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.
Two-layer networks learn faster with batch reuse, overcoming information and leap exponents.
Paper analyzes error exponent in agnostic PAC learning.
Study the link between entropy and market efficiency using fractal properties.
We consider strictly stationary heavy tailed time series whose finite-dimensional exponent measures are concentrated on axes, and hence their extremal properties cannot be tackled using classical multivariate regular variation that is suitable for time series with extremal dependence. We recover relevant information ab…
Optimal batch size minimizes training time for neural networks.
Neural network learns low-dimensional polynomials with SGD near information-theoretic limit.
Random subgroups in hyperbolic spaces have full limit sets and bounded critical exponents.
New learning rate approach reveals phase transitions in SGD performance.
Lyapunov exponents help understand RNN stability.
This work improves online SGD's sample complexity for multi-index models by considering higher-order terms.
We study the behaviour of a Hilbert geometry when going to infinity along a geodesic line. We prove that all the information is contained in the shape of the boundary at the endpoint of this geodesic line and have to introduce a regularity property of convex functions to make this link precise. The point of view is a d…
We assume the market price to diffuse in a hierarchical comb of barriers, the heights of which represent the importance of new information entering the market. We find fat tails with the desired exponent for the price change distribution, and effective multifractality for intermediate times.
In many machine learning applications, crowdsourcing has become the primary means for label collection. In this paper, we study the optimal error rate for aggregating labels provided by a set of non-expert workers. Under the classic Dawid-Skene model, we establish matching upper and lower bounds with an exact exponent …
A single algebraic identity unifies information-theoretic variational results.
Active-LATHE boosts error exponent for learning homogeneous trees.
This study investigates empirically whether the degree of stock market efficiency is related to the prediction power of future price change using the indices of twenty seven stock markets. Efficiency refers to weak-form efficient market hypothesis (EMH) in terms of the information of past price changes. The prediction …
Study a market with uncertain informed traders, finding price impact depends on both asset value and informed trader count distribution.
Online SGD achieves consistent estimation in high-dimensional non-convex inference tasks.
The problem of maximum-likelihood (ML) estimation of discrete tree-structured distributions is considered. Chow and Liu established that ML-estimation reduces to the construction of a maximum-weight spanning tree using the empirical mutual information quantities as the edge weights. Using the theory of large-deviations…
A measure called relative cluster entropy distinguishes between correlated and uncorrelated sequences.
Study shows a specific Carnot group violates a curvature exponent bound.
New groups found with critical exponents close to but less than max.
Kurdyka-Lojasiewicz (KL) exponent plays an important role in estimating the convergence rate of many contemporary first-order methods. In particular, a KL exponent of for a suitable potential function is related to local linear convergence. Nevertheless, KL exponent is in general extremely hard to estimate. I…
We introduce a new formulation of asset trading games in continuous time in the framework of the game-theoretic probability established by Shafer and Vovk (Probability and Finance: It's Only a Game! (2001) Wiley). In our formulation, the market moves continuously, but an investor trades in discrete times, which can dep…
New proof for certain groups in higher dimensions.
This paper investigates the presence of long memory in corporate bond and stock indices of six European Union countries from July 1998 to February 2015. We compute the Hurst exponent by means of the DFA method and using a sliding window in order to measure long range dependence. We detect that Hurst exponents behave di…
New convergence bounds for online learning with heavy-tailed noise.
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.
We consider the problem of determining the Lévy exponent in a Lévy model for asset prices given the price data of derivatives. The model, formulated under the real-world measure , consists of a pricing kernel together with one or more non-dividend-paying risky assets driven by the same Lév…
Proves critical exponent for positive representations in discrete subgroups.
Constructs free semigroups with critical exponents close to but less than ambient groups.
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.
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 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 …
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.
We use high-frequency data of 1364 Chinese A-share stocks traded on the Shanghai Stock Exchange and Shenzhen Stock Exchange to investigate the intraday patterns in the bid-ask spreads. The daily periodicity in the spread time series is confirmed by Lomb analysis and the intraday bid-ask spreads are found to exhibit …
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…