The multimarginal optimal transport formulation of adversarial multiclass classification
Authors: Nicolás García Trillos, Matt Jacobs, Jakwang Kim
JMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Examples with synthetic and real data illustrate our results. Keywords: Adversarial learning, Multiclass classification, Optimal transport, Multimarginal optimal transport, Wasserstein barycenter, Generalized barycenter problem |
| Researcher Affiliation | Academia | Nicol as Garc ıa Trillos EMAIL Jakwang Kim EMAIL Department of Statistics University of Wisconsin-Madison 1300 University Avenue, Madison, Wisconsin 53706, USA Matt Jacobs EMAIL Department of Mathematics Purdue University 150 N University St, West Lafayette, Indiana 47907, USA |
| Pseudocode | No | The paper describes mathematical formulations and theoretical equivalences but does not contain any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain any explicit statements about the release of source code for the methodology described, nor does it provide a link to a code repository. It mentions using 'MOT Sinkhorn algorithm' from another work, not providing their own. |
| Open Datasets | Yes | Our numerical results for a subsample of MNIST and CIFAR 10, shown in Figure 6, are obtained using the algorithm discussed in Lin, Ho, Cuturi, and Jordan (2019), also known as MOT Sinkhorn algorithm; see subsection 5.3 for more details. |
| Dataset Splits | No | The paper mentions using 'samples belonging to one of four possible classes' from MNIST and CIFAR 10, but it does not specify any exact training/test/validation splits, proportions, or methodologies for these datasets. |
| Hardware Specification | No | The paper describes numerical experiments but does not provide any specific details about the hardware (e.g., CPU, GPU models, memory) used for running these experiments. |
| Software Dependencies | No | The paper mentions using the 'Sinkhorn algorithm' and 'MOT Sinkhorn algorithm' but does not specify any particular software names with version numbers for their implementation (e.g., Python, PyTorch, TensorFlow, or specific library versions). |
| Experiment Setup | Yes | We emphasize that Figure 6 only provides approximations of the true adversarial risk R µ. Indeed, recall that R µ = 1 B µ. Approximating B µ using the MOT Sinkhorn algorithm will always produce an upper bound for B µ since the regularization term effectively restricts the solution space of (2). Thus, the multimarginal Sinkhorn algorithm always yields a lower bound for the true R µ. Of course, one can always compute a tighter lower bound by reducing the regularization parameter η at the expense of increasing the computational burden. As way of conclusion for this section we provide pointers to the literature discussing the computational complexity of the Wasserstein barycenter problem; Wasserstein barycenter problems are specific instances in the MOT family. On the one hand, Altschuler and Boix-Adser a (2022) prove certain computational hardness of the barycenter problem in the dimension of the feature space (here X). On the other hand, Altschuler and Boix Adsera (2021) present an algorithm that can get an approximate solution of the optimal barycenter in polynomial time for a fixed dimension of the feature space. While our MOT is not the standard barycenter problem, it is still a generalized version thereof, and thus, it is reasonable to expect that the structure of our problem can be used in the design of algorithms that perform better than off-the-shelf MOT solvers. We leave this task for future work. |