Commit 31318be2 authored by Philipp Arras's avatar Philipp Arras
Browse files

Typo

parent 8075b373
Pipeline #105565 passed with stages
in 33 minutes and 19 seconds
...@@ -56,7 +56,7 @@ Geometric Variational Inference (geoVI) ...@@ -56,7 +56,7 @@ Geometric Variational Inference (geoVI)
For non-linear posterior distributions :math:`\mathcal{P}(\xi|d)` an approximation with a Gaussian :math:`\mathcal{Q}(\xi)` in the coordinates :math:`\xi` is sub-optimal, as higher order interactions are ignored. For non-linear posterior distributions :math:`\mathcal{P}(\xi|d)` an approximation with a Gaussian :math:`\mathcal{Q}(\xi)` in the coordinates :math:`\xi` is sub-optimal, as higher order interactions are ignored.
A better approximation can be achieved by constructing a coordinate system :math:`y = g\left(\xi\right)` in which the posterior is close to a Gaussian, and perform VI with a Gaussian :math:`\mathcal{Q}(y)` in these coordinates. A better approximation can be achieved by constructing a coordinate system :math:`y = g\left(\xi\right)` in which the posterior is close to a Gaussian, and perform VI with a Gaussian :math:`\mathcal{Q}(y)` in these coordinates.
This approach is called Geometric Variation Inference (geoVI). This approach is called Geometric Variational Inference (geoVI).
It is discussed in detail in [2]_. It is discussed in detail in [2]_.
One useful coordinate system is obtained in case the metric :math:`M` of the posterior can be expressed as the pullback of the Euclidean metric by :math:`g`: One useful coordinate system is obtained in case the metric :math:`M` of the posterior can be expressed as the pullback of the Euclidean metric by :math:`g`:
......
Markdown is supported
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment