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.