Optimal transport mapping via input convex neural networks
Authors: Ashok Makkuva, Amirhossein Taghvaei, Sewoong Oh, Jason Lee
ICML 2020 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Numerical experiments confirm the accuracy of the learned transport map. In this section, first we qualitatively illustrate our proposed approach (see Figure 3) on the following two-dimensional synthetic datasets: (a) Checkerboard, (b) Mixture of eight Gaussians. |
| Researcher Affiliation | Academia | 1Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign. 2Department of Mechanical and Aerospace Engineering, University of California, Irvine. 3Department of Electrical Engineering, Princeton University, 4Allen School of Computer Science & Engineering, University of Washington. |
| Pseudocode | Yes | Algorithm 1 The numerical procedure to solve the optimization problem (9). |
| Open Source Code | Yes | Source code is available at https://github.com/AmirTag/OT-ICNN. |
| Open Datasets | Yes | We consider the standard MNIST dataset (Le Cun et al., 1998) with the goal of learning the optimal transport map from the set of images corresponding to first five digits {0, 1, 2, 3, 4} to the last five digits {5, 6, 7, 8, 9}. |
| Dataset Splits | No | The paper describes generating samples from source (Q) and target (P) distributions or using full datasets like MNIST by selecting specific digits as source/target. It does not provide explicit numerical training, validation, or test split percentages or counts for reproducibility in the conventional sense, nor does it refer to specific predefined splits in their context of use. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., GPU/CPU models, memory) used for running the experiments. |
| Software Dependencies | No | The paper mentions using 'Adam (Kingma & Ba, 2014)' as an optimizer but does not provide specific version numbers for any software libraries or dependencies used in the implementation. |
| Experiment Setup | Yes | Input: Source dist. Q, Target dist. P, Batch size M, Generator iterations K, Total iterations T for t = 1, . . . , T do Sample batch {Xi}M i=1 P for k = 1, . . . , K do Sample batch {Yi}M i=1 Q Update θg to minimize (9) using Adam method end for Update θf to maximize (9) using Adam method Projection: w max(w, 0), for all w {W l} θf end for and We utilize our minimax formulation in (6) to learn the optimal transport map. We parametrize the convex functions f and g using the same ICNN architecture (Figure 2). ... we relax this constraint for g ... and instead introduce a regularization term R(θg) = λ X Wl θg max( Wl, 0) 2 F , (8) |