Frederik Möbius Rygaard,Søren Hauberg
Frederik Möbius Rygaard
Computing geodesics for Riemannian manifolds is a difficult task that often relies on numerical approximations. However, these approximations tend to be either numerically unstable, have slow convergence, or scale poorly with manifold dimen...
Gibbs manifolds [0.03%]
吉布斯流形
Dmitrii Pavlov,Bernd Sturmfels,Simon Telen
Dmitrii Pavlov
Gibbs manifolds are images of affine spaces of symmetric matrices under the exponential map. They arise in applications such as optimization, statistics and quantum physics, where they extend the ubiquitous role of toric geometry. The Gibbs...
John Armstrong,Damiano Brigo,Emilio Ferrucci
John Armstrong
In Armstrong et al. (Proc Lond Math Soc (3) 119(1):176-213, 2019) the authors define three projections of R d -valued stochastic differential equations (SDEs) onto submanifolds: the Stratonovich, Itô-vector and Itô-jet projections. In t...
H S Battey,D R Cox,Su Hyeong Lee
H S Battey
Models whose associated likelihood functions fruitfully factorise are an important minority allowing elimination of nuisance parameters via partial likelihood, an operation that is valuable in both Bayesian and frequentist inferences, parti...
Johannes Müller,Guido Montúfar
Johannes Müller
We study the convergence of several natural policy gradient (NPG) methods in infinite-horizon discounted Markov decision processes with regular policy parametrizations. For a variety of NPGs and reward functions we show that the trajectorie...
Amanjit Singh Kainth,Ting-Kam Leonard Wong,Frank Rudzicz
Amanjit Singh Kainth
The logarithmic divergence is an extension of the Bregman divergence motivated by optimal transport and a generalized convex duality, and satisfies many remarkable properties. Using the geometry induced by the logarithmic divergence, we int...
Eric Smith
Eric Smith
Two-field functional integrals (2FFI) are an important class of solution methods for generating functions of dissipative processes, including discrete-state stochastic processes, dissipative dynamical systems, and decohering quantum densiti...
Pseudo-Riemannian geometry encodes information geometry in optimal transport [0.03%]
伪黎曼几何通过最优运输编码信息几何
Ting-Kam Leonard Wong,Jiaowen Yang
Ting-Kam Leonard Wong
Optimal transport and information geometry both study geometric structures on spaces of probability distributions. Optimal transport characterizes the cost-minimizing movement from one distribution to another, while information geometry ori...