  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.
