Wasserstein Task Embedding for Measuring Task Similarities
- URL: http://arxiv.org/abs/2208.11726v1
- Date: Wed, 24 Aug 2022 18:11:04 GMT
- Title: Wasserstein Task Embedding for Measuring Task Similarities
- Authors: Xinran Liu, Yikun Bai, Yuzhe Lu, Andrea Soltoggio, Soheil Kolouri
- Abstract summary: Measuring similarities between different tasks is critical in a broad spectrum of machine learning problems.
We leverage the optimal transport theory and define a novel task embedding for supervised classification.
We show that the proposed embedding leads to a significantly faster comparison of tasks compared to related approaches.
- Score: 14.095478018850374
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Measuring similarities between different tasks is critical in a broad
spectrum of machine learning problems, including transfer, multi-task,
continual, and meta-learning. Most current approaches to measuring task
similarities are architecture-dependent: 1) relying on pre-trained models, or
2) training networks on tasks and using forward transfer as a proxy for task
similarity. In this paper, we leverage the optimal transport theory and define
a novel task embedding for supervised classification that is model-agnostic,
training-free, and capable of handling (partially) disjoint label sets. In
short, given a dataset with ground-truth labels, we perform a label embedding
through multi-dimensional scaling and concatenate dataset samples with their
corresponding label embeddings. Then, we define the distance between two
datasets as the 2-Wasserstein distance between their updated samples. Lastly,
we leverage the 2-Wasserstein embedding framework to embed tasks into a vector
space in which the Euclidean distance between the embedded points approximates
the proposed 2-Wasserstein distance between tasks. We show that the proposed
embedding leads to a significantly faster comparison of tasks compared to
related approaches like the Optimal Transport Dataset Distance (OTDD).
Furthermore, we demonstrate the effectiveness of our proposed embedding through
various numerical experiments and show statistically significant correlations
between our proposed distance and the forward and backward transfer between
tasks.
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