arXiv research

We explore the connection between two problems that have arisen independently in the signal processing and related fields: the estimation of the geometric mean of a set of symmetric positive definite (SPD) matrices and their approximate joint diagonalization (AJD). Today there is a considerable interest in estimating t…

The space of all probability measures having positive density function on a connected compact smooth manifold $M$, denoted by $\mathcal{P}(M)$, carries the Fisher information metric $G$. We define the geometric mean of probability measures by the aid of which we investigate information geometry of $\mathcal{P}(M)$, equ…

The paper uses geometric methods to classify medical data histograms.

Warped product affects divergences in information geometry.

Study of Lévy flights on Zoll surfaces, revealing geometric information.

The information bottleneck (IB) approach to clustering takes a joint distribution $P\!\left(X,Y\right)$ and maps the data $X$ to cluster labels $T$ which retain maximal information about $Y$ (Tishby et al., 1999). This objective results in an algorithm that clusters data points based upon the similarity of their condit…

This paper proposes a new geometric framework for asset pricing.

Geometric approach combines asset returns and investor views for better portfolio optimization.

Autoencoder shapes QAM symbols for improved GMI performance.

We extend the theory of asymmetric information in mispricing models for stocks following geometric Brownian motion to constant relative risk averse investors. Mispricing follows a continuous mean--reverting Ornstein--Uhlenbeck process. Optimal portfolios and maximum expected log--linear utilities from terminal wealth f…

A new method for distributed PCA using matrix β-mean.

New method identifies shared topics in LLM inputs and outputs for better detection of hallucinations.

In the paper, a mean-square minimization problem under terminal wealth constraint with partial observations is studied. The problem is naturally connected to the mean-variance hedging problem under incomplete information. A new approach to solving this problem is proposed. The paper provides a solution when the underly…

Enhances quantum circuit synthesis using deep learning and geometric methods.

The paper defines and studies the geometric mean for tensors and its associated Riemannian geometry.

Proves uniqueness of geometric flow in various Riemannian manifolds.

Study reveals how to determine area and curvature from fluid flow resonances.

Proposes a new regularizer for semi-supervised learning on multilayer graphs.

Discuss knots in $S_{g} imes S^{1}$, introducing rotating information and invariants.

Modeling bone microarchitecture adaptation using geometric flows.

Geometrically describes surfaces with parallel mean curvature in warped product spaces.

Geometric Mean Market Makers super-hedge impermanent loss without models.

In high dimensions, the mean and geometric median are nearly identical.

Here are studied pairs of transversal foliations with singularities, defined on the Elliptic region (where the Gaussian curvature $\mathcal K$ is positive) of an oriented surface immersed in $\mathbb R^3$. The leaves of the foliations are the lines of geometric mean curvature, along which the normal curvature is given …

The visual systems of many mammals, including humans, is able to integrate the geometric information of visual stimuli and to perform cognitive tasks already at the first stages of the cortical processing. This is thought to be the result of a combination of mechanisms, which include feature extraction at single cell l…

The Freund family of distributions becomes a Riemannian 4-manifold with Fisher information as metric; we derive the induced $α$-geometry, i.e., the $α$-curvature, $α$-Ricci curvature with its eigenvales and eigenvectors, the $α$-scalar curvature etc. We show that the Freund manifold has a positive constant 0-scalar cur…

Bi-forms extend contrast functions to handle torsion in information geometry.

Investigates geometric mean reversion process using Lie symmetry method.

Let $\mathcal{N}$ be the space of Gaussian distribution functions over $\mathbb{R}$, regarded as a 2-dimensional statistical manifold parameterized by the mean $μ$ and the deviation $σ$. In this paper we show that the tangent bundle of $\mathcal{N}$, endowed with its natural Kähler structure, is the Siegel-Jacobi space…

Study of J-Hermitian matrices and geometric mean definition.

FRESH combines patient-level and aggregate-level data for better clinical decision making.

Constructs constant mean curvature surfaces using geometric flow.

Estimates mean curvature flow with geometric bounds.

Signed networks allow to model positive and negative relationships. We analyze existing extensions of spectral clustering to signed networks. It turns out that existing approaches do not recover the ground truth clustering in several situations where either the positive or the negative network structures contain no noi…

A new geometric method for clustering SPD data improves upon Euclidean and Riemannian approaches.

We analyze the variance of Fisher information estimators in deep learning models.

The paper finds inequalities in Grassmannian geometry.

New algorithms exploit mean bounds to improve bandit problem performance.

Novel coarse extrinsic curvature for Riemannian submanifolds.

The paper refines classical covariance asymptotics using geometric information geometry.

The paper studies constant mean curvature hypersurfaces in Finsler manifolds.

New market makers improve on existing models in DeFi.

CP$^2$ uses geometric information to improve conformal prediction robustness.

A multi-step framework tackles online unsupervised domain adaptation with novel mean-target subspace computation.

This paper extends liquidity returns in geometric mean markets to time-varying weights.

Bayesian model selection via mean-field variational approximation improves efficiency and accuracy.

Paper proposes a robust method for federated ICA with geometric median aggregation.

Study applies Huisken formula to mean curvature flow in Ricci soliton background.