Tree-AMP: Compositional Inference with Tree Approximate Message Passing
Authors: Antoine Baker, Florent Krzakala, Benjamin Aubin, Lenka Zdeborová
JMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We introduce Tree-AMP, standing for Tree Approximate Message Passing, a python package for compositional inference in high-dimensional tree-structured models. ... In Section 4, we illustrate the package on a few examples. ... We compare the Tree-AMP performance on this inference task to the Bayes optimal theoretical prediction from (Barbier et al., 2019) to two state of the art algorithms for this task: Hamiltonian Monte-Carlo from the Py MC3 package (Salvatier et al., 2016) and Lasso (L1-regularized linear regression) from the Scikit-Learn package (Pedregosa et al., 2011). |
| Researcher Affiliation | Academia | Antoine Baker EMAIL Florent Krzakala EMAIL Laboratoire de Physique CNRS, Ecole Normale Sup erieure, PSL University Paris, France Benjamin Aubin EMAIL Lenka Zdeborov a EMAIL Institut de Physique Th eorique CNRS, CEA, Universit e Paris-Saclay Saclay, France |
| Pseudocode | Yes | Algorithm 1: Generic Tree-AMP algorithm; Algorithm 2: Expectation propagation in Tree-AMP (Gaussian beliefs); Algorithm 3: Tree-AMP algorithm for the teacher prior second moments; Algorithm 4: Tree-AMP State evolution (replica symmetric mismatched setting); Algorithm 5: Tree-AMP State evolution (Bayes-optimal setting) |
| Open Source Code | Yes | The source code is publicly available at https://github.com/sphinxteam/tramp and the documentation at https://sphinxteam.github.io/tramp.docs. |
| Open Datasets | Yes | Let us consider a signal x RN (with N = 784) drawn from the MNIST data set. We want to reconstruct the original image from a corrupted observation y = ϕ(x) RN |
| Dataset Splits | Yes | The above experiments have been performed with parameters (N, ρ, ) = (1000, 0.05, 0.01) and have been averaged over 100 samples. ... (upper) sparse DFT denoising with (N, ρ, ) = (100, 0.02, 0.1) and (lower) sparse gradient denoising with (N, ρ, ) = (400, 0.04, 0.01). ... (right-upper) Band-inpainting ϕinp,Iband α with α = 0.3 (right-lower) Uniforminpainting ϕinp,Iuni α with α = 0.5. ... MSE averaged over 25 instances of EP match perfectly the MSE predicted by SE. |
| Hardware Specification | No | The paper does not provide specific details about the hardware used for the experiments. |
| Software Dependencies | No | We compare the Tree-AMP performance on this inference task to the Bayes optimal theoretical prediction from (Barbier et al., 2019) to two state of the art algorithms for this task: Hamiltonian Monte-Carlo from the Py MC3 package (Salvatier et al., 2016) and Lasso (L1-regularized linear regression) from the Scikit-Learn package (Pedregosa et al., 2011). ... The Keras-VAE architecture is summarized in Figure 8 and the training procedure on the MNIST data set follows closely the canonical one detailed in (Keras-VAE). |
| Experiment Setup | Yes | The above experiments have been performed with parameters (N, ρ, ) = (1000, 0.05, 0.01) and have been averaged over 100 samples. ... ep.iterate(max_iter =200) ... (with ns = 1000 distribution samples and NUTS sampler) and Lasso (green) from Scikit-Learn (with the optimal regularization parameter obtained beforehand by simulation). ... (N, ρ, ) = (100, 0.02, 0.1) and (N, ρ, ) = (400, 0.04, 0.01). ... se.iterate(max_iter =200) |