What is the connection between Random Forest and information geometry?

Random Forest implicitly operates on a manifold of probability distributions, connecting to information geometry.

Each tree produces a probability distribution over classes in leaf nodes. The ensemble averages these distributions, effectively operating in the space of probability simplices. Information geometry studies this space using metrics like Fisher information. RF averaging can be interpreted as performing Euclidean projections in this curved statistical manifold, though without explicit geodesic optimization.