Geometrical Insights for Unsupervised Learning

After arguing that choosing the right probability distance is critical for achieving the elusive goals of unsupervised learning, we compare the geometric properties of the two currently most promising distances: (1) the earth-mover distance, and (2) the energy distance, also known as maximum mean discrepancy. These insights allow us to give a fresh viewpoint on reported experimental results and to risk a couple predictions. Joint work with Leon Bottou, Martin Arjovsky, David Lopez-Paz, and Maxime Oquab.