Related papers: Fisher-Rao distance and pullback SPD cone distance…
The Fisher-Rao distance is the geodesic distance between probability distributions in a statistical manifold equipped with the Fisher metric, which is a natural choice of Riemannian metric on such manifolds. It has recently been applied to…
The Fisher-Rao distance between two probability distributions of a statistical model is defined as the Riemannian geodesic distance induced by the Fisher information metric. In order to calculate the Fisher-Rao distance in closed-form, we…
We present a simple method to approximate Rao's distance between multivariate normal distributions based on discretizing curves joining normal distributions and approximating Rao's distances between successive nearby normal distributions on…
Choosing the Fisher information as the metric tensor for a Riemannian manifold provides a powerful yet fundamental way to understand statistical distribution families. Distances along this manifold become a compelling measure of statistical…
When dealing with a parametric statistical model, a Riemannian manifold can naturally appear by endowing the parameter space with the Fisher information metric. The geometry induced on the parameters by this metric is then referred to as…
This paper is a strongly geometrical approach to the Fisher distance, which is a measure of dissimilarity between two probability distribution functions. The Fisher distance, as well as other divergence measures, are also used in many…
The Fisher-Rao geodesic distance on the statistical manifold consisting of zero-mean p-dimensional multivariate Gaussians appears without proof in several places (such as Steven Smith's "Covariance, Subspace, and Intrinsic Cramer-Rao…
The Fisher information metric or the Fisher-Rao metric corresponds to a natural Riemannian metric defined on a parameterized family of probability density functions. As in the case of Riemannian geometry, we can define a distance in terms…
Distances between probability distributions that take into account the geometry of their sample space,like the Wasserstein or the Maximum Mean Discrepancy (MMD) distances have received a lot of attention in machine learning as they can, for…
Clustering categorical distributions in the finite-dimensional probability simplex is a fundamental task met in many applications dealing with normalized histograms. Traditionally, the differential-geometric structures of the probability…
This work presents an explicit description of the Fisher-Rao Riemannian metric on the Hilbert manifold of equivalent centered Gaussian measures on an infinite-dimensional Hilbert space. We show that the corresponding quantities from the…
The symmetric Kullback-Leibler centroid also called the Jeffreys centroid of a set of mutually absolutely continuous probability distributions on a measure space provides a notion of centrality which has proven useful in many tasks…
Collections of probability distributions arise in a variety of applications ranging from user activity pattern analysis to brain connectomics. In practice these distributions can be defined over diverse domain types including finite…
A deep neural network is a hierarchical nonlinear model transforming input signals to output signals. Its input-output relation is considered to be stochastic, being described for a given input by a parameterized conditional probability…
Hilbert-Schmidt distance is one of the prominent distance measures in quantum information theory which finds applications in diverse problems, such as construction of entanglement witnesses, quantum algorithms in machine learning, and…
The contribution of this work is the introduction of a multivariate circular-linear (or poly- cylindrical) distribution obtained by combining the projected and the skew-normal. We show the flexibility of our proposal, its property of…
Bayesian inference typically requires the computation of an approximation to the posterior distribution. An important requirement for an approximate Bayesian inference algorithm is to output high-accuracy posterior mean and uncertainty…
We present a methodology for clustering N objects which are described by multivariate time series, i.e. several sequences of real-valued random variables. This clustering methodology leverages copulas which are distributions encoding the…
We consider the problems of clustering, classification, and visualization of high-dimensional data when no straightforward Euclidean representation exists. Typically, these tasks are performed by first reducing the high-dimensional data to…
We consider an inference on the eigenvalues of the covariance matrix of a multivariate normal distribution. The family of multivariate normal distributions with a fixed mean is seen as a Riemannian manifold with Fisher information metric.…