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.
Deviation inequalities for stochastic approximation methods.
Deviation inequalities and limit laws for random walks on metric spaces.
New inequality criterion for a mean field equation on spheres.
We study random walks on groups with the feature that, roughly speaking, successive positions of the walk tend to be "aligned". We formalize and quantify this property by means of the notion of deviation inequalities. We show that deviation inequalities have several consequences including Central Limit Theorems, the lo…
New Gini indices capture more nuanced income inequality.
The paper improves inequalities for nearly spherical sets using quermassintegrals.
Novel concentration inequalities are obtained for the missing mass, i.e. the total probability mass of the outcomes not observed in the sample. We derive distribution-free deviation bounds with sublinear exponents in deviation size for missing mass and improve the results of Berend and Kontorovich (2013) and Yari Saeed…
In this paper, we study the risk bounds for samples independently drawn from an infinitely divisible (ID) distribution. In particular, based on a martingale method, we develop two deviation inequalities for a sequence of random variables of an ID distribution with zero Gaussian component. By applying the deviation ineq…
Proves inequality linking function deviation to gradient norm on compact manifolds.
We are concerned with obtaining novel concentration inequalities for the missing mass, i.e. the total probability mass of the outcomes not observed in the sample. We not only derive - for the first time - distribution-free Bernstein-like deviation bounds with sublinear exponents in deviation size for missing mass, but …
This paper presents new deviation inequalities that are valid uniformly in time under adaptive sampling in a multi-armed bandit model. The deviations are measured using the Kullback-Leibler divergence in a given one-dimensional exponential family, and may take into account several arms at a time. They are obtained by c…
Sharp inequalities for matrix means with unknown variance.
Stress shocks are often calculated as multiples of the standard deviation of a history set. This paper investigates how many standard deviations are required to guarantee that this shock exceeds any observation within the history set, given the additional constraint of kurtosis. The results of this analysis are then us…
Sharp concentration results for sums of heavy-tailed random variables.
In this paper, we study non-asymptotic deviation bounds of the least squares estimator in Gaussian AR() processes. By relying on martingale concentration inequalities and a tail-bound for distributed variables, we provide a concentration bound for the sample covariance matrix of the process output. With this, …
The paper provides bounds for high-dimensional U-statistics with novel order-explicit inequalities.
Study on discrepancy principle for learning algorithms in nonparametric regression.
Sharp concentration bounds for i.i.d. variables.
New inequality on sphere generalizes circle inequality.
In this paper, we are concerned with obtaining distribution-free concentration inequalities for mixture of independent Bernoulli variables that incorporate a notion of variance. Missing mass is the total probability mass associated to the outcomes that have not been seen in a given sample which is an important quantity…
Improved concentration inequalities for sub-Weibull variables enhance statistical and machine learning applications.
Paper develops a new inequality for non-causal machine learning.
Sharp upper bounds derived for Alexandrov-Fenchel deficit using weighted Minkowski integral formulas.
This article provides a new toolbox to derive sparse recovery guarantees from small deviations on extreme singular values or extreme eigenvalues obtained in Random Matrix Theory. This work is based on Restricted Isometry Constants (RICs) which are a pivotal notion in Compressed Sensing and High-Dimensional Statistics a…
Mounting evidences are being gathered suggesting that income and wealth distribution in various countries or societies follow a robust pattern, close to the Gibbs distribution of energy in an ideal gas in equilibrium, but also deviating significantly for high income groups. Application of physics models seem to provide…
We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in learning theory and generalization bounds for unbounded loss functions.
Paper extends nonparametric regression bounds for dependent -mixing samples.
Unified proof for various bandit algorithms with logarithmic regret.
We obtain a sharp lower bound on the isoperimetric deficit of a general polygon in terms of the variance of its side lengths, the variance of its radii, and its deviation from being convex. Our technique involves a functional minimization problem on a suitably constructed compact manifold and is based on the spectral t…
The paper proves inequalities for hyperbolic sets and curves.
We provide a brief tutorial on the use of concentration inequalities as they apply to system identification of state-space parameters of linear time invariant systems, with a focus on the fully observed setting. We draw upon tools from the theories of large-deviations and self-normalized martingales, and provide both d…
New algorithm reduces sketching dimension to effective problem size.
The paper characterizes Pólya's conjecture for spheres and hemispheres, deriving inequalities and bounds.
Trading strategy uses Hoeffding's Inequality to predict financial regime change.
We analyze the probabilistic variance of a solution of Liouville's equation for curvature, given suitable bounds on the Gaussian curvature. The related systolic geometry was recently studied by Horowitz, Katz, and Katz, where we obtained a strengthening of Loewner's torus inequality containing a "defect term", similar …
In this paper, we present the Bennett-type generalization bounds of the learning process for i.i.d. samples, and then show that the generalization bounds have a faster rate of convergence than the traditional results. In particular, we first develop two types of Bennett-type deviation inequality for the i.i.d. learning…
Short proof shows how ridge regression works with random data.
Study sharp inequalities for perimeter functionals in capillarity and convex cones.
The paper develops bounds for predictive values in binary classification.
Extends probabilistic approach for Kahler-Einstein metrics on Fano manifolds.
Paper develops robust methods for large-scale testing without tuning parameters.
Given a finite family of functions, the goal of model selection aggregation is to construct a procedure that mimics the function from this family that is the closest to an unknown regression function. More precisely, we consider a general regression model with fixed design and measure the distance between functions by …
Mathematical study of excess growth rate connects info theory with finance.
The study provides a theory for causal machine learning with generalization bounds.
Unified stopping rules ensure accurate policies in contextual learning.
In this paper, we propose a novel framework to analyze the theoretical properties of the learning process for a representative type of domain adaptation, which combines data from multiple sources and one target (or briefly called representative domain adaptation). In particular, we use the integral probability metric t…
Introduces Star-Shaped deviation measures for risk analysis.
Improved bounds for Monte Carlo Rademacher Averages using self-bounding functions.