Related papers: Interest Rates and Information Geometry
We consider the space of probabilities {P(x)}, where the x are coordinates of a configuration space. Under the action of the translation group there is a natural metric over the space of parameters of the group given by the Fisher-Rao…
In this paper we consider the space of those probability distributions which maximize the $q$-R\'enyi entropy. These distributions have the same parameter space for every $q$, and in the $q=1$ case these are the normal distributions. Some…
We introduce diffusion geometry as a new framework for geometric and topological data analysis. Diffusion geometry uses the Bakry-Emery $\Gamma$-calculus of Markov diffusion operators to define objects from Riemannian geometry on a wide…
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…
We introduce a new information-geometric structure associated with the dynamics on discrete objects such as graphs and hypergraphs. The presented setup consists of two dually flat structures built on the vertex and edge spaces,…
Geometry constitutes a core set of intuitions present in all humans, regardless of their language or schooling [1]. Could brain's built in machinery for processing geometric information take part in uncertainty representation? For decades…
We study a natural Wasserstein gradient flow on manifolds of probability distributions with discrete sample spaces. We derive the Riemannian structure for the probability simplex from the dynamical formulation of the Wasserstein distance on…
We formulate the Riemannian calculus of the probability set embedded with $L^2$-Wasserstein metric. This is an initial work of transport information geometry. Our investigation starts with the probability simplex (probability manifold)…
The infinite-dimensional Hilbert sphere $S^\infty$ has been widely employed to model density functions and shapes, extending the finite-dimensional counterpart. We consider the Fr\'echet mean as an intrinsic summary of the central tendency…
Classical asset pricing relies on the risk-neutral measure $Q$ for valuation, yet its economic interpretation is typically anchored in a physical measure $P$. This creates an inherent asymmetry: pricing is governed by $Q$, while meaning…
We derive rates of contraction of posterior distributions on nonparametric or semiparametric models based on Gaussian processes. The rate of contraction is shown to depend on the position of the true parameter relative to the reproducing…
We study the statistical geometry of random chords on n-dimensional spheres by deriving explicit analytical expressions for the chord length distribution and its associated structural properties. A critical threshold emerges at dimension…
This paper is concerned with finite dimensional models for the entire term structure for energy futures. As soon as a finite dimensional set of possible yield curves is chosen, one likes to estimate the dynamic behaviour of the yield curve…
We study random graphs with latent geometric structure, where the probability of each edge depends on the underlying random positions corresponding to the two endpoints. We focus on the setting where this conditional probability is a…
We study the geometrical properties of the utility space (the space of expected utilities over a finite set of options), which is commonly used to model the preferences of an agent in a situation of uncertainty. We focus on the case where…
A filament consists of local maximizers of a smooth function $f$ when moving in a certain direction. A filamentary structure is an important feature of the shape of an object and is also considered as an important lower dimensional…
The space of probability densities is an infinite-dimensional Riemannian manifold, with Riemannian metrics in two flavors: Wasserstein and Fisher--Rao. The former is pivotal in optimal mass transport (OMT), whereas the latter occurs in…
A Hilbert space embedding for probability measures has recently been proposed, with applications including dimensionality reduction, homogeneity testing, and independence testing. This embedding represents any probability measure as a mean…
The Convolution and Master equations governing the time behavior of the term structure of Interest Rates are set up both for continuous variables and for their discretised forms. The notion of Seed is introduced. The discretised theoretical…
We provide an Information-Geometric formulation of Classical Mechanics on the Riemannian manifold of probability distributions, which is an affine manifold endowed with a dually-flat connection. In a non-parametric formalism, we consider…