De Erlend Grong
Apparaît dans la collection : Geometric Sciences in Action: from geometric statistics to shape analysis / Les sciences géometriques en action: des statistiques géometriques à l'analyse de forme
We discuss how to simulate bridge processes by conditioning a stochastic process on a manifold whose generator is a hypo-elliptic operator. This operator is, up to a drift-term, the sub-Laplacian of a bracketgenerating sub-Riemannian structure, meaning in particular that it has positive smooth density everywhere. The logarithmic gradient of this density is called the score, and we show that it is needed to describe the generator of the bridge process. We therefore discuss several methods for how we can estimate the score using a neural network, with examples. The results are from a joint work with Stefan Sommer (Copenhagen) and Karen Habermann (Warwick).
De Mikhail Gromov
De Andrey Malyutin
