Explore the intersection of statistics and computer science in machine learning through this 42-minute conference talk by Jean-Philippe Vert from Google Brain. Delve into innovative approaches for embedding permutations and relaxing ranking operators to integrate them into differentiable machine learning architectures. Discover how to analyze and predict preferences using continuous space representations of discrete combinatorial objects. Examine the SUQUAN and Kendall embeddings, optimal transport techniques, and applications such as soft top-k loss and learning to sort. Gain insights into the cross-fertilization between statistics and computer science in the era of Big Data, and understand the algorithmic paradigms underpinning modern machine learning.