Wasserstein Distance Guided Representation Learning for Domain Adaptation

Domain adaptation aims at generalizing a high-performance learner on a target domain via utilizing the knowledge distilled from a source domain which has a different but related data distribution. One solution to domain adaptation is to learn domain invariant feature representations while the learned representations should also be discriminative in prediction. To learn such representations, domain adaptation frameworks usually include a domain invariant representation learning approach to measure and reduce the domain discrepancy, as well as a discriminator for classification. Inspired by Wasserstein GAN, in this paper we propose a novel approach to learn domain invariant feature representations, namely Wasserstein Distance Guided Representation Learning (WDGRL). WDGRL utilizes a neural network, denoted by the domain critic, to estimate empirical Wasserstein distance between the source and target samples and optimizes the feature extractor network to minimize the estimated Wasserstein distance in an adversarial manner. The theoretical advantages of Wasserstein distance for domain adaptation lie in its gradient property and promising generalization bound. Empirical studies on common sentiment and image classification adaptation datasets demonstrate that our proposed WDGRL outperforms the state-of-the-art domain invariant representation learning approaches.Comment: The Thirty-Second AAAI Conference on Artificial Intelligence (AAAI 2018

A Numerical Method to solve Optimal Transport Problems with Coulomb Cost

In this paper, we present a numerical method, based on iterative Bregman projections, to solve the optimal transport problem with Coulomb cost. This is related to the strong interaction limit of Density Functional Theory. The first idea is to introduce an entropic regularization of the Kantorovich formulation of the Optimal Transport problem. The regularized problem then corresponds to the projection of a vector on the intersection of the constraints with respect to the Kullback-Leibler distance. Iterative Bregman projections on each marginal constraint are explicit which enables us to approximate the optimal transport plan. We validate the numerical method against analytical test cases

Ambulance Emergency Response Optimization in Developing Countries

The lack of emergency medical transportation is viewed as the main barrier to the access of emergency medical care in low and middle-income countries (LMICs). In this paper, we present a robust optimization approach to optimize both the location and routing of emergency response vehicles, accounting for uncertainty in travel times and spatial demand characteristic of LMICs. We traveled to Dhaka, Bangladesh, the sixth largest and third most densely populated city in the world, to conduct field research resulting in the collection of two unique datasets that inform our approach. This data is leveraged to develop machine learning methodologies to estimate demand for emergency medical services in a LMIC setting and to predict the travel time between any two locations in the road network for different times of day and days of the week. We combine our robust optimization and machine learning frameworks with real data to provide an in-depth investigation into three policy-related questions. First, we demonstrate that outpost locations optimized for weekday rush hour lead to good performance for all times of day and days of the week. Second, we find that significant improvements in emergency response times can be achieved by re-locating a small number of outposts and that the performance of the current system could be replicated using only 30% of the resources. Lastly, we show that a fleet of small motorcycle-based ambulances has the potential to significantly outperform traditional ambulance vans. In particular, they are able to capture three times more demand while reducing the median response time by 42% due to increased routing flexibility offered by nimble vehicles on a larger road network. Our results provide practical insights for emergency response optimization that can be leveraged by hospital-based and private ambulance providers in Dhaka and other urban centers in LMICs

Training generative models from privatized data

Local differential privacy is a powerful method for privacy-preserving data collection. In this paper, we develop a framework for training Generative Adversarial Networks (GANs) on differentially privatized data. We show that entropic regularization of optimal transport - a popular regularization method in the literature that has often been leveraged for its computational benefits - enables the generator to learn the raw (unprivatized) data distribution even though it only has access to privatized samples. We prove that at the same time this leads to fast statistical convergence at the parametric rate. This shows that entropic regularization of optimal transport uniquely enables the mitigation of both the effects of privatization noise and the curse of dimensionality in statistical convergence. We provide experimental evidence to support the efficacy of our framework in practice

Mirror Sinkhorn: Fast Online Optimization on Transport Polytopes

Optimal transport is an important tool in machine learning, allowing to capture geometric properties of the data through a linear program on transport polytopes. We present a single-loop optimization algorithm for minimizing general convex objectives on these domains, utilizing the principles of Sinkhorn matrix scaling and mirror descent. The proposed algorithm is robust to noise, and can be used in an online setting. We provide theoretical guarantees for convex objectives and experimental results showcasing it effectiveness on both synthetic and real-world data.Comment: ICML 202