Learning to Embed Distributions via Maximum Kernel Entropy

Empirical data can often be considered as samples from a set of probability distributions. Kernel methods have emerged as a natural approach for learning to classify these distributions. Although numerous kernels between distributions have been proposed, applying kernel methods to distribution regression tasks remains challenging, primarily because selecting a suitable kernel is not straightforward. Surprisingly, the question of learning a data-dependent distribution kernel has received little attention. In this paper, we propose a novel objective for the unsupervised learning of data-dependent distribution kernel, based on the principle of entropy maximization in the space of probability measure embeddings. We examine the theoretical properties of the latent embedding space induced by our objective, demonstrating that its geometric structure is well-suited for solving downstream discriminative tasks. Finally, we demonstrate the performance of the learned kernel across different modalities.

SKADA-Bench: Benchmarking Unsupervised Domain Adaptation Methods with Realistic Validation

Unsupervised Domain Adaptation (DA) consists of adapting a model trained on a labeled source domain to perform well on an unlabeled target domain with some data distribution shift. While many methods have been proposed in the literature, fair and realistic evaluation remains an open question, particularly due to methodological difficulties in selecting hyperparameters in the unsupervised setting. With SKADA-Bench, we propose a framework to evaluate DA methods and present a fair evaluation of existing shallow algorithms, including reweighting, mapping, and subspace alignment. Realistic hyperparameter selection is performed with nested cross-validation and various unsupervised model selection scores, on both simulated datasets with controlled shifts and real-world datasets across diverse modalities, such as images, text, biomedical, and tabular data with specific feature extraction. Our benchmark highlights the importance of realistic validation and provides practical guidance for real-life applications, with key insights into the choice and impact of model selection approaches. SKADA-Bench is open-source, reproducible, and can be easily extended with novel DA methods, datasets, and model selection criteria without requiring re-evaluating competitors. SKADA-Bench is available on GitHub at https://github.com/scikit-adaptation/skada-bench.