Efficient Low Rank Convex Bounds for Pairwise Discrete Graphical Models

Authors: Valentin Durante, George Katsirelos, Thomas Schiex

ICML 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental Experiments show that the BCD approach compares favorably to the penalized approach and to usual linear bounds relying on convergent message passing approaches. 3. Experiments 3.2. Experiments on random instances 3.3. Experiments on a real instance
Researcher Affiliation Academia 1Universit e F ed erale de Toulouse, ANITI, INRAE, UR 875, 31326 Toulouse, France 2MIA-Paris-Math ematiques et Informatique Appliqu ees, INRAE, 75231 Paris, France.
Pseudocode No The paper describes the algorithms in detail, but it does not include formally labeled pseudocode or algorithm blocks.
Open Source Code Yes We implemented the row-by-row updates with the dualized exactly-one constraints (LR-LAS) as well as the BCD update method (LR-BCD) in C++ (code available at github.com/Val Durante/LR-BCD) with the Eigen3 (Guennebaud et al., 2010) sparse matrix library (MPL2 licence).
Open Datasets Yes This instance has been made available in the Cost Function Library, in the real/fish category.
Dataset Splits No The paper does not specify distinct training, validation, and test splits with percentages or counts for the datasets used. It describes how random instances were generated and uses a single real-world instance.
Hardware Specification Yes All experiments were run on a single thread on a server equipped with a Xeon Gold 6248R CPU@3.00GHz and 1TB of RAM running Debian Linux 4.19.98-1.
Software Dependencies Yes We implemented the row-by-row updates with the dualized exactly-one constraints (LR-LAS) as well as the BCD update method (LR-BCD) in C++ (code available at github.com/Val Durante/LR-BCD) with the Eigen3 (Guennebaud et al., 2010) sparse matrix library (MPL2 licence). We use rank r = p 2(d + 1) by default for LR-LAS and r = p 2(n + d + 1) for LR-BCD but also tried variants with fixed lower ranks. The penalty coefficient ρ is set as the sum of the maximum of all the binary and unary functions. Thus, it enforces the theoretical assumption of the Lasserre dualization result. They are compared with exact LP (local polytope) bounds and message passing MAP/MRF algorithms Min-Sum and TRW-S. The LP bounds are computed using CPLEX 20.1.0.0. We used Open-GM2 (Kappes et al., 2015), an efficient C++ MIT-licensed library, in release 3.3.7, available at https://github.com/opengm for Min-Sum (maximum number of iterations of 100, minimal message distance of 0.01 and damping of 0.8) and TRW-S (maximum number of iterations 100, 000, tolerance of 10 5, TABLE mode).
Experiment Setup Yes We use rank r = p 2(d + 1) by default for LR-LAS and r = p 2(n + d + 1) for LR-BCD but also tried variants with fixed lower ranks. The penalty coefficient ρ is set as the sum of the maximum of all the binary and unary functions. Thus, it enforces the theoretical assumption of the Lasserre dualization result. ... for Min-Sum (maximum number of iterations of 100, minimal message distance of 0.01 and damping of 0.8) and TRW-S (maximum number of iterations 100, 000, tolerance of 10 5, TABLE mode).