Kyumin Choi

Jiwoo Yoon, Kyumin Choi, Jaewoong Choi

Conditional Optimal Transport (COT) problem aims to find a transport map between conditional source and target distributions while minimizing the transport cost. Recently, these transport maps have been utilized in conditional generative modeling tasks to establish efficient mappings between the distributions. However, classical COT inherits a fundamental limitation of optimal transport, i.e., sensitivity to outliers, which arises from the hard distribution matching constraints. This limitation becomes more pronounced in a conditional setting, where each conditional distribution is estimated from a limited subset of data. To address this, we introduce the Conditional Unbalanced Optimal Transport (CUOT) framework, which relaxes conditional distribution-matching constraints through Csiszár divergence penalties while strictly preserving the conditioning marginals. We establish a rigorous formulation of the CUOT problem and derive its dual and semi-dual formulations. Based on the semi-dual form, we propose Conditional Unbalanced Optimal Transport Maps (CUOTM), an outlier-robust conditional generative model built upon a triangular $c$-transform parameterization. We theoretically justify the validity of this parameterization by proving that the optimal triangular map satisfies the $c$-transform relationships. Our experiments on 2D synthetic and image-scale datasets demonstrate that CUOTM achieves superior outlier robustness and competitive distribution-matching performance compared to existing COT-based baselines, while maintaining high sampling efficiency.

Andres Ferraro, Dmitry Bogdanov, Kyumin Choi et al.

There are many offline metrics that can be used as a reference for evaluation and optimization of the performance of recommender systems. Hybrid recommendation approaches are commonly used to improve some of those metrics by combining different systems. In this work we focus on music recommendation and propose a new way to improve recommendations, with respect to a desired metric of choice, by combining multiple systems for each user individually based on their expected performance. Essentially, our approach consists in predicting an expected error that each system will produce for each user based on their previous activity. To this end, we propose to train regression models for different metrics predicting the performance of each system based on a number of features characterizing previous user behavior in the system. We then use different fusion strategies to combine recommendations generated by each system. Following this approach one can optimize the final hybrid system with respect to the desired metric of choice. As a proof of concept, we conduct experiments combining two recommendation systems, a Matrix Factorization model and a popularity-based recommender. We use the data provided by Melon, a Korean music streaming service, to train and evaluate the performance of the systems.