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Found 10 papers, 7 papers with code
New Perspectives on Regularization and Computation in Optimal Transport-Based Distributionally Robust Optimization
We study optimal transport-based distributionally robust optimization problems where a fictitious adversary, often envisioned as nature, can choose the distribution of the uncertain problem parameters by reshaping a prescribed reference distribution at a finite transportation cost.
Discrete Optimal Transport with Independent Marginals is #P-Hard
We study the computational complexity of the optimal transport problem that evaluates the Wasserstein distance between the distributions of two K-dimensional discrete random vectors.
Semi-Discrete Optimal Transport: Hardness, Regularization and Numerical Solution
Semi-discrete optimal transport problems, which evaluate the Wasserstein distance between a discrete and a generic (possibly non-discrete) probability measure, are believed to be computationally hard.
Bridging Bayesian and Minimax Mean Square Error Estimation via Wasserstein Distributionally Robust Optimization
The proposed model can be viewed as a zero-sum game between a statistician choosing an estimator -- that is, a measurable function of the observation -- and a fictitious adversary choosing a prior -- that is, a pair of signal and noise distributions ranging over independent Wasserstein balls -- with the goal to minimize and maximize the expected squared estimation error, respectively.
Optimistic Distributionally Robust Optimization for Nonparametric Likelihood Approximation
The likelihood function is a fundamental component in Bayesian statistics.
Calculating Optimistic Likelihoods Using (Geodesically) Convex Optimization
A fundamental problem arising in many areas of machine learning is the evaluation of the likelihood of a given observation under different nominal distributions.
Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning
The goal of data-driven decision-making is to learn a decision from finitely many training samples that will perform well on unseen test samples.
Wasserstein Distributionally Robust Kalman Filtering
Despite the non-convex nature of the ambiguity set, we prove that the estimation problem is equivalent to a tractable convex program.
Regularization via Mass Transportation
The goal of regression and classification methods in supervised learning is to minimize the empirical risk, that is, the expectation of some loss function quantifying the prediction error under the empirical distribution.
Distributionally Robust Logistic Regression
This paper proposes a distributionally robust approach to logistic regression.
