Slicing Unbalanced Optimal Transport
Authors: Clément Bonet, Kimia Nadjahi, Thibault Sejourne, Kilian FATRAS, Nicolas Courty
TMLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We finally conduct an empirical analysis of our loss functions and methodology on both synthetic and real datasets, to illustrate their computational efficiency, relevance and applicability to real-world scenarios including geophysical data. |
| Researcher Affiliation | Academia | Clément Bonet EMAIL CREST, ENSAE, IP Paris, Palaiseau, France Kimia Nadjahi EMAIL CNRS, ENS, Paris, France Thibault Séjourné EMAIL LTS4, EPFL, Lausanne, Switzerland Kilian Fatras EMAIL Mila, Mc Gill University, Montreal, Canada Nicolas Courty EMAIL IRISA, Université Bretagne-Sud, Vannes, France |
| Pseudocode | Yes | Algorithm 1 Norm(α, β, f, g, ρ1, ρ2) Algorithm 2 SUOT Algorithm 3 USOT Algorithm 4 FWStep(f, g, r, s, γ) Algorithm 5 Sliced OTLoss(α, β, {θ}, p) Algorithm 6 Sliced OTPotentials Backprop(α, β, {θ}, p) Algorithm 7 Barycenter((αb)b, (ωb)b, ρ1, ρ2, lr) |
| Open Source Code | Yes | 1The code is available at https://github.com/clbonet/Slicing_Unbalanced_Optimal_Transport. |
| Open Datasets | Yes | We consider the BBCSport dataset (Kusner et al., 2015), a standard benchmark with small documents for which OT can be used effectively, and the Goodreads dataset (Maharjan et al., 2017) on two tasks (genre and likability predictions)... We use the Climate Net dataset (Prabhat et al., 2021), and more specifically the TMQ (precipitable water) indicator. The Climate Net dataset is a human-expert-labeled curated dataset which captures tropical cyclones (TCs), among other things. |
| Dataset Splits | Yes | We consider the BBCSport dataset (Kusner et al., 2015)... We average over the 5 same train/test split of (Kusner et al., 2015). The movie reviews dataset (Pang et al., 2002)... We take five different random 75/25 train/test split. This dataset, proposed in (Maharjan et al., 2017)... The five train/test split are randomly drawn with 75/25 proportions. |
| Hardware Specification | Yes | All the benchmark methods are computed using the Python OT library (Flamary et al., 2021) on a Nvidia Tesla V100 GPU. Computations have been performed with a NVIDIA Tesla V100 GPU. |
| Software Dependencies | No | The paper mentions using Python OT library, PyTorch, and Torch Vision, but does not provide specific version numbers for these software components. |
| Experiment Setup | Yes | For sliced methods, we average over 3 computations of the loss matrix and report the standard deviation in Table 1. The number of neighbors was selected via cross validation. The results for UOT, Sinkh UOT, SUOT and USOT are reported for ρ yielding the best accuracy among a grid (see Appendix C.1 for more details), and we display an ablation of this parameter on the BBCSport dataset in Figure 2. For every results, we iterate the gradient flow for 100 iterations, and the learning rate γ is set to 10 2. We run the barycenter algorithm for 500 iterations (with K = 64 projections)... |