Distance Measure Machines
This work addresses the challenge of efficiently learning from probability distributions for machine learning applications, offering a novel framework with practical improvements in performance and computational tractability.
The paper tackles the problem of learning with probability distributions by introducing a distance-based discriminative framework that uses dissimilarity embeddings to reference templates, proving that low-error linear decision functions can be achieved with high probability for empirical distributions. Experimental results show that Wasserstein distance embedding outperforms kernel mean embeddings and is more tractable than estimating pairwise Kullback-Leibler divergence.
This paper presents a distance-based discriminative framework for learning with probability distributions. Instead of using kernel mean embeddings or generalized radial basis kernels, we introduce embeddings based on dissimilarity of distributions to some reference distributions denoted as templates. Our framework extends the theory of similarity of Balcan et al. (2008) to the population distribution case and we show that, for some learning problems, some dissimilarity on distribution achieves low-error linear decision functions with high probability. Our key result is to prove that the theory also holds for empirical distributions. Algorithmically, the proposed approach consists in computing a mapping based on pairwise dissimilarity where learning a linear decision function is amenable. Our experimental results show that the Wasserstein distance embedding performs better than kernel mean embeddings and computing Wasserstein distance is far more tractable than estimating pairwise Kullback-Leibler divergence of empirical distributions.