On Wasserstein geometry of the space of Gaussian measures Export

@misc{citeulike:2244343, abstract = {The space which consists of measures having finite second moment is an infinite dimensional metric space endowed with Wasserstein distance, while the space of Gaussian measures on Euclidean space is parameterized by mean and covariance matrices, hence a finite dimensional manifold. By restricting to the space of Gaussian measures inside the space of probability measures, we manege to provide detailed descriptions of the Wasserstein geometry from a Riemannian geometric viewpoint. In particular, using the results from the Monge-Kantrovich transport theory, an explicit expression of geodesics interpolating two Gaussian measures. It follows that the space of Gaussian measures is geodesically convex in the space of probability measures. Also, a Riemannian metric which induces the Wasserstein distance is specified. Using the Riemannian metric, a formula for the sectional curvatures of the space of Gaussian measures on the plane is written out in terms of the eigenvalues of the covariance matrix.}, author = {Takatsu, Asuka}, citeulike-article-id = {2244348}, citeulike-linkout-0 = {http://arxiv.org/abs/0801.2250}, eprint = {0801.2250}, keywords = {bibtex-import, gaussian, information-geometry, otarie, transport}, month = {Jan}, posted-at = {2008-01-17 10:53:23}, priority = {2}, title = {On Wasserstein geometry of the space of Gaussian measures}, url = {http://arxiv.org/abs/0801.2250}, year = {2008} }

TY - GEN ID - citeulike:2244343 L3 - citeulike-article-id:2244348 N2 - The space which consists of measures having finite second moment is an infinite dimensional metric space endowed with Wasserstein distance, while the space of Gaussian measures on Euclidean space is parameterized by mean and covariance matrices, hence a finite dimensional manifold. By restricting to the space of Gaussian measures inside the space of probability measures, we manege to provide detailed descriptions of the Wasserstein geometry from a Riemannian geometric viewpoint. In particular, using the results from the Monge-Kantrovich transport theory, an explicit expression of geodesics interpolating two Gaussian measures. It follows that the space of Gaussian measures is geodesically convex in the space of probability measures. Also, a Riemannian metric which induces the Wasserstein distance is specified. Using the Riemannian metric, a formula for the sectional curvatures of the space of Gaussian measures on the plane is written out in terms of the eigenvalues of the covariance matrix. TI - On Wasserstein geometry of the space of Gaussian measures KW - bibtex-import KW - gaussian KW - information-geometry KW - otarie KW - transport AU - Takatsu, Asuka PY - 2008/Jan// UR - http://arxiv.org/abs/0801.2250 ER -