Fisher-Rao Information Geometry
Statistical manifolds, geodesics and curvature on probability space
Manifold Settings
Family:
Gaussian (mu, sigma)
Bernoulli simplex
Point A: mu =
0.00
Point A: sigma =
1.00
Point B: mu =
2.00
Point B: sigma =
2.00
Distances
Fisher-Rao dist:
-
KL div D(p||q):
-
Euclidean dist:
-
Scalar curvature:
-1/2
Key Equations
g_ij(theta) = E[d_i log p * d_j log p]
Gaussian: ds^2 = dmu^2/sigma^2 + 2 dsigma^2/sigma^2
Geodesic: d2theta/dt2 + Gamma*dtheta*dtheta = 0
Dually flat: exp families have alpha-connections