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.
The paper constructs random concave functions on the unit simplex.
A method for diffusion on probability simplex for generative models.
Paper solves graph matching problem using convex relaxation to the simplex.
A new optimization method for probability simplex problems.
Consider a structured matrix factorization model where one factor is restricted to have its columns lying in the unit simplex. This simplex-structured matrix factorization (SSMF) model and the associated factorization techniques have spurred much interest in research topics over different areas, such as hyperspectral u…
The paper triangulates Heisenberg groups with horizontal and straight simplexes.
Study classifies submanifolds in probability simplex.
Study optimal transport on simplex boundary, proving transport map and potential regularity.
The Bezier simplex fitting is a novel data modeling technique which exploits geometric structures of data to approximate the Pareto front of multi-objective optimization problems. There are two fitting methods based on different sampling strategies. The inductive skeleton fitting employs a stratified subsampling from e…
PRISM identifies simplex vertices from noisy data.
We establish the second part of Milnor's conjecture on the volume of simplexes in hyperbolic and spherical spaces. A characterization of the closure of the space of the angle Gram matrices of simplexes is also obtained.
A function is exponentially concave if its exponential is concave. We consider exponentially concave functions on the unit simplex. In a previous paper we showed that gradient maps of exponentially concave functions provide solutions to a Monge-Kantorovich optimal transport problem and give a better gradient approximat…
A hyperbolic 3-simplex reflection group is a Coxeter group arising as a lattice in the isometry group of hyperbolic 3-space, with fundamental domain a geodesic simplex (possibly with some ideal vertices). The classification of these groups is known, and there are exactly 9 cocompact examples, and 23 non-cocompact examp…
We introduce the non-pure versions of simplicial balls and spheres with minimum number of vertices. These are a special type of non-homogeneous balls and spheres (NH-balls and NH-spheres) satisfying a minimality condition on the number of maximal simplices. The main result is that minimal NH-balls and NH-spheres are pr…
In 1973, J. Cheeger and J. Simons raised the following question that still remains open and is known as the Rational Simplex Problem: Given a geodesic simplex in the spherical 3-space so that all of its interior dihedral angles are rational multiples of , is it true that its volume is a rational multiple of the volu…
The paper explores trading off consistency and dimensionality in convex surrogates for multiclass classification.
Concrete distribution properties examined on simplex.
A new method for SSMF improves upon existing algorithms.
A faster Wasserstein k-means algorithm for histogram data reduces computation and maintains clustering quality.
Proposes an accuracy-preserving calibration method for DNNs.
On the probability simplex, we can consider the standard information geometric structure with the e- and m-affine connections mutually dual with respect to the Fisher metric. The geometry naturally defines submanifolds simultaneously autoparallel for the both affine connections, which we call {\em doubly autoparallel s…
The paper finds the shortest time to exploit arbitrage in multi-stock markets.
Given a convex body, the -Busemann Random Simplex Inequality is closely related to the centroid body for and , and only in these cases it can be proved using the -Busemann-Petty centroid inequality. We define a convex body and prove an isoperimetric inequality for …
The paper is devoted to modeling optimal exercise strategies of the behavior of investors and issuers working with convertible bonds. This implies solution of the problems of stock price modeling, payoff computation and min-max optimization. Stock prices (underlying asset) were modeled under the assumption of the geome…
Algorithm learns latent simplex from perturbed points in input-sparsity time.
We show an efficient algorithm for the following problem: Given uniformly random points from an arbitrary n-dimensional simplex, estimate the simplex. The size of the sample and the number of arithmetic operations of our algorithm are polynomial in n. This answers a question of Frieze, Jerrum and Kannan [FJK]. Our resu…
We provide an elementary proof of a simple, efficient algorithm for computing the Euclidean projection of a point onto the probability simplex. We also show an application in Laplacian K-modes clustering.
New framework estimates staged tree models using hierarchical clustering on the probability simplex.
CAST predicts distribution-valued time series by stabilizing and transporting simplex-supported successors.
Timelike geometry of spherical simplices is shown to be isometric to vector spaces.
Novel simplex-valued distribution improves on existing models.
In the present paper we calculate the Gromov-Hausdorff distance between an arbitrary simplex (a metric space all whose non-zero distances are the same) and a finite metric space whose non-zero distances take two distinct values (so-called -distance spaces). As a corollary, a complete solution to generalized Borsuk p…
We present two identities (contiguity relation and variation formula) concerning the volume of a spherically faced simplex in the Euclidean space. These identities are described in terms of Cayley-Menger determinants and their differentials involved with hypersphere arrangements. They are derived as a limit of fundamen…
Investigates VaR behavior for sums of one-sided random variables, showing impossibilities and conditions for super-additivity.
We study a natural intrinsic definition of geometric simplices in Riemannian manifolds of arbitrary dimension , and exploit these simplices to obtain criteria for triangulating compact Riemannian manifolds. These geometric simplices are defined using Karcher means. Given a finite set of vertices in a convex set on t…
Paper studies weighted Fermat-Frechet problem for simplex edge lengths.
Principal circle bundle over a PL polyhedron can be triangulated and thus obtains combinatorics. The triangulation is assembled from triangulated circle bundles over simplices. To every triangulated circle bundle over a simplex we associate a necklace (in combinatorial sense). We express rational local formulas for all…
Researchers correct earlier work on surgeries of Gieseking's hyperbolic simplex manifold.
Study shows asymptotic behavior of metric near singular points of a Monge-Ampère equation.
The paper sets sample complexity bounds for learning high-dimensional simplices in noisy data.
A theory of cellwise contamination for compositional data using log-ratios.
Stochastic gradient Markov chain Monte Carlo (SGMCMC) has become a popular method for scalable Bayesian inference. These methods are based on sampling a discrete-time approximation to a continuous time process, such as the Langevin diffusion. When applied to distributions defined on a constrained space the time-discret…
First introduced by Fernholz in stochastic portfolio theory, functionally generated portfolio allows its investment performance to be attributed to directly observable and easily interpretable market quantities. In previous works we showed that Fernholz's multiplicatively generated portfolio has deep connections with o…
Neural networks exhibit simplex symmetry in their final and penultimate layers.
Log-concavity proven for multinomial likelihoods under specific constraints.
Unfolding paths in Outer space accumulate on a simplex, not converge.
This work generalizes a geometric Laplacian determinant description to higher dimensions.
We introduce a new distance metric for non-linear embeddings of Tempered Exponential Measures.