The content delves into the Fisher-Rao distance, a geodesic distance between probability distributions, focusing on finding closed-form expressions. It covers examples of discrete and continuous distributions, highlighting their relation to negative multinomial distributions and hyperbolic models. The work aims to make these complex concepts more understandable by providing concrete examples and explanations.
The Fisher–Rao distance is explored in different contexts such as machine learning applications, supervised and unsupervised learning problems. The article emphasizes the importance of closed-form expressions for this distance, which are challenging to find due to the complexity of differential geometry problems. It also discusses numerical methods proposed for cases where closed-form solutions are not available.
Furthermore, the content reviews information geometry preliminaries and hyperbolic geometry results to provide a comprehensive understanding of statistical manifolds. It includes detailed explanations of key metrics like the Fisher information matrix and geodesic distances in different distributions.
Overall, the article serves as a valuable resource for those interested in understanding the intricacies of the Fisher–Rao distance and its applications in statistical analysis.
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