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 Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Estimation of Stochastic Optimal Transport Maps
Authors: Sloan Nietert, Ziv Goldfeld
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Empirical experiments are provided which validate our theory and demonstrate the utility of the proposed framework in settings where existing theory fails. These contributions constitute the first general-purpose theory for map estimation, compatible with a wide spectrum of real-world applications where optimal transport may be intrinsically stochastic. |
| Researcher Affiliation | Academia | Sloan Nietert EPFL EMAIL Ziv Goldfeld Cornell University EMAIL |
| Pseudocode | Yes | Algorithm 1: Randomized Rounding for Efficient OT Kernel Estimation |
| Open Source Code | Yes | All code needed to reproduce our experiments and figures is available at https://github.com/ sbnietert/map-estimation. |
| Open Datasets | Yes | To empirically validate our theory, we run experiments in two synthetic settings with OT maps whose irregularities limit the utility of the Lp objective and prevent application of existing theory. For Setting A, we fix µ and ν as uniform discrete measures over N = 2000 points, obtained as i.i.d. samples from Unif({0} [0, 1]d 1) and 1 2 Unif({ 1} [0, 1]d 1) + 1 2 Unif({1} [0, 1]d 1), respectively. In the N limit, the optimal kernel satisfies κ (0,x2:d) = Unif({( 1, x2:d), (1, x2:d)}). For our discrete µ and ν, there is an optimal deterministic map T induced by a permutation, but it is highly oscillatory. For Setting B, we set µ and ν as discrete distributions over N samples from Unif([ 1, 1]d) and f Unif([ 1, 1]d), respectively, where f(x) = x + (sign(x1), . . . , sign(xd)) pushes each orthant of the cube away from the origin. |
| Dataset Splits | No | The paper uses synthetic data which are generated as i.i.d. samples for each experiment run, rather than using predefined dataset splits. "Now, for each setting and sample size n {10, 20, . . . , 100}, we take n i.i.d. samples from µ and ν and compute the p = 1 nearest-neighbor map estimate ˆT NN n [Manole et al., 2024] and the rounding kernel estimate ˆκround n (Section 3)." |
| Hardware Specification | Yes | We note that all experiments were performed on an M1 Mac Book Air with 16GB RAM and 8 CPU cores. |
| Software Dependencies | No | The paper mentions the use of a "Python Optimal Transport solver [Flamary et al., 2021]" but does not specify a version number for this solver or any other software dependencies. |
| Experiment Setup | Yes | For Setting A, we fix µ and ν as uniform discrete measures over N = 2000 points, obtained as i.i.d. samples from Unif({0} [0, 1]d 1) and 1 2 Unif({ 1} [0, 1]d 1) + 1 2 Unif({1} [0, 1]d 1), respectively. ... Repeating this process for K = 100 iterations, we compute mean errors for each sample size and dimension d {3, 5, 10}, along with bootstrapped 10% and 90% quantiles (via 1000 bootstrap resamples). In Figure 3 (left), we compare the E1 vs L1 performance of the NN estimator under Setting A (where the latter is well-defined since each ˆT NN n is a deterministic map). As expected, L1 performance is quite poor, with error always greater than 1. Although we currently lack formal guarantees for the NN estimator (and our setting lies outside of existing theory), it achieves strong E1 performance, with faster rates in lower dimensions. In Figure 3 (center), we compare the NN and rounding estimators under E1, the latter enjoying formal guarantees by Theorem 2. Empirically, the NN estimator performs better, but this gap diminishes in high dimensions. We suspect that low-dimensional performance of the rounding estimator is more sensitive to its side-length hyperparameter, which we have simply set to n 1/(d+2) as per the proof of Theorem 2. |