A covariance representation and an elementary proof of the Gaussian concentration inequality
- URL: http://arxiv.org/abs/2410.06937v1
- Date: Wed, 9 Oct 2024 14:30:55 GMT
- Title: A covariance representation and an elementary proof of the Gaussian concentration inequality
- Authors: Christian Houdré,
- Abstract summary: Via a covariance representation based on characteristic functions, a known elementary proof of the Gaussian concentration inequality is presented.
A few other applications are briefly mentioned.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Via a covariance representation based on characteristic functions, a known elementary proof of the Gaussian concentration inequality is presented. A few other applications are briefly mentioned.
Related papers
- Theoretical Insights for Diffusion Guidance: A Case Study for Gaussian
Mixture Models [59.331993845831946]
Diffusion models benefit from instillation of task-specific information into the score function to steer the sample generation towards desired properties.
This paper provides the first theoretical study towards understanding the influence of guidance on diffusion models in the context of Gaussian mixture models.
arXiv Detail & Related papers (2024-03-03T23:15:48Z) - Causal Modeling with Stationary Diffusions [89.94899196106223]
We learn differential equations whose stationary densities model a system's behavior under interventions.
We show that they generalize to unseen interventions on their variables, often better than classical approaches.
Our inference method is based on a new theoretical result that expresses a stationarity condition on the diffusion's generator in a reproducing kernel Hilbert space.
arXiv Detail & Related papers (2023-10-26T14:01:17Z) - Approximation of optimization problems with constraints through kernel
Sum-Of-Squares [77.27820145069515]
We show that pointwise inequalities are turned into equalities within a class of nonnegative kSoS functions.
We also show that focusing on pointwise equality constraints enables the use of scattering inequalities to mitigate the curse of dimensionality in sampling the constraints.
arXiv Detail & Related papers (2023-01-16T10:30:04Z) - A note on the smallest eigenvalue of the empirical covariance of causal
Gaussian processes [1.223779595809275]
We present a proof for bounding the smallest eigenvalue of the empirical covariance in a causal Gaussian process.
We establish a one-sided tail inequality for Gaussian quadratic forms using a causal decomposition.
arXiv Detail & Related papers (2022-12-19T14:44:37Z) - SARAH-based Variance-reduced Algorithm for Stochastic Finite-sum
Cocoercive Variational Inequalities [137.6408511310322]
We consider the problem of finite-sum cocoercive variational inequalities.
For strongly monotone problems it is possible to achieve linear convergence to a solution using this method.
arXiv Detail & Related papers (2022-10-12T08:04:48Z) - Generalized Talagrand Inequality for Sinkhorn Distance using Entropy
Power Inequality [28.676190269627828]
We prove an HWI-type inequality making use of the infinitesimal displacement convexity of optimal transport map.
We derive two Talagrand-type inequalities using the saturation of EPI that corresponds to a numerical term in our expression.
arXiv Detail & Related papers (2021-09-17T09:44:27Z) - Some Hoeffding- and Bernstein-type Concentration Inequalities [47.24550702683417]
We prove concentration inequalities for functions of independent random variables under sub-gaussian and sub-exponential conditions.
The utility of the inequalities is demonstrated by an extension of the now classical method of Rademacher complexities to Lipschitz function classes and unbounded sub-exponential distribution.
arXiv Detail & Related papers (2021-02-11T23:09:13Z) - Concentration inequality for U-statistics of order two for uniformly
ergodic Markov chains [0.0]
We prove a concentration inequality for U-statistics of order two for uniformly ergodic Markov chains.
We show that we can recover the convergence rate of Arcones and Gin'e who proved a concentration result for U-statistics of independent random variables and canonical kernels.
arXiv Detail & Related papers (2020-11-20T15:14:34Z) - On the complex behaviour of the density in composite quantum systems [62.997667081978825]
We study how the probability of presence of a particle is distributed between the two parts of a composite fermionic system.
We prove that it is a non-perturbative property and we find out a large/small coupling constant duality.
Inspired by the proof of KAM theorem, we are able to deal with this problem by introducing a cut-off in energies that eliminates these small denominators.
arXiv Detail & Related papers (2020-04-14T21:41:15Z) - Some compact notations for concentration inequalities and user-friendly
results [2.7920304852537536]
The new expressions describe the typical sizes and tails of random variables.
They bridge classical notations and modern non-asymptotic tail bounds together.
arXiv Detail & Related papers (2019-12-31T18:03:19Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.