RIKEN Center for Advanced Intelligence Project

Optimal transport supports clustering, dictionary learning and domain adaptation, but high-dimensional data often force projections that discard information. Charles Bouveyron develops an alternative for Gaussian distributions with parsimonious covariance structure and low intrinsic dimension. A low-dimensional decomposition of empirical covariance matrices gives an efficient, robust closed form for the 2-Wasserstein distance without projecting the data. An explicit Monge map uses exact covariance square roots and inverse square roots. Numerical comparisons demonstrate analytical and computational benefits, including competitiveness with model-free approaches for non-Gaussian data and applications to unsupervised domain adaptation for classification.

How can learning systems recommend actions that prevent an undesirable predicted outcome? Rehearsal learning approaches this problem through influence relations, but existing parametric assumptions can limit its use in complex systems. This talk presents a non-parametric method based on conditional mean embeddings. It expresses the objective in a reproducing kernel Hilbert space, replaces a discontinuous desirability indicator with a smooth Probit surrogate, and uses nested kernel ridge regression to estimate outcome distributions conditional on actions. The resulting estimator can be identified from observational data and has finite-sample error bounds and consistency guarantees. Synthetic and semi-synthetic experiments assess its effectiveness and flexibility.