New Metric and Connections in Statistical Manifolds

We define a metric and a family of $α$-connections in statistical manifolds, based on $φ$-divergence, which emerges in the framework of $φ$-families of probability distributions. This metric and $α$-connections generalize the Fisher information metric and Amari's $α$-connections. We also investigate the parallel transport associated with the $α$-connection for $α=1$.

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