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.
Paper shows stability of metric reconstruction for orbifolds from spectral data.
We study generalizations of Reifenberg's Theorem for measures in under assumptions on the Jones' -numbers, which appropriately measure how close the support is to being contained in a subspace. Our main results, which holds for general measures without density assumptions, give effective measure bounds…
The paper provides precise estimates for isoperimetric inequalities on weighted manifolds.
The variability of the clusters generated by clustering techniques in the domain of latitude and longitude variables of fatal crash data are significantly unpredictable. This unpredictability, caused by the randomness of fatal crash incidents, reduces the accuracy of crash frequency (i.e., counts of fatal crashes per c…
Paper analyzes arbitrage in uncertain markets, providing quantitative asset pricing.
New MRI method maps tissue parameters more accurately by ignoring voxel independence.
We prove a quantitative version of Obata's Theorem involving the shape of functions with null mean value when compared with the cosine of distance functions from single points. The deficit between the diameters of the manifold and of the corresponding sphere is bounded likewise. These results are obtained in the genera…
The purpose of this paper is to analyze the isoperimetric inequality for symmetric log-convex probability measures on the line. Using geometric arguments we first re-prove that extremal sets in the isoperimetric inequality are intervals or complement of intervals (a result due to Bobkov and Houdré). Then we give a quan…
The study evaluates how well local explanations align with model predictions.
The paper measures and limits the extent of non-smooth points in Alexandrov spaces.
This paper improves the robustness of risk estimation for financial positions.
Study graph products of groups, classifying them up to measure equivalence and rigidity.
ATD measures language distance using neural models, recovering linguistic groupings.
The paper proves a quantitative rigidity result for spaces with specific curvature bounds.
The VIX is used to enhance quantitative trading strategies.
On a Riemannian manifold with a positive lower bound on the Ricci tensor, the distance of isoperimetric sets from geodesic balls is quantitatively controlled in terms of the gap between the isoperimetric profile of the manifold and that of a round sphere of suitable radius. The deficit between the diameters of the mani…
Deep belief networks can approximate any multivariate density with binary hidden units.
Quantifies Schur's theorem for curves in CAT(k) spaces.
Model risk has a huge impact on any risk measurement procedure and its quantification is therefore a crucial step. In this paper, we introduce three quantitative measures of model risk when choosing a particular reference model within a given class: the absolute measure of model risk, the relative measure of model risk…
The author suggests using non-Euclidean geometry for psychometric models.
We prove that a metric measure space equipped with a Dirichlet form admitting an Euclidean heat kernel is necessarily isometric to the Euclidean space. This helps us providing an alternative proof of Colding's celebrated almost rigidity volume theorem via a quantitative version of our main result. We also discuss the c…
"What are the origins of risks?" and "How material are they?" -- these are the two most fundamental questions of any risk analysis. Quantitative Structuring -- a technology for building financial products -- provides economically meaningful answers for both of these questions. It does so by considering risk as an inves…
Study sharp inequalities for perimeter functionals in capillarity and convex cones.
Study on convergence of exponential probability measures with applications to maximum entropy models and SGLD.
We prove that a wide class of correlated stochastic volatility models exactly measure an empirical fact in which past returns are anticorrelated with future volatilities: the so-called ``leverage effect''. This quantitative measure allows us to fully estimate all parameters involved and it will entail a deeper study on…
New cyclicity measures defined in weighted Besov spaces, with stability and geometric analysis.
The paper studies degenerate and nonlocal elliptic operators on Poincaré-Einstein manifolds.
New proofs and inequalities for capillarity problems quantify asymmetries.
Sig-SDE model integrates signatures with SDEs for financial data.
We provide sharp stability estimates for the Alexandrov Soap Bubble Theorem in the hyperbolic space. The closeness to a single sphere is quantified in terms of the dimension, the measure of the hypersurface and the radius of the touching ball condition. As consequence we obtain a new pinching result for hypersurfaces i…
Decisions by Machine Learning (ML) models have become ubiquitous. Trusting these decisions requires understanding how algorithms take them. Hence interpretability methods for ML are an active focus of research. A central problem in this context is that both the quality of interpretability methods as well as trust in ML…
Quantitative CLTs show neural network distributions converge to Gaussian as width increases.
The paper examines stability of the Sobolev inequality in metric spaces with curvature dimension conditions.
We introduce a quantitative condition on orbits of dynamical systems which measures their aperiodicity. We show the existence of sequences in the Bernoulli-shift and geodesics on closed hyperbolic manifolds which are as aperiodic as possible with respect to this condition.
In this paper we propose a measure of clustering quality or accuracy that is appropriate in situations where it is desirable to evaluate a clustering algorithm by somehow comparing the clusters it produces with ``ground truth' consisting of classes assigned to the patterns by manual means or some other means in whose v…
A quantitative model is presented linking the rate of inflation and unemployment to the change in the level of labor force. The link between the involved variables is a linear one with all coefficients of individual and generalized models obtained empirically. To achieve the best fit between measured and predicted time…
Sharp inequalities and symmetries on Riemannian surfaces quantified.
Novel framework detects lead-lag relationships in Chinese A-share market.
We present the Procrustes measure, a novel measure based on Procrustes rotation that enables quantitative comparison of the output of manifold-based embedding algorithms (such as LLE (Roweis and Saul, 2000) and Isomap (Tenenbaum et al, 2000)). The measure also serves as a natural tool when choosing dimension-reduction …
We introduce an invariant linked to some foundational questions in geometric measure theory and provide bounds on this invariant by decomposing an arbitrary cycle into uniformly rectifiable pieces. Our invariant measures the difficulty of cutting a nonorientable closed manifold or mod-2 cycle in into ori…
Scores measure certainty and doubt in classification predictions.
Sharp estimates for mean curvature flow confirm bounded diameter conjecture.
The paper explores proper actions and their relation to representation theory, with new quantitative methods.
Enhances financial optimization under model uncertainty using subsampling.
Purpose: To investigate the feasibility of myelin water content quantification using fast dual-echo steady-state (DESS) scans and machine learning with kernels. Methods: We optimized combinations of steady-state (SS) scans for precisely estimating the fast-relaxing signal fraction ff of a two-compartment signal model, …
A quantitative check of weak efficiency in US dollar/German mark exchange rates is developed using high frequency data. We show the existence of long term return anomalies. We introduce a technique to measure the available information and show it can be profitable following a particular trading rule.
This paper was presented and written for two seminars: a national UK University Risk Conference and a Risk Management industry workshop. The target audience is therefore a cross section of Academics and industry professionals. The current ongoing global credit crunch has highlighted the importance of risk measurement i…
In this paper we show that in some cases the E.Hopf rigidity phenomenon admits quantitative interpretation. More precisely we estimate from above the measure of the set swept by minimal orbits. These estimates are sharp, i.e. if occupies the whole phase space we recover the E.Hopf rigidity. …