Minimax Distribution Estimation in Wasserstein Distance
This provides theoretical foundations for distribution estimation in machine learning and statistics, though it appears incremental as it builds on existing minimax framework.
This paper tackles the problem of estimating probability distributions under Wasserstein distance loss by providing statistical minimax upper and lower bounds, using only metric properties like covering/packing numbers and weak moment assumptions.
The Wasserstein metric is an important measure of distance between probability distributions, with applications in machine learning, statistics, probability theory, and data analysis. This paper provides upper and lower bounds on statistical minimax rates for the problem of estimating a probability distribution under Wasserstein loss, using only metric properties, such as covering and packing numbers, of the sample space, and weak moment assumptions on the probability distributions.