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 [1].
Optimal Transport for Stationary Markov Chains via Policy Iteration
Authors: Kevin O'Connor, Kevin McGoff, Andrew B. Nobel
JMLR 2022 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We validate our theoretical results empirically through a simulation study, demonstrating that the approximate algorithm exhibits faster overall runtime with low error. Finally, we extend the setting and application of our methods to hidden Markov models, and illustrate the potential use of the proposed algorithms in practice with an application to computer-generated music. |
| Researcher Affiliation | Academia | Kevin O Connor EMAIL Department of Statistics and Operations Research University of North Carolina, Chapel Hill Chapel Hill, NC 27599, USA; Kevin Mc Goff EMAIL Department of Mathematics and Statistics University of North Carolina, Charlotte Charlotte, NC 28223, USA; Andrew B. Nobel EMAIL Department of Statistics and Operations Research University of North Carolina, Chapel Hill Chapel Hill, NC 27599, USA |
| Pseudocode | Yes | Algorithm 1: Exact OTC; Algorithm 1a: Exact TCE; Algorithm 1b: Exact TCI; Algorithm 2: Entropic OTC; Algorithm 2a: Approx TCE; Algorithm 2b: Entropic TCI; Algorithm 3: Approx OT; Algorithm 4: Sinkhorn; Algorithm 5: Round |
| Open Source Code | Yes | Matlab implementations of Exact OTC and Entropic OTC as well as code for reproducing the experimental results to follow are available at https://github.com/oconnor-kevin/OTC. For Approx OT and related OT algorithms, we used the implementation found at https://github.com/JasonAltschuler/OptimalTransportNIPS17. |
| Open Datasets | Yes | We analyzed a data set of 36 pieces of classical music from 3 different classical composers (Bach, Beethoven and Mozart) downloaded from https://www.mfiles.co.uk/classical-midi.htm. |
| Dataset Splits | No | The paper describes generating synthetic data for a simulation study and using a dataset of computer-generated music, but it does not specify explicit training/test/validation splits for these datasets. For the music application, it mentions HMMs were 'trained' but not how the data was split for this training. |
| Hardware Specification | No | The paper mentions 'matrices in the computing environment to exceed the available memory on the machine we were using' but does not provide any specific hardware details such as GPU/CPU models or memory size. |
| Software Dependencies | No | The paper states 'Matlab implementations of Exact OTC and Entropic OTC' but does not provide specific version numbers for Matlab or any other key software libraries or dependencies used in the implementations. |
| Experiment Setup | Yes | In all runs of Entropic OTC, we choose L and T adaptively as described in Remark 10 with tolerance (ε) equal to 10 12 and upper bounds of 100 and 1000, respectively. For each choice of ξ {75, 100, 200}, we use 50, 100, and 200 Sinkhorn iterations, respectively. ... when running Entropic OTC, we use L = 100, T = 1000, ξ = 50, and 20 Sinkhorn iterations. |