The Monge Gap: A Regularizer to Learn All Transport Maps
Authors: Théo Uscidda, Marco Cuturi
ICML 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We evaluate the ability of our method to recover OT maps between both synthetic ( 6.2,6.3) and real ( 6.4) datasets. |
| Researcher Affiliation | Collaboration | 1CREST, ENSAE 2Apple. Correspondence to: Th eo Uscidda <theo.uscidda@ensae.fr>, Marco Cuturi <cuturi@apple.com>. |
| Pseudocode | Yes | Algorithm 1 The vanilla-MLP+Mc ρ method for OT map estimation with generic costs. ... Algorithm 2 The struct-MLP+Mc ρ + Cρ method for OT map estimation with strictly convex costs. |
| Open Source Code | Yes | The monge gap, along with a Map Estimator to estimate OT maps, are implemented in the OTT-JAX (Cuturi et al., 2022) package.1 ... 1https://github.com/ott-jax/ott |
| Open Datasets | Yes | We use the ICNN based Korotin et al. (2021) s benchmark ... proteomic dataset used in (Bunne et al., 2021), consisting of two melanoma cell lines. Patient data is analyzed using (i) 4i (Gut et al., 2018), and sc RNA sequencing (Tang et al., 2009). |
| Dataset Splits | No | For each dataset, we perform a 60%-40% train-test split on both conrol and treated cells, and evaluate the models on the 40% of unseen control and treated cells. The paper does not explicitly mention a separate validation split. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., exact GPU/CPU models, processor types, or memory amounts) used for running its experiments. |
| Software Dependencies | No | The paper mentions software like OTT-JAX, JAX framework, ADAM, and specific neural network components, but does not provide specific version numbers for these software dependencies (e.g., 'PyTorch 1.9', 'JAX 0.3.17'). |
| Experiment Setup | Yes | Entropic regularization. Whenever we run the Sinkhorn algorithm on a cost matrix C, we set ε = 0.01 mean(C). ... All MLPs are initialized with the Identity initializer and have hidden layer sizes [128, 64, 64]. They are trained with ADAM (Kingma and Ba, 2014) for Kiters = 10,000 iterations with a learning rate η = 0.01 and a batch size n = 1024. |