Subspace Detours: Building Transport Plans that are Optimal on Subspace Projections
Authors: Boris Muzellec, Marco Cuturi
NeurIPS 2019 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We consider applications to semantic mediation between elliptic word embeddings and domain adaptation with Gaussian mixture models. In section 6 we showcase the behavior of MK and MI transports on (noisy) synthetic data, show how using a mediating subspace can be applied to selecting meanings for polysemous elliptical word embeddings, and experiment using MK maps with the minimizing algorithm on a domain adaptation task with Gaussian mixture models. |
| Researcher Affiliation | Collaboration | Boris Muzellec CREST, ENSAE boris.muzellec@ensae.fr Marco Cuturi Google Brain and CREST, ENSAE cuturi@google.com |
| Pseudocode | Yes | Algorithm 1 MK Subspace Selection |
| Open Source Code | No | The paper does not provide a statement or link to open-source code for the described methodology. |
| Open Datasets | Yes | We use the Office Home dataset [31], which comprises 15000 images from 65 different classes across 4 domains: Art, Clipart, Product and Real World. |
| Dataset Splits | No | The paper does not explicitly provide specific training/validation/test splits, percentages, or absolute sample counts for data partitioning. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., CPU/GPU models, memory) used for running experiments. |
| Software Dependencies | No | The paper does not list specific software dependencies with version numbers. |
| Experiment Setup | Yes | First, a k-means quantization of both images is computed. Then, the colors of the pixels within each source cluster are modified according to the optimal transport map between both color distributions. We compare this approach with classic full OT maps and a sliced OT approach (with 100 random projections). We represent the source as a GMM by fitting one Gaussian per source class and defining mixture weights proportional to class frequencies, and we fit a GMM with the same number of components on the target. We use Algorithm 1 between the empirical covariance matrices of the source and target datasets to select the supporting subspace E, for different values of the supporting dimension k (Figure 7). |