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通过预测分配实现超大规模网络社区检测AI 解读

Massive network datasets are becoming increasingly common in scientific applications. Existing community detection methods encounter significant computational challenges for such massive networks due to two reasons. First, the full network needs to be stored and analyzed on a single server, leading to high memory costs. Second, existing methods typically use matrix factorization or iterative optimization using the full network, resulting in high runtimes. We propose a…

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对《非参数经验贝叶斯分析的置信区间》的讨论AI 解读

We would like to start with congratulating the authors. Empirical Bayes estimation is a very old, well studied problem. However, construction of confidence intervals in empirical Bayes setting has ...

动态网络模型与图函数估计AI 解读

In the present paper, we consider a dynamic stochastic network model. The objective is estimation of the tensor of connection probabilities $\mathbf{{\Lambda}}$ when it is generated by a Dynamic Stochastic Block Model (DSBM) or a dynamic graphon. In particular, in the context of the DSBM, we derive a penalized least squares estimator $\widehat{\boldsymbol{\Lambda}}$ of $\mathbf{{\Lambda}}$ and show that $\widehat{\boldsymbol{\Lambda}}$ satisfies an oracle inequality and also…

有无稀疏性时反卷积密度线性泛函估计的极小极大理论AI 解读

The present paper considers the problem of estimating a linear functional $\Phi=\int_{-\infty}^{\infty}\varphi(x)f(x)\,dx$ of an unknown deconvolution density $f$ on the basis of $n$ i.i.d. observations, $Y_{1},\ldots,Y_{n}$ of $Y=\theta+\xi$, where $\xi$ has a known pdf $g$, and $f$ is the pdf of $\theta$. The objective of the present paper is to develop the a general minimax theory of estimating $\Phi$, and to relate this problem to estimation of functionals $\Phi_{n}=n^{-1}\sum_{i=1}^{n}\varphi(\theta_{i})$…

基于时域数据的拉普拉斯反卷积及其动态对比增强成像应用AI 解读

Summary We consider the problem of Laplace deconvolution with noisy discrete non-equally spaced observations on a finite time interval. We propose a new method for Laplace deconvolution which is based on expansions of the convolution kernel, the unknown function and the observed signal over a Laguerre functions basis (which acts as a surrogate eigenfunction basis of the Laplace convolution operator) using a regression setting. The expansion results in a small system of…

利用过完备字典求解线性不适定问题AI 解读

In the present paper, we consider the application of overcomplete dictionaries to the solution of general ill-posed linear inverse problems. In the context of regression problems, there has been an enormous amount of effort to recover an unknown function using an overcomplete dictionary. One of the most popular methods, Lasso and its variants, is based on maximizing the likelihood, and relies on stringent assumptions on the dictionary, the so-called compatibility conditions,…

稀疏高维变系数模型的非渐近极小极大研究AI 解读

The objective of the present paper is to develop a minimax theory for the varying coefficient model in a nonasymptotic setting. We consider a high-dimensional sparse varying coefficient model where only few of the covariates are present and only some of those covariates are time dependent. Our analysis allows the time-dependent covariates to have different degrees of smoothness and to be spatially inhomogeneous. We develop the minimax lower bounds for the quadratic risk and…

含潜在奇异点的空间非均匀线性逆问题AI 解读

The objective of the present paper is to introduce the concept of a spatially inhomogeneous linear inverse problem where the degree of ill-posedness of operator $Q$ depends not only on the scale but also on location. In this case, the rates of convergence are determined by the interaction of four parameters, the smoothness and spatial homogeneity of the unknown function $f$ and degrees of ill-posedness and spatial inhomogeneity of operator $Q$. Estimators obtained in the…

函数反卷积模型的收敛率等价性与采样策略AI 解读

Using the asymptotical minimax framework, we examine convergence rates equivalency between a continuous functional deconvolution model and its real-life discrete counterpart over a wide range of Besov balls and for the L2-risk. For this purpose, all possible models are divided into three groups. For the models in the first group, which we call uniform, the convergence rates in the discrete and the continuous models coincide no matter what the sampling scheme is chosen, and…

周期设定下的函数型反卷积：均匀情形AI 解读

We extend deconvolution in a periodic setting to deal with functional data. The resulting functional deconvolution model can be viewed as a generalization of a multitude of inverse problems in mathematical physics where one needs to recover initial or boundary conditions on the basis of observations from a noisy solution of a partial differential equation. In the case when it is observed at a finite number of distinct points, the proposed functional deconvolution model can…

正态均值问题中贝叶斯检验与估计结合方法的最优性AI 解读

We consider a problem of recovering a high-dimensional vector μ observed in white noise, where the unknown vector μ is assumed to be sparse. The objective of the paper is to develop a Bayesian formalism which gives rise to a family of l0-type penalties. The penalties are associated with various choices of the prior distributions πn(⋅) on the number of nonzero entries of μ and, hence, are easy to interpret. The resulting Bayesian estimators lead to a general thresholding rule…

高斯与非高斯噪声下贝叶斯小波收缩规则的频率学派最优性AI 解读

The present paper investigates theoretical performance of various Bayesian wavelet shrinkage rules in a nonparametric regression model with i.i.d. errors which are not necessarily normally distributed. The main purpose is comparison of various Bayesian models in terms of their frequentist asymptotic optimality in Sobolev and Besov spaces. We establish a relationship between hyperparameters, verify that the majority of Bayesian models studied so far achieve theoretical…

非参数密度反卷积的自适应小波估计量AI 解读

The problem of estimating a density $g$ based on a sample $X_1, X_2,\dots, X_n$ from $p = q*g$ is considered. Linear and nonlinear wavelet estimators based on Meyer-type wavelets are constructed. The estimators are asymptotically optimal and adaptive if $g$ belongs to the Sobolev space $H^{\alpha}$ . Moreover, the estimators considered in this paper adjust automatically to the situation when $g$ is supersmooth.