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 how KL exponent is preserved via inf-projection for optimization problems.
The paper proves a margin inequality for separating hyperplanes, useful for analyzing algorithmic bias.
Introduces PPMM algorithm for nonconvex robust regression problems.
New convergence analysis for ADAM algorithm in non-convex optimization with adaptive step size.
This paper improves inverse problem solving with weakly convex regularisers and proves convergence.
PPGD solves nonconvex nonsmooth optimization problems without KL property.
New method tackles nonconvex-nonconcave problems with local KL condition.
Paper develops accelerated APCD for nonconvex nonsmooth problems with performance guarantees.
New algorithm solves -norm constrained multilinear logistic regression for tensor data.
Training deep neural networks (DNNs) efficiently is a challenge due to the associated highly nonconvex optimization. The backpropagation (backprop) algorithm has long been the most widely used algorithm for gradient computation of parameters of DNNs and is used along with gradient descent-type algorithms for this optim…
Paper analyzes convergence rates of SGD for non-convex functions under various assumptions.
Infinite 2-groups of bounded exponent cannot act faithfully on compact manifolds.
Study shows a specific Carnot group violates a curvature exponent bound.
New groups found with critical exponents close to but less than max.
In this paper we study nonconvex penalization using Bernstein functions whose first-order derivatives are completely monotone. The Bernstein function can induce a class of nonconvex penalty functions for high-dimensional sparse estimation problems. We derive a thresholding function based on the Bernstein penalty and di…
New proof for certain groups in higher dimensions.
Extends Nash-Kuiper theorem to higher Hölder exponents.
In this paper, we show how the sampling properties of the Hurst exponent methods of estimation change with the presence of heavy tails. We run extensive Monte Carlo simulations to find out how rescaled range analysis (R/S), multifractal detrended fluctuation analysis (MF-DFA), detrending moving average (DMA) and genera…
Study of deep neural networks using finite-time Lyapunov exponents.
Study proves boundedness of operators in variable exponent Morrey spaces.
Constructs free semigroups with critical exponents close to but less than ambient groups.
Proves critical exponent for positive representations in discrete subgroups.
We study the asymptotic behavior of the Lyapunov exponent in a meromorphic family of random products of matrices in SL(2, C), as the parameter converges to a pole. We show that the blow-up of the Lyapunov exponent is governed by a quantity which can be interpreted as the non-Archimedean Lyapunov exponent of the family.…
Study critical exponents in normal subgroups of higher rank Lie groups.
We empirically investigated the relationships between the degree of efficiency and the predictability in financial time-series data. The Hurst exponent was used as the measurement of the degree of efficiency, and the hit rate calculated from the nearest-neighbor prediction method was used for the prediction of the dire…
New bounds on geodesic dimension and curvature exponent in Carnot groups.
Study approximates top Lyapunov exponents for surface mapping classes.
Cubic-regularized Newton's method (CR) is a popular algorithm that guarantees to produce a second-order stationary solution for solving nonconvex optimization problems. However, existing understandings of the convergence rate of CR are conditioned on special types of geometrical properties of the objective function. In…
Study on curvature exponent of sub-Finsler Heisenberg groups, proving N_min ≥ 5.
We study the relationship between the Lyapunov exponents of the geodesic flow of a closed negatively curved manifold and the geometry of the manifold. We show that if each periodic orbit of the geodesic flow has exactly one Lyapunov exponent on the unstable bundle then the manifold has constant negative curvature. We a…
In this paper, we consider the convergence of an abstract inexact nonconvex and nonsmooth algorithm. We promise a pseudo sufficient descent condition and a pseudo relative error condition, which are both related to an auxiliary sequence, for the algorithm; and a continuity condition is assumed to hold. In fact, a lot o…
In this paper, we study the Kurdyka-Łojasiewicz (KL) exponent, an important quantity for analyzing the convergence rate of first-order methods. Specifically, we develop various calculus rules to deduce the KL exponent of new (possibly nonconvex and nonsmooth) functions formed from functions with known KL exponents. In …
Paper analyzes error exponent in agnostic PAC learning.
In previous work, the author fully classified orbit closures in genus three with maximally many (four) zero Lyapunov exponents of the Kontsevich-Zorich cocycle. In this paper, we prove that there are no higher dimensional orbit closures in genus three with any zero Lyapunov exponents. Furthermore, if a Teichmüller curv…
In the presence of a layer of metaprobabilities (from uncertainty concerning the parameters), the asymptotic tail exponent corresponds to the lowest possible tail exponent regardless of its probability. The problem explains "Black Swan" effects, i.e., why measurements tend to chronically underestimate tail contribution…
Study critical exponents on hyperbolic surfaces with long boundaries using Weil-Petersson measures.
Optimizes trading returns using Hurst exponent and Q-learning.
Global Nash-Kuiper theorem extended for compact manifolds with optimal Hölder exponent.
We apply the Hurst exponent idea for investigation of DJIA index time-series data. The behavior of the local Hurst exponent prior to drastic changes in financial series signal is analyzed. The optimal length of the time-window over which this exponent can be calculated in order to make some meaningful predictions is di…
mfBm models and forecasts volatility with different Hurst exponents and correlations.
We study the Bouchaud-Mézard model on a regular random network. By assuming adiabaticity and independency, and utilizing the generalized central limit theorem and the Tauberian theorem, we derive an equation that determines the exponent of the probability distribution function of the wealth as . Th…
The common assumption of universal behavior in stock market data can sometimes lead to false conclusions. In statistical physics, the Hurst exponents characterizing long-range correlations are often closely related to universal exponents. We show, that in the case of time series of the traded value, these Hurst exponen…
This study examines Bitcoin's market efficiency, liquidity, and multifractality over time.
We consider Lyapunov exponents for flat bundles over hyperbolic curves defined via parallel transport over the geodesic flow. We refine a lower bound obtained by Eskin, Kontsevich, Moeller and Zorich showing that the sum of the first k exponents is greater or equal than the sum of the degree of any rank k holomorphic s…
In this paper we propose a new approach to estimation of the tail exponent in financial stock markets. We begin the study with the finite sample behavior of the Hill estimator under α-stable distributions. Using large Monte Carlo simulations, we show that the Hill estimator overestimates the true tail exponent and can …
This paper investigates the scaling dependencies between measures of "activity" and of "size" for companies included in the FTSE 100. The "size" of companies is measured by the total market capitalization. The "activity" is measured with several quantities related to trades (transaction value per trade, transaction val…
New method solves complex constrained optimization problems.
Classifies GL(2,R)-invariant subvarieties with zero Lyapunov exponents.