Minimax estimation of discontinuous optimal transport maps: The semi-discrete case
Authors: Aram-Alexandre Pooladian, Vincent Divol, Jonathan Niles-Weed
ICML 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We confirm these results in numerical experiments, and provide experiments for other settings, not covered by our theory, which indicate that the entropic estimator is a promising methodology for other discontinuous transport map estimation problems. |
| Researcher Affiliation | Academia | 1Center for Data Science, New York University, NY, USA 2CEREMADE, Universit e Paris Dauphine-PSL, Paris, France 3Courant Institute of Mathematical Sciences, New York University, NY, USA. |
| Pseudocode | No | The paper does not contain any pseudocode or clearly labeled algorithm blocks. |
| Open Source Code | No | The paper does not provide an explicit statement or link for the open-sourcing of the code for its methodology. |
| Open Datasets | No | The paper uses synthetic data generated by the authors for their experiments, as stated in Section 4.3: "To create the following plots, we draw two sets of n i.i.d. points from P, (X1, . . . , Xn) and (X 1, . . . , X n), and create target points Yi = T0(X i), where T0 is known to us in advance in order to generate the data." It does not refer to a publicly available or open dataset. |
| Dataset Splits | No | The paper does not explicitly provide training/validation/test dataset splits. It describes generating synthetic data for evaluation, but without specifying partitioning ratios. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware used to run its experiments (e.g., GPU/CPU models, memory). |
| Software Dependencies | No | The paper does not list specific software dependencies with version numbers (e.g., library names with versions). |
| Experiment Setup | Yes | To create the following plots, we draw two sets of n i.i.d. points from P, (X1, . . . , Xn) and (X 1, . . . , X n), and create target points Yi = T0(X i), where T0 is known to us in advance in order to generate the data. Our estimators are computed on the data (X1, . . . , Xn) and (Y1, . . . , Yn), and we evaluate the Mean-Squared error criterion MSE( ˆT) = ˆT T0 2 L2(P ) of a given map estimator ˆT using Monte Carlo integration, using 50000 newly sampled points from P. We plot the means across 10 repeated trials, accompanied by their standard deviations. First consider P = Unif([0, 1]d) and create atoms {y1, . . . , y J} by partitioning the points along the first coordinate for all j [J]: (yj)[1] = (j 1/2)/J , (yj)[2] = = (yj)[d] = 0.5 . We choose uniform qj = 1/J for j [J]. |