A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Discusses new probabilistic morphisms and geometric methods in machine and statistical learning.
I introduce a new geometrical approach to thermo--statistical mechanics. Here I highlight the main physical ideas, and how do they translate into geometrical language. I contrast the present approach with previous thermo--statistical--geometrical formalisms, (pseudo-)Riemannian [Weinhold 1975; Ruppeiner 1979] as well a…
Flexible approach for normal approximations in geometric and topological statistics.
The paper introduces a statistical version of contact CR-product for Sasakian statistical manifolds.
The study of record statistics of correlated series is gaining momentum. In this work, we study the records statistics of the time series of select stock market data and the geometric random walk, primarily through simulations. We show that the distribution of the age of records is a power law with the exponent lyi…
Graph Neural Networks improve financial time series forecasting accuracy.
Sharp inequalities and solitons studied in statistical submersions.
Fisher width is a geometric measure of complexity on statistical manifolds.
Study geometric properties of SGL submanifolds in a specific manifold.
Geometric structures are lifted to higher tangent bundles preserving statistical properties.
This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix estimation, and noisy matrix completion. We propose computationally feasible conv…
Geometric regularisation improves statistical models by avoiding degeneracy loci.
Information geometry provides a geometric approach to families of statistical models. The key geometric structures are the Fisher quadratic form and the Amari-Chentsov tensor. In statistics, the notion of sufficient statistic expresses the criterion for passing from one model to another without loss of information. Thi…
This paper introduces online algorithms to estimate robust geometric median in large data streams.
Geometric framework for SPD matrices preserving subspace structures.
Geometrically decomposes Kähler functions on toric manifolds.
Study geodesic paths on flat surfaces, comparing length and singularity counts.
Introduces a new geometric method for optimal experimental design.
Warped product affects divergences in information geometry.
Study explores geometric structure and prior for beta-logistic distribution.
The paper introduces new geometric methods to analyze radar electromagnetic wave statistics.
Researchers study the geometric properties of a specific type of stable processes.
Information geometry offers new tools for statistical analysis.
Evaluating data separation in a geometrical space is fundamental for pattern recognition. A plethora of dimensionality reduction (DR) algorithms have been developed in order to reveal the emergence of geometrical patterns in a low dimensional visible representation space, in which high-dimensional samples similarities …
We propose a geometric algorithm for topic learning and inference that is built on the convex geometry of topics arising from the Latent Dirichlet Allocation (LDA) model and its nonparametric extensions. To this end we study the optimization of a geometric loss function, which is a surrogate to the LDA's likelihood. Ou…
Optimal transport and information geometry both study geometric structures on spaces of probability distributions. Optimal transport characterizes the cost-minimizing movement from one distribution to another, while information geometry originates from coordinate-invariant properties of statistical inference. Their con…
Machine learning methods struggle with geometric data, but shape space analysis provides a framework for studying and analyzing geometric variability.
Lightlike hypersurfaces of a statistical manifold are studied. It is shown that a lightlike hypersurface of a statistical manifold is not a statistical manifold with respect to the induced connections, but the screen distribution has a canonical statistical structure. Some relations between induced geometric objects wi…
Unified geometric interpretation of statistical estimation inequalities.
This paper deals with the applications of an optimization method on submanifolds, that is, geometric inequalities can be considered as optimization problems. In this regard, we obtain optimal Casorati inequalities and Chen-Ricci inequality for a statistical submanifold in a statistical warped product manifold of type $…
New geometric methods improve optimization and data science problems.
A quantum system can be entirely described by the Kähler structure of the projective space P(H) associated to the Hilbert space H of possible states; this is the so-called geometrical formulation of quantum mechanics. In this paper, we give an explicit link between the geometrical formulation (of finite dimensional qua…
In this paper, we examine a geometrical projection algorithm for statistical inference. The algorithm is based on Pythagorean relation and it is derivative-free as well as representation-free that is useful in nonparametric cases. We derive a bound of learning rate to guarantee local convergence. In special cases of m-…
Exponential families are a particular class of statistical manifolds which are particularly important in statistical inference, and which appear very frequently in statistics. For example, the set of normal distributions, with mean μ and deviation σ, form a 2-dimensional exponential family. In this paper, we show that …
Study on lightlike geometry in indefinite Sasakian statistical manifolds.
Python tools for 3D shape analysis on Kendall's space.
In information geometry, one of the basic problem is to study the geomet-ric properties of statistical manifold. In this paper, we study the geometricstructure of the generalized normal distribution manifold and show that it has constant α-Gaussian curvature. Then for any positive integerp, we con-struct ap-dimensional…
We apply the geometric-topology surgery theory on spacetime manifolds to study the constraints of quantum statistics data in 2+1 and 3+1 spacetime dimensions. First, we introduce the fusion data for worldline and worldsheet operators capable creating anyon excitations of particles and strings, well-defined in gapped st…
Study classifies mappings of bivariate normal densities, revealing three types with distinct geometric and statistical properties.
The paper outlines future work in random sets theory.
Capacity control, the bias/variance dilemma, and learning unknown functions from data, are all concerned with identifying effective and consistent fits of unknown geometric loci to random data points. A geometric locus is a curve or surface formed by points, all of which possess some uniform property. A geometric locus…
In this paper, we introduce the concept of principal bundles on statistical manifolds. After necessary preliminaries on information geometry and principal bundles on manifolds, we study the -structure of frame bundles over statistical manifolds with respect to -connections, by giving geometric structures. The man…
This report concerns the problem of dimensionality reduction through information geometric methods on statistical manifolds. While there has been considerable work recently presented regarding dimensionality reduction for the purposes of learning tasks such as classification, clustering, and visualization, these method…
Abstract: Geometrically reformulates estimation theory for finite-dimensional C*-algebras.
The Wintgen inequality (1979) is a sharp geometric inequality for surfaces in the 4-dimensional Euclidean space involving the Gauss curvature (intrinsic invariant) and the normal curvature and squared mean curvature (extrinsic invariants), respectively. In the present paper we obtain a Wintgen inequality for statistica…
Enhanced 3D shape analysis using information geometry.
Characterizes connections on normal distributions manifold.
Study compares geometric approaches for shape and deformation statistics.