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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Kahler geometry methods in Gaussian Gabor frame theory
高斯 Gabor框架理论 Kahler几何
2023/11/6
We investigate the frame set of regular multivariate Gaussian Gabor frames using methods from Kahler geometry such as Hormander's $\dbar$-L2 estimate with singular weight, Demailly's Calabi--Yau metho...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A Sparse Expansion of (Deep) Gaussian Processes
深层 高斯过程 稀疏展开
2023/4/18
Conventional inferential methods for (deep) Gaussian Processes models can suffer from high computational complexity as they require large-scale operations with kernel matrices for training and inferen...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：mcGP: mesh-clustered Gaussian process emulator for partial differential equation systems
mcGP 偏微分方程组 网格聚类 高斯过程 仿真器
2023/4/18
Partial differential equations (PDEs) have become an essential tool for modeling complex physical systems. Such equations are typically solved numerically via mesh-based methods, such as the finite el...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Functional-Input Gaussian Processes
泛函 输入 高斯过程
2023/4/25
Surrogate modeling based on Gaussian processes (GPs) has received increasing attention in the analysis of complex problems in science and engineering. Despite extensive studies on GP modeling, the dev...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Percolation in Strongly Correlated Systems: The Massless Gaussian Field
强相关系统 渗透 无质量 高斯场
2023/5/5
In this talk, we will show several results for correlated nearest neighbor site percolation on Z^d. In particular, we will show that in three dimensions the strongly correlated massless harmonic cryst...
A Gaussian upper bound for the iterated kernels of Markov chains is obtained under some natural conditions. This result applies in particular to simple random walks on any locally compact unimodular g...
On large deviations in testing simple hypotheses for locally stationary Gaussian processes
Hypothesis testing Likelihood ratio Large deviations Locally stationary Gaussian processes Hoeffding bound Stein’s lemma Chernoff bound
2015/8/25
We derive a large deviation result for the log-likelihood ratio for testing simple hypotheses in locally stationary Gaussian processes. This result allows us to find explicitly the rates of exponentia...
Asymptotic Equivalence of Spectral Density Estimation and Gaussian White Noise
Stationary Gaussian process spectral density Sobolev classes Le Cam distance asymptotic equivalence Whittle likelihood log-periodogram regression nonparametric Gaussian scale model signal in Gaussian white noise
2015/8/25
We consider the statistical experiment given by a sample y(1), . . . , y(n) of a stationary Gaussian process with an unknown smooth spectral density f. Asymptotic equivalence, in the sense of Le Cam’s...
ASYMPTOTIC EQUIVALENCE OF SPECTRAL DENSITY ESTIMATION AND GAUSSIAN WHITE NOISE
ASYMPTOTIC EQUIVALENCE SPECTRAL DENSITY ESTIMATION GAUSSIAN WHITE NOISE
2015/8/25
We consider the statistical experiment given by a sample y(1), . . . , y(n) of a stationary Gaussian process with an unknown smooth spectral density f . Asymptotic equivalence, in the sense of Le Cam’...
ASYMPTOTIC EQUIVALENCE OF DENSITY ESTIMATION AND GAUSSIAN WHITE NOISE
ASYMPTOTIC EQUIVALENCE DENSITY ESTIMATION GAUSSIAN WHITE NOISE
2015/8/25
Signal recovery in Gaussian white noise with variance tending to zero has served for some time as a representative model for nonparametric curve estimation, having all the essential traits in a pure f...
Asymptotic Equivalence of Density Estimation and Gaussian White Noise
Asymptotic Equivalence Density Estimation Gaussian White Noise
2015/8/25
Signal recovery in Gaussian white noise with variance tending to zero has served for some time as a representative model for nonparametric curve estimation, having all the essential traits in a pure f...
Optimal Multiple Testing Under a Gaussian Prior on the Effect Sizes
Effect Sizes Multiple Testing
2015/8/21
We develop a new method for frequentist multiple testing with Bayesian prior information.
Our procedure nds a new set of optimal p-value weights called the Bayes weights. Prior
information is relev...
The LASSO risk for gaussian matrices
Noisy linear observation vector image processing the matrix sequence
2015/8/20
We consider the problem of learning a coecient vector x0 2 R N from noisy linear observation y = Ax0 + w 2 R n. In many contexts (ranging from model selection to image processing) it is desirable to ...
In previous works, we showed that the internal DLA cluster on Zd with t particles is almost surely spherical up to a maximal error of O(log t) if d = 2 and O(√log t) if d ≥ 3. This paper addresses “av...
Mixed state estimation for a linear Gaussian Markov model
Discrete dynamical system Boolean state of continuous linear transmission Boolean state variables noise markov chain
2015/8/10
We consider a discrete-time dynamical system with Boolean and continuous states, with the continuous state propagating linearly in the continuous and Boolean state variables, and an additive Gaussian ...