首页|Researchers at Shanghai Jiao Tong University Release New Data on Machine Learnin g (A Machine Learning Framework for Geodesics Under Spherical Wasserstein-fisher -rao Metric and Its Application for Weighted Sample Generation)
Researchers at Shanghai Jiao Tong University Release New Data on Machine Learnin g (A Machine Learning Framework for Geodesics Under Spherical Wasserstein-fisher -rao Metric and Its Application for Weighted Sample Generation)
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By a News Reporter-Staff News Editor at Robotics & Machine Learning Daily News Daily News-Current study results on Machine Learn ing have been published. According to news reporting from Shanghai, People's Rep ublic of China, by NewsRx journalists, research stated, "Wasserstein- Fisher-Rao (WFR) distance is a family of metrics to gauge the discrepancy of two Radon meas ures, which takes into account both transportation and weight change. Spherical WFR distance is a projected version of WFR distance for probability measures so that the space of Radon measures equipped with WFR can be viewed as metric cone over the space of probability measures with spherical WFR." Financial support for this research came from National Key R &D Pro gram of China. The news correspondents obtained a quote from the research from Shanghai Jiao To ng University, "Compared to the case for Wasserstein distance, the understanding of geodesics under the spherical WFR is less clear and still an ongoing researc h focus. In this paper, we develop a deep learning framework to compute the geod esics under the spherical WFR metric, and the learned geodesics can be adopted t o generate weighted samples. Our approach is based on a Benamou-Brenier type dyn amic formulation for spherical WFR. To overcome the difficulty in enforcing the boundary constraint brought by the weight change, a Kullback-Leibler divergence term based on the inverse map is introduced into the cost function. Moreover, a new regularization term using the particle velocity is introduced as a substitut e for the Hamilton-Jacobi equation for the potential in dynamic formula." According to the news reporters, the research concluded: "When used for sample g eneration, our framework can be beneficial for applications with given weighted samples, especially in the Bayesian inference, compared to sample generation wit h previous flow models."
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