arXiv research

Study large deviations in life insurance portfolios without identical distributions.

The paper provides a finite-sample deviation bound for stable autoregressive processes.

Simple bounds for covariance and Gram matrices across various settings.

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.

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.

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.

New margin-based learning guarantees improve generalization bounds.

Sharp bounds for Dirichlet sums lead to improved Bayesian algorithm analysis.

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…

Paper quantifies label shift robustly.

This paper achieves optimal regret bounds for locally private linear contextual bandit.

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…

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 bounds for Monte Carlo Rademacher Averages using self-bounding functions.

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…

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.

The paper provides bounds for high-dimensional U-statistics with novel order-explicit inequalities.

Random walks on hyperbolic spaces follow predictable large deviation principles.

Exact LAD line fitting via PALB with linear scaling and speed.

The paper develops bounds for predictive values in binary classification.

We study utility indifference prices and optimal purchasing quantities for a non-traded contingent claim in an incomplete semi-martingale market with vanishing hedging errors. We make connections with the theory of large deviations. We concentrate on sequences of semi-complete markets where in the $n^{th}$ market, the …

The paper improves generative models to avoid replicating observed examples.

Suppose $k$ centers are fit to $m$ points by heuristically minimizing the $k$-means cost; what is the corresponding fit over the source distribution? This question is resolved here for distributions with $p\geq 4$ bounded moments; in particular, the difference between the sample cost and distribution cost decays with $…

Identifies arms with rewards significantly different from the majority.

This paper introduces a new bound to explain generalization in over-parameterized models.

Optimal adaptive experiment for choosing best treatment with binary outcomes.

We analyze cross-correlations between price fluctuations of different stocks using methods of random matrix theory (RMT). Using two large databases, we calculate cross-correlation matrices C of returns constructed from (i) 30-min returns of 1000 US stocks for the 2-yr period 1994--95 (ii) 30-min returns of 881 US stock…

Sharp large deviations and Gibbs conditioning for portfolio credit risk models.

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 …

Improved bounds for estimating discrete distributions in KL divergence.

Introduces Star-Shaped deviation measures for risk analysis.

We study contextual linear bandit problems under feature uncertainty, where the features are noisy and have missing entries. To address the challenges posed by this noise, we analyze Bayesian oracles given the observed noisy features. Our Bayesian analysis reveals that the optimal hypothesis can significantly deviate f…

Paper extends nonparametric regression bounds for dependent $\beta$-mixing samples.

Improved adaptive algorithms for identifying the best arm in MABs with fixed budget.