相关论文: On Concentration and Revisited Large Deviations An…

This paper gives a review of concentration inequalities which are widely employed in non-asymptotical analyses of mathematical statistics in a wide range of settings, from distribution-free to distribution-dependent, from sub-Gaussian to…

In this article, we derive concentration inequalities for the cross-validation estimate of the generalization error for stable predictors in the context of risk assessment. The notion of stability has been first introduced by \cite{DEWA79}…

We introduce estimation and test procedures through divergence optimization for discrete or continuous parametric models. This approach is based on a new dual representation for divergences. We treat point estimation and tests for simple…

Score-based statistical models play an important role in modern machine learning, statistics, and signal processing. For hypothesis testing, a score-based hypothesis test is proposed in \cite{wu2022score}. We analyze the performance of this…

A refinement of Bennett's inequality is introduced which is strictly tighter than the classical bound. The new bound establishes the convergence of the average of independent random variables to its expected value. It also carefully…

Softmax distributions are widely used in machine learning, including Large Language Models (LLMs), where the attention unit uses softmax distributions. We abstract the attention unit as the softmax model, where given a vector input, the…

In statistical inference problems, we wish to obtain lower bounds on the minimax risk, that is to bound the performance of any possible estimator. A standard technique to obtain risk lower bounds involves the use of Fano's inequality. In an…

This paper proposes self-normalized tests for multistep conditional predictive ability in forecast comparison. By normalizing the sample mean of the transformed loss differential using functionals of its cumulative sum (CUSUM) process,…

The hypothesis of randomness is fundamental in statistical machine learning and in many areas of nonparametric statistics; it says that the observations are assumed to be independent and coming from the same unknown probability…

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…

We develop a recursive approach for deriving closed-form solutions to both conditional and unconditional moments of affine jump diffusions with state-independent jump intensities. Using these moment solutions, we construct closed-form…

Constant-specified and exponential concentration inequalities play an essential role in the finite-sample theory of machine learning and high-dimensional statistics area. We obtain sharper and constants-specified concentration inequalities…

Differential analysis is a routine procedure in the statistical analysis toolbox across many applied fields, including quantitative proteomics, the main illustration of the present paper. The state-of-the-art limma approach uses a…

In this paper, we derive a new version of Hanson-Wright inequality for a sparse bilinear form of sub-Gaussian variables. Our results are generalization of previous deviation inequalities that consider either sparse quadratic forms or dense…

The concept of refinement from probability elicitation is considered for proper scoring rules. Taking directions from the axioms of probability, refinement is further clarified using a Hilbert space interpretation and reformulated into the…

In applied settings, tests of hypothesis where a nuisance parameter is only identifiable under the alternative often reduces into one of Testing One Hypothesis Multiple times (TOHM). Specifically, a fine discretization of the space of the…

This paper concerns the construction of tests for universal hypothesis testing problems, in which the alternate hypothesis is poorly modeled and the observation space is large. The mismatched universal test is a feature-based technique for…

This paper establishes sharp dimension-free concentration and expectation bounds for the deviation of a sample cross-covariance matrix from its mean. For sub-Gaussian random vectors, we prove a high-probability operator-norm bound governed…

We investigate the parameter recovery of Markov-switching ordinary differential processes from discrete observations, where the differential equations are nonlinear additive models. This framework has been widely applied in biological…

We consider large-scale studies in which thousands of significance tests are performed simultaneously. In some of these studies, the multiple testing procedure can be severely biased by latent confounding factors such as batch effects and…