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.
LLMs learn peaked distributions slowly due to power-law losses.
The study uses the Merton model to estimate PD and finds a phase transition affecting convergence speed.
We introduce a new statistical tool (the TP-statistic and TE-statistic) designed specifically to compare the behavior of the sample tail of distributions with power-law and exponential tails as a function of the lower threshold u. One important property of these statistics is that they converge to zero for power laws o…
Study shows how anisotropic data affects learning dynamics in phase retrieval.
Study shows how heavy-tailed Hawkes processes can model rough volatility in financial markets.
The paper investigates heavy-tailed behavior in offline SGD, showing it approximates power-law tails.
This work analyzes neural scaling laws using power-law data spectra and derives analytical expressions for generalization error.
This paper addresses the statistical properties of time series driven by rational bubbles a la Blanchard and Watson (1982), corresponding to multiplicative maps, whose study has recently be revived recently in physics as a mechanism of intermittent dynamics generating power law distributions. Using insights on the beha…
The study introduces a high-dimensional tail index model for viral post analysis.
Optimal trading strategy derived for nonlinear price impact models.
Models of auctions or tendering processes are introduced. In every round of bidding the players select their bid from a probability distribution and whenever a bid is unsuccessful, it is discarded and replaced. For simple models, the probability distributions evolve to a stationary power law with the exponent dependent…
New SDE model from machine learning optimization with unique stationary distribution.
A universal learner achieves best rates for all distributions.
We examine random variables in the power law/regularly varying class with stochastic tail exponent, the exponent having its own distribution. We show the effect of stochasticity of on the expectation and higher moments of the random variable. For instance, the moments of a right-tailed or right-asymmetric varia…
Superposition accelerates training to a universal power-law exponent.
Power laws detected in financial data, modeled with random multipliers.
Polynomial networks converge to Gaussian processes at a rate of O(n^(-1/2)).
Analyzes financial return distributions over various time scales.
Unified model explains market dynamics, linking order flow, volatility, and impact.
Study on KRR with power-law data, showing better sample complexity.
We use data on wealth of the richest persons taken from the "rich lists" provided by business magazines like Forbes to verify if upper tails of wealth distributions follow, as often claimed, a power-law behaviour. The data sets used cover the world's richest persons over 1996-2012, the richest Americans over 1988-2012,…
It is generally recognized that economical systems, and more in general complex systems, are characterized by power law distributions. Sometime, these distributions show a changing of the slope in the tail so that, more appropriately, they show a multi-power law behavior. We present a method to derive analytically a tw…
It has always been a great challenge for clustering algorithms to automatically determine the cluster numbers according to the distribution of datasets. Several approaches have been proposed to address this issue, including the recent promising work which incorporate Bayesian Nonparametrics into the -means clusterin…
Study non-integer power-law potentials for Schrödinger operators using Lie-Rinehart algebras.
The role of kernels is central to machine learning. Motivated by the importance of power-law distributions in statistical modeling, in this paper, we propose the notion of power-law kernels to investigate power-laws in learning problem. We propose two power-law kernels by generalizing Gaussian and Laplacian kernels. Th…
I consider the problem of the optimal limit order price of a financial asset in the framework of the maximization of the utility function of the investor. The analytical solution of the problem gives insight on the origin of the recently empirically observed power law distribution of limit order prices. In the framewor…
We introduce the stochastic multiplicative point process modelling trading activity of financial markets. Such a model system exhibits power-law spectral density S(f) ~ 1/f**beta, scaled as power of frequency for various values of beta between 0.5 and 2. Furthermore, we analyze the relation between the power-law autoco…
Non-Markovian point process shows power-law scaling, similar to nonlinear Markovian process.
In this paper we tackle the problem of estimating the power-law tail exponent of income distributions by using the Hill's estimator. A subsample semi-parametric bootstrap procedure minimising the mean squared error is used to choose the power-law cutoff value optimally. This technique is applied to personal income data…
We focus on emergence of the power-law cross-correlations from processes with both short and long term memory properties. In the case of correlated error-terms, the power-law decay of the cross-correlation function comes automatically with the characteristics of separate processes. Bivariate Hurst exponent is then equa…
We present a model for random simple graphs with a degree distribution that obeys a power law (i.e., is heavy-tailed). To attain this behavior, the edge probabilities in the graph are constructed from Bertoin-Fujita-Roynette-Yor (BFRY) random variables, which have been recently utilized in Bayesian statistics for the c…
Extends rough Heston model solution to general λ.
This note presents an operational measure of fat-tailedness for univariate probability distributions, in where 0 is maximally thin-tailed (Gaussian) and 1 is maximally fat-tailed. Among others,1) it helps assess the sample size needed to establish a comparative needed for statistical significance, 2) allows…
We introduce preferential behavior into the study on statistical mechanics of money circulation. The computer simulation results show that the preferential behavior can lead to power laws on distributions over both holding time and amount of money held by agents. However, some constraints are needed in generation mecha…
Paper proves SVV model reproduces power-law skew in implied volatilities.
One of the first steps to understand and forecast economic downturns is identifying their frequency distribution, but it remains uncertain. This problem is common in phenomena displaying power-law-like distributions. Power laws play a central role in complex systems theory; therefore, the current limitations in the ide…
We respond to the issues discussed by Farmer and Lillo (FL) related to our proposed approach to understanding the origin of power-law distributions in stock price fluctuations. First, we extend our previous analysis to 1000 US stocks and perform a new estimation of market impact that accounts for splitting of large ord…
Volatility models must be rough to match market skew.
Study uses OT to simulate markets, revealing power-law returns are driven by informational effect.
Auto-regressive conditionally heteroskedastic (ARCH) family models are still used, by practitioners in business and economic policy making, as a conditional volatility forecasting models. Furthermore ARCH models still are attracting an interest of the researchers. In this contribution we consider the well known GARCH(1…
The study finds significant power-law cross correlations in Bitcoin's return-volatility dynamics.
Robust CD method for real-world time series with power-law distributions.
Critical volatility triggers log-normal to power-law transitions in interconnected systems.
We study the relaxation dynamics of a financial market just after the occurrence of a crash by investigating the number of times the absolute value of an index return is exceeding a given threshold value. We show that the empirical observation of a power law evolution of the number of events exceeding the selected thre…
This work investigates power laws in deep neural network ensembles and predicts their performance.
Unified theory for neural scaling laws in hierarchically compositional data.
P2P lending activities have grown rapidly and have caused the huge and complex networks of debtor-creditor relationships. The aim of this study was to study the underlying structural characteristics of networks formed by debtor-creditor relationships. According attributes of P2P lending, this paper model the networks o…
We focus on power-law coherency as an alternative approach towards studying power-law cross-correlations between simultaneously recorded time series. To be able to study empirical data, we introduce three estimators of the power-law coherency parameter based on popular techniques usually utilized for studying pow…