We propose a numerical algorithm for the computation of multi-marginal optimal transport (MMOT) p... more We propose a numerical algorithm for the computation of multi-marginal optimal transport (MMOT) problems involving general measures that are not necessarily discrete. By developing a relaxation scheme in which marginal constraints are replaced by finitely many linear constraints and by proving a specifically tailored duality result for this setting, we approximate the MMOT problem by a linear semiinfinite optimization problem. Moreover, we are able to recover a feasible and approximately optimal solution of the MMOT problem, and its sub-optimality can be controlled to be arbitrarily close to 0 under mild conditions. The developed relaxation scheme leads to a numerical algorithm which can compute a feasible approximate optimizer of the MMOT problem whose theoretical sub-optimality can be chosen to be arbitrarily small. Besides the approximate optimizer, the algorithm is also able to compute both an upper bound and a lower bound on the optimal value of the MMOT problem. The difference...
Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, 2017
Data trustworthiness is a crucial issue in real-world participatory sensing applications. Without... more Data trustworthiness is a crucial issue in real-world participatory sensing applications. Without considering this issue, different types of worker misbehavior, especially the challenging collusion attacks, can result in biased and inaccurate estimation and decision making. We propose a novel trust-based mixture of Gaussian processes (GP) model for spatial regression to jointly detect such misbehavior and accurately estimate the spatial field. We develop a Markov chain Monte Carlo (MCMC)-based algorithm to efficiently perform Bayesian inference of the model. Experiments using two real-world datasets show the superior robustness of our model compared with existing approaches.
The cyber risk insurance market is at a nascent stage of its development, even as the magnitude o... more The cyber risk insurance market is at a nascent stage of its development, even as the magnitude of cyber losses is significant and the rate of cyber risk events is increasing. Existing cyber risk insurance products as well as academic studies have been focusing on classifying cyber risk events and developing models of these events, but little attention has been paid to proposing insurance risk transfer strategies that incentivize mitigation of cyber loss through adjusting the premium of the risk transfer product. To address this important gap, we develop a Bonus-Malus model for cyber risk insurance. Specifically, we propose a mathematical model of cyber risk insurance and cybersecurity provisioning supported with an efficient numerical algorithm based on dynamic programming. Through a numerical experiment, we demonstrate how a properly designed cyber risk insurance contract with a Bonus-Malus system can resolve the issue of moral hazard and benefit the insurer.
We propose a numerical algorithm for the computation of multi-marginal optimal transport (MMOT) p... more We propose a numerical algorithm for the computation of multi-marginal optimal transport (MMOT) problems involving general measures that are not necessarily discrete. By developing a relaxation scheme in which marginal constraints are replaced by finitely many linear constraints and by proving a specifically tailored duality result for this setting, we approximate the MMOT problem by a linear semiinfinite optimization problem. Moreover, we are able to recover a feasible and approximately optimal solution of the MMOT problem, and its sub-optimality can be controlled to be arbitrarily close to 0 under mild conditions. The developed relaxation scheme leads to a numerical algorithm which can compute a feasible approximate optimizer of the MMOT problem whose theoretical sub-optimality can be chosen to be arbitrarily small. Besides the approximate optimizer, the algorithm is also able to compute both an upper bound and a lower bound on the optimal value of the MMOT problem. The difference...
Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, 2017
Data trustworthiness is a crucial issue in real-world participatory sensing applications. Without... more Data trustworthiness is a crucial issue in real-world participatory sensing applications. Without considering this issue, different types of worker misbehavior, especially the challenging collusion attacks, can result in biased and inaccurate estimation and decision making. We propose a novel trust-based mixture of Gaussian processes (GP) model for spatial regression to jointly detect such misbehavior and accurately estimate the spatial field. We develop a Markov chain Monte Carlo (MCMC)-based algorithm to efficiently perform Bayesian inference of the model. Experiments using two real-world datasets show the superior robustness of our model compared with existing approaches.
The cyber risk insurance market is at a nascent stage of its development, even as the magnitude o... more The cyber risk insurance market is at a nascent stage of its development, even as the magnitude of cyber losses is significant and the rate of cyber risk events is increasing. Existing cyber risk insurance products as well as academic studies have been focusing on classifying cyber risk events and developing models of these events, but little attention has been paid to proposing insurance risk transfer strategies that incentivize mitigation of cyber loss through adjusting the premium of the risk transfer product. To address this important gap, we develop a Bonus-Malus model for cyber risk insurance. Specifically, we propose a mathematical model of cyber risk insurance and cybersecurity provisioning supported with an efficient numerical algorithm based on dynamic programming. Through a numerical experiment, we demonstrate how a properly designed cyber risk insurance contract with a Bonus-Malus system can resolve the issue of moral hazard and benefit the insurer.
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Papers by Qikun Xiang