Learning Elastic Costs to Shape Monge Displacements
Authors: Michal Klein, Aram-Alexandre Pooladian, Pierre Ablin, Eugene Ndiaye, Jonathan Niles-Weed, Marco Cuturi
NeurIPS 2024 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We illustrate the soundness of our procedure on synthetic data, generated using our first contribution, in which we show near-perfect recovery of A s subspace using only samples. We demonstrate the applicability of this method by showing predictive improvements on single-cell data tasks. |
| Researcher Affiliation | Collaboration | Michal Klein Apple EMAIL Aram-Alexandre Pooladian NYU EMAIL Pierre Ablin Apple EMAIL Eugène Ndiaye Apple EMAIL Jonathan Niles-Weed NYU EMAIL Marco Cuturi Apple EMAIL |
| Pseudocode | Yes | Algorithm 1 MBO-ESTIMATOR(X, Y; γ, τ, ε) ... Algorithm 2 GROUND-TRUTH OT MAP T h g ... Algorithm 3 RECOVER-THETA: (X, Y; γ, θ0) |
| Open Source Code | No | We will release the entire codebase for experiments in coming weeks, as python notebooks/tutorials. |
| Open Datasets | Yes | using single-cell RNA sequencing data from [Srivatsan et al., 2020]. |
| Dataset Splits | Yes | We then use 80% train/20% test folds to benchmark two MBO estimators |
| Hardware Specification | No | Although no claim is made in terms of compute performance, the fairly small scale of the experiments allows to execute these runs on a single GPU. |
| Software Dependencies | No | In practice, we use the JAXOPT [Blondel et al., 2021] library to run proximal gradient descent. ... Our code implements a parameterized Reg TICost class, added to OTT-JAX [Cuturi et al., 2022]. ... We plot the Sinkhorn divergence (cf. Feydy et al. [2019]) for the ℓ2 2 cost for reference (see the documentation in OTT-JAX [Cuturi et al., 2022]). |
| Experiment Setup | Yes | We report performance after 1000 iterations of Riemannian gradient descent, with a step-size η of 0.1/ i + 1 at iteration i. |