Information theory is a study of probability and statistics using the techniques of differential geometry. The area covers statistical model, Fisher metric, $\alpha$ connection, canonical divergence etc.
Questions tagged [information-geometry]
133 questions
2
votes
1 answer
local geometry interpretation of binary hypothesis testing
In information geometry, suppose
$$
\mathcal{N}_{\epsilon}^{\mathcal{X}}\triangleq\left\{P\in \mathcal{P}^{\mathcal{X}}:\sum_{x\in\mathcal{X}}\frac{(P(x)-P_0(x)^2}{P_0(x)}\leq \epsilon^2\right\}
$$
where $\mathcal{P}^{\mathcal{X}}$ is the space of…
zhaofeng-shu33
- 418
1
vote
0 answers
what are the prerequisites/background needed to understanding Amari's "Information geometry and its applications"?
Someone suggested Shun-ichi Amari's book "Information geometry and its applications", because they said it deeply explains some topic we were discussing.
I've tried reading it and found it extremely bewildering; I have some math background and can…
ham burglar
- 179
1
vote
1 answer
Locality of canonical Bregman divergence on dually flat manifolds
In many texts on information geometry one can find a proof that given a Bregman divergence, i.e. a divergence function of the form $$D_f(p\|q) = f(p)-f(q)+\nabla f(q)\cdot(p-q)$$ for some convex function $f$, there exists a canonical dually flat…
NDewolf
- 1,663