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.
Simple bounds for covariance and Gram matrices across various settings.
New margin-based learning guarantees improve generalization bounds.
In a coordinate free form are found the (deviation) equations satisfied by the (infinitesimal) deviation vector, relative velocity, relative momentum, relative acceleration and relative energy of two point particles in a differentiable manifold the tangent bundle of which is endowed with a linear transport along paths,…
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.
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…
Study large deviations in life insurance portfolios without identical distributions.
The study optimizes distribution estimation from samples with relative entropy error, adapting to sparse distributions.
How can we design safe reinforcement learning agents that avoid unnecessary disruptions to their environment? We show that current approaches to penalizing side effects can introduce bad incentives, e.g. to prevent any irreversible changes in the environment, including the actions of other agents. To isolate the source…
The concepts of relative velocity and acceleration, deviation velocity and acceleration and relative momentum of point particles in spaces (manifolds), the tangent bundle of which is equipped with a transport along paths, are introduced. If the tangent bundle is endowed also with a metric, it gives rise also to the not…
New DP algorithms with margin guarantees for various hypothesis sets.
MPC framework reduces execution costs and schedule deviations in trading.
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, …
New method improves optimization algorithms without Lipschitz smoothness.
Proposes new deviation measures using Minkowski gauges.
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…
Study large deviations rates for SGD with strongly convex functions.
Large deviations for fat tailed distributions, i.e. those that decay slower than exponential, are not only relatively likely, but they also occur in a rather peculiar way where a finite fraction of the whole sample deviation is concentrated on a single variable. The regime of large deviations is separated from the regi…
We quantify the sensitivity of the Eisenberg-Noe clearing vector to estimation errors in the bilateral liabilities of a financial system in a stylized setting. The interbank liabilities matrix is a crucial input to the computation of the clearing vector. However, in practice central bankers and regulators must often es…
Deviation inequalities and limit laws for random walks on metric spaces.
In this paper, we derive generic bounds on the maximum deviations in prediction errors for sequential prediction via an information-theoretic approach. The fundamental bounds are shown to depend only on the conditional entropy of the data point to be predicted given the previous data points. In the asymptotic case, the…
Researchers introduce a method to assess the safety of interpretable machine learning models.
Uniform deviation bounds limit the difference between a model's expected loss and its loss on an empirical sample uniformly for all models in a learning problem. As such, they are a critical component to empirical risk minimization. In this paper, we provide a novel framework to obtain uniform deviation bounds for loss…
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…
We prove polynomial upper bounds for the deviation of ergodic averages for the straight line flow on every translation surface in almost every direction, in particular for those surfaces arising from rational polygonal billiards.
Method generates plausible financial stress scenarios using large deviations.
Improved median of means estimator with tighter bounds.
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…
Large deviation principle for deep neural networks with ReLU activation.
Study on U-statistics with heavy-tailed samples, providing tail bounds and LDP.
The paper provides a new uniform tail bound for empirical processes.
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…
The paper improves inequalities for nearly spherical sets using quermassintegrals.
Sharp concentration bounds for i.i.d. variables.
Sharp bounds for Dirichlet sums lead to improved Bayesian algorithm analysis.
This paper describes a new online convex optimization method which incorporates a family of candidate dynamical models and establishes novel tracking regret bounds that scale with the comparator's deviation from the best dynamical model in this family. Previous online optimization methods are designed to have a total a…
We prove a Weyl-type fractal upper bound for the spectrum of the damped wave equation, on a negatively curved compact manifold. It is known that most of the eigenvalues have an imaginary part close to the average of the damping function. We count the number of eigenvalues in a given horizontal strip deviating from this…
MOVDA improves skill ratings by considering margin of victory deviations.
Three training methods for language models are shown to be variations of one another.
Paper quantifies label shift robustly.
This paper achieves optimal regret bounds for locally private linear contextual bandit.
The cross-correlations between price fluctuations of 201 frequently traded stocks in the National Stock Exchange (NSE) of India are analyzed in this paper. We use daily closing prices for the period 1996-2006, which coincides with the period of rapid transformation of the market following liberalization. The eigenvalue…
Machine learning classifies gravitational wave signals to test General Relativity.
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…
We clarify what fairness guarantees we can and cannot expect to follow from unconstrained machine learning. Specifically, we characterize when unconstrained learning on its own implies group calibration, that is, the outcome variable is conditionally independent of group membership given the score. We show that under r…
Improved bounds for Monte Carlo Rademacher Averages using self-bounding functions.
Vanishing gradients hinder reinforcement finetuning of language models.
We study two-layer belief networks of binary random variables in which the conditional probabilities Pr[childlparents] depend monotonically on weighted sums of the parents. In large networks where exact probabilistic inference is intractable, we show how to compute upper and lower bounds on many probabilities of intere…
Study compares costs and arbitrage in CEXs vs DEXs, finding DEXs better for large trades.