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Connection between fisher information and Information geometry

As you encountered in 20260412T190320-geometry_of_data_hw4, what is the connection between this statistical measure and Reimannian geometry?

I don’t have the full explanation yet. But fisher information matrix satisfies the requirements for a Reimannian metric and apparently induces that metric on the statistical manifold (don’t know what that is).

So this can be thought of as the distance between distributions.