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.
This paper investigates the statistical properties of within-country GDP and industrial production (IP) growth rate distributions. Many empirical contributions have recently pointed out that cross-section growth rates of firms, industries and countries all follow Laplace distributions. In this work, we test whether als…
Optimal learning rate schedules for SGD in changing data distributions.
problem Minimizing regret in online learning with changing data distributions.
method Characterized optimal schedules for linear regression, proposed schedules for general convex and non-convex losses, and defined a notion of regret for non-convex losses.
result Upper and lower bounds for regret with constants for convex losses, and an upper bound on total expected regret for non-convex losses.
We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling properties and distributions reported for growth rates of complex systems in a variety…
We study convergence rates of variational posterior distributions for nonparametric and high-dimensional inference. We formulate general conditions on prior, likelihood, and variational class that characterize the convergence rates. Under similar "prior mass and testing" conditions considered in the literature, the rat…
We introduce a new statistical test of the hypothesis that a balanced panel of firms have the same growth rate distribution or, more generally, that they share the same functional form of growth rate distribution. We applied the test to European Union and US publicly quoted manufacturing firms data, considering functio…
The paper analyzes and improves the learning rates of distributed kernel ridge regression.
problem Generalization performance and learning rates of distributed kernel ridge regression.
method The paper derives optimal learning rates for DKRR in expectation and probability, proposes a communication strategy to improve learning performance, and evaluates these through theory and experiments.
result The communication strategy significantly improves the learning performance of DKRR, as demonstrated by both theoretical assessments and numerical experiments.
We introduce a simple agent-based model which allows us to analyze three stylized facts: a fat-tailed size distribution of companies, a `tent-shaped' growth rate distribution, the scaling relation of the growth rate variance with firm size, and the causality between them. This is achieved under the simple hypothesis th…
Recent work on follow the perturbed leader (FTPL) algorithms for the adversarial multi-armed bandit problem has highlighted the role of the hazard rate of the distribution generating the perturbations. Assuming that the hazard rate is bounded, it is possible to provide regret analyses for a variety of FTPL algorithms f…
Motivated by machine learning applications in networks of sensors, internet-of-things (IoT) devices, and autonomous agents, we propose techniques for distributed stochastic convex learning from high-rate data streams. The setup involves a network of nodes---each one of which has a stream of data arriving at a constant …
New bounds on generalization error for distributed learning using rate-distortion theory.
problem Establishing upper bounds on generalization error for distributed learning algorithms.
method Using rate-distortion theory, the paper introduces new bounds that depend on the compressibility of each client's algorithm.
result The bounds suggest that the generalization error of the distributed setting decays faster than that of the centralized one with a factor of O(log(K)/K).
We consider a model for interest rates, where the short rate is given by a time-homogenous, one-dimensional affine process in the sense of Duffie, Filipovic and Schachermayer. We show that in such a model yield curves can only be normal, inverse or humped (i.e. endowed with a single local maximum). Each case can be cha…
Study improves distributional regression evaluation with CRPS, finding optimal rates of convergence.
problem Improving probabilistic forecasts in meteorology using distributional regression.
method Extends theoretical properties of CRPS evaluation to include covariates and finite sample sizes, analyzing convergence rates for different methods.
result Optimal minimax rate of convergence for distributional regression methods is achieved by k-nearest neighbor and kernel methods.
In large-scale distributed learning, security issues have become increasingly important. Particularly in a decentralized environment, some computing units may behave abnormally, or even exhibit Byzantine failures -- arbitrary and potentially adversarial behavior. In this paper, we develop distributed learning algorithm…
This paper corrects an error in [Keller-Ressel, M. and Steiner T. "Yield curve shapes and the asymptotic short rate distribution in affine one-factor models." Finance and Stochastics 12.2 (2008): 149-172]. The error concerns the correct expression for the boundary between normal and humped yield curve behavior in affin…
We study the tick dynamical behavior of the yen-dollar exchange rate using the rescaled range analysis in financial market. It is found that the multifractal Hurst exponents with the short and long-run memory effects can be obtained from the yen-dollar exchange rate. This exists one crossover for the Hurst exponents at…
We report the proof that the extension of Gibrat's law in the middle scale region is unique and the probability distribution function (pdf) is also uniquely derived from the extended Gibrat's law and the law of detailed balance. In the proof, two approximations are employed. The pdf of growth rate is described as tent-…
Research shows minimal communication limits adaptive function estimation rates.
problem Adaptive estimation of a smooth function under minimal communication constraints.
method Investigates the L∞-risk and L2-risk under different numbers of servers.
result For L∞-risk, optimal rates cannot be achieved under minimal communication. For L2-risk, adaptivity is possible but depends on server number and sample size.