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 analyzes error exponent in agnostic PAC learning.
Active-LATHE boosts error exponent for learning homogeneous trees.
Study analyzes deep learning's performance on variable exponent Besov space, highlighting adaptivity benefits.
Paper studies distributed learning with limited communication bits, achieving optimal error exponents.
Extends Nash-Kuiper theorem to higher Hölder exponents.
We characterize the asymptotic performance of nonparametric one- and two-sample testing. The exponential decay rate or error exponent of the type-II error probability is used as the asymptotic performance metric, and an optimal test achieves the maximum rate subject to a constant level constraint on the type-I error pr…
The problem of learning tree-structured Gaussian graphical models from independent and identically distributed (i.i.d.) samples is considered. The influence of the tree structure and the parameters of the Gaussian distribution on the learning rate as the number of samples increases is discussed. Specifically, the error…
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 …
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 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…
Adaptive algorithm identifies best arm with abstention, showing phase transition from polynomial to exponential error probability.
mfBm models and forecasts volatility with different Hurst exponents and correlations.
The study examines Kernel Ridge Regression error rates across noiseless and noisy conditions.
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…
New bounds link generalization to stochastic optimizer's lower tail exponents.
We study how the round-off (or discretization) error changes the statistical properties of a Gaussian long memory process. We show that the autocovariance and the spectral density of the discretized process are asymptotically rescaled by a factor smaller than one, and we compute exactly this scaling factor. Consequentl…
The higher-end tail of the wealth distribution in India is studied using recently published lists of the wealth of richest Indians between the years 2002-4. The resulting rank distribution seems to imply a power-law tail for the wealth distribution, with a Pareto exponent between 0.81 and 0.92 (depending on the year un…
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 empirically analyze the most volatile component of the electricity price time series from two North-American wholesale electricity markets. We show that these time series exhibit fluctuations which are not described by a Brownian Motion, as they show multi-scaling, high Hurst exponents and sharp price movements. We …
This paper is concerned with the squared F(robenius)-norm regularized factorization form for noisy low-rank matrix recovery problems. Under a suitable assumption on the restricted condition number of the Hessian for the loss function, we derive an error bound to the true matrix for the non-strict critical points with r…
New algorithm for multi-player bandits with collision-dependent rewards.
Direct measurements of Gini coefficients by conventional arithmetic calculations are a poor estimator, even if paradoxically, they include the entire population, as because of super-additivity they cannot lend themselves to comparisons between units of different size, and intertemporal analyses are vitiated by the popu…
How many training data are needed to learn a supervised task? It is often observed that the generalization error decreases as where is the number of training examples and an exponent that depends on both data and algorithm. In this work we measure when applying kernel methods to real datasets. For …
Gradient flossing stabilizes RNN training by controlling Lyapunov exponents.
This paper studies clustering of data sequences using the k-medoids algorithm. All the data sequences are assumed to be generated from \emph{unknown} continuous distributions, which form clusters with each cluster containing a composite set of closely located distributions (based on a certain distance metric between di…
New method approximates short immersions as C^{1,θ} isometric immersions for n ≥ 3.
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…
Bitcoin volatility analysis shows decreasing HE with longer sampling periods.
New learning rate approach reveals phase transitions in SGD performance.
Deep learning (DL) creates impactful advances following a virtuous recipe: model architecture search, creating large training data sets, and scaling computation. It is widely believed that growing training sets and models should improve accuracy and result in better products. As DL application domains grow, we would li…
We investigate the waiting-time distribution of the absolute return in the Korean stock-market index KOSPI. We define the waiting time as a time interval during which the normalized absolute return remains continuously below a threshold . Through an exponential bin plot, we observe that the waiting-time distributi…
Study shows how to learn optimal policies quickly in stochastic control problems.
Estimates roughness of volatility from discrete variance data.
Lyapunov exponents help understand RNN stability.
The paper studies entropy calibration in language models and finds that miscalibration improves slowly with scale.
The study shows how geometric Weyl bulk-density exponent rigidifies spectral encodings in O-regularly varying classes.
A single algebraic identity unifies information-theoretic variational results.
Study tests rough fractional volatility model across different time scales, revealing new volatility patterns.
We study nonzero-sum hypothesis testing games that arise in the context of adversarial classification, in both the Bayesian as well as the Neyman-Pearson frameworks. We first show that these games admit mixed strategy Nash equilibria, and then we examine some interesting concentration phenomena of these equilibria. Our…
We consider the binomial approximation of the American put price in the Black-Scholes model (with continuous dividend yield). Our main result is that the error of approximation is α where n is the number of time periods and the exponent is a positive number, the value of which may differ according …
Paper relaxes symmetry conditions for universal feature selection in noisy data.
Neural network learns low-dimensional polynomials with SGD near information-theoretic limit.
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…
New proof for certain groups in higher dimensions.
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…
RQMC improves kernel-based learning by reducing deterministic error and offering computational advantages.