott Pesme, Giacomo Meanti, Michael Arbel, Julien Mairal
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this work, we revisit denoising-based iterative schemes from a theoretical perspective, focusing on the case where the negative log-density p is log-concave and potentially ill-conditioned. ... Our analysis thus provides a theoretical foundation for a class of empirically successful but previously heuristic methods. ... The proof of convergence with explicit rates of the MMSE Averaging iterates towards the proximal operator, while conceptually intuitive, requires a careful blend of inexact optimisation analysis and tools from partial differential equations most notably the heat equation to control how the minimiser of the smoothed objective Fσ evolves with the noise level. |
| Researcher Affiliation | Academia | Scott Pesme Giacomo Meanti Michael Arbel Julien Mairal Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, LJK EMAIL |
| Pseudocode | Yes | Algorithm 1 Approximate Proximal Gradient Descent (Approx PGD) Require: Noisy image y, step size τ > 0, parameter λ > 0, number of inner steps (kn)n 1 Initialise: ˆx(0) y for n = 0, 1, 2, . . . do 1. Data fidelity gradient descent step z(n+1) 0 ˆx(n) τλ f(ˆx(n)) 2. Approximate proximal step ˆx(n+1) prox τ ln p(z(n+1) 0 ) for k = 0, . . . , kn+1 1 do τ k+1 αk 1 k+2 z(n+1) k+1 (1 αk)MMSEσk(z(n+1) k ) + αkz(n+1) 0 end for ˆx(n+1) z(n+1) kn+1 end for |
| Open Source Code | Yes | Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material? Answer: [Yes] Justification: code is provided in the supplementary material and will be publicly released after publication. |
| Open Datasets | No | The paper does not conduct experiments on external, publicly available datasets. The 'Numerical Visualisations' section uses a simple, toy 2D Gaussian prior for illustration purposes only, which is a synthetic setup and not an open dataset. |
| Dataset Splits | No | The paper does not use any specific datasets that require training, testing, or validation splits. The 'Numerical Visualisations' section employs a toy 2D Gaussian prior for illustrative purposes, which does not involve data splitting. |
| Hardware Specification | No | Question: For each experiment, does the paper provide sufficient information on the computer resources (type of compute workers, memory, time of execution) needed to reproduce the experiments? Answer: [No] Justification: the experiments are small and run on a personal laptop. |
| Software Dependencies | No | The paper does not explicitly mention any specific software dependencies or version numbers (e.g., Python, PyTorch, TensorFlow, or specific solvers). |
| Experiment Setup | Yes | The MMSE Averaging iterates with parameters αk = 1/(k + 2), σ2 k = τ/(k + 1) and initialised at x0 = y satisfy... (Theorem 1) ... For τ 1 λLf and a number of steps in the inner loop which increases as kn = c n1+η for c, η > 0, under Assumptions 1 to 3 the approximate proximal gradient descent iterates (ˆx(n))n from Algorithm 1... (Theorem 2) |