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非同质多层网络的全局与逐层社区检测AI 解读

In network applications, it has become increasingly common to obtain datasets in the form of multiple networks observed on the same set of subjects, where each network is obtained in a related but different experiment condition or application scenario. Such datasets can be modeled by multilayer networks where each layer is a separate network itself while different layers are associated and share some common information. The present paper studies community detection in a…

尖峰随机矩阵模型中的最优信号检测：似然比检验与线性谱统计量AI 解读

We study signal detection by likelihood ratio tests in a number of spiked random matrix models, including but not limited to Gaussian mixtures and spiked Wishart covariance matrices. We work directly with multi-spiked cases in these models and with flexible priors on signal components that allow dependence across spikes. We derive asymptotic normality for the log-likelihood ratios when the signal-to-noise ratios are below certain bounds. In addition, the log-likelihood…

对《通过边抽样进行网络交叉验证》的讨论AI 解读

We congratulate the authors for their exciting paper (Li et al., 2020) on the difficult problem of network model selection. The authors have proposed an interesting cross-validation procedure that selects the best network model according to the criterion ... One of the main novelties of the method is the use of matrix completion to reconstruct a full network |$\{\skew6\hat{A}_{ij}\}_{1\leq i\neq j\leq n}$| from the partial set of observations |$\{A_{ij}\}_{(i,\,j)\in\Omega}$|…

度修正块模型中的社区检测AI 解读

Community detection is a central problem of network data analysis. Given a network, the goal of community detection is to partition the network nodes into a small number of clusters, which could often help reveal interesting structures. The present paper studies community detection in Degree-Corrected Block Models (DCBMs). We first derive asymptotic minimax risks of the problem for a misclassification proportion loss under appropriate conditions. The minimax risks are shown…

稀疏典型相关分析：自适应估计与计算障碍AI 解读

Canonical correlation analysis is a classical technique for exploring the relationship between two sets of variables. It has important applications in analyzing high dimensional datasets originated from genomics, imaging and other fields. This paper considers adaptive minimax and computationally tractable estimation of leading sparse canonical coefficient vectors in high dimensions. Under a Gaussian canonical pair model, we first establish separate minimax estimation rates…

连续处理效应双重稳健估计的非参数方法AI 解读

Summary Continuous treatments (e.g. doses) arise often in practice, but many available causal effect estimators are limited by either requiring parametric models for the effect curve, or by not allowing doubly robust covariate adjustment. We develop a novel kernel smoothing approach that requires only mild smoothness assumptions on the effect curve and still allows for misspecification of either the treatment density or outcome regression. We derive asymptotic properties and…

阈值化 Wirtinger 流实现含噪稀疏相位恢复的最优收敛速率AI 解读

This paper considers the noisy sparse phase retrieval problem: recovering a sparse signal $\mathbf{x}\in\mathbb{R}^{p}$ from noisy quadratic measurements $y_{j}=(\mathbf{a}_{j}'\mathbf{x})^{2}+\varepsilon_{j}$, $j=1,\ldots,m$, with independent sub-exponential noise $\varepsilon_{j}$. The goals are to understand the effect of the sparsity of $\mathbf{x}$ on the estimation precision and to construct a computationally feasible estimator to achieve the optimal rates adaptively.…

稀疏典型相关分析中的极小极大估计AI 解读

Canonical correlation analysis is a widely used multivariate statistical technique for exploring the relation between two sets of variables. This paper considers the problem of estimating the leading canonical correlation directions in high-dimensional settings. Recently, under the assumption that the leading canonical correlation directions are sparse, various procedures have been proposed for many high-dimensional applications involving massive data sets. However, there…

《自适应非参数贝叶斯可信集的频率学覆盖》讨论AI 解读

Discussion of "Frequentist coverage of adaptive nonparametric Bayesian credible sets" by Szab\'o, van der Vaart and van Zanten [arXiv:1310.4489v5].

极小极大子矩阵检测的计算障碍AI 解读

This paper studies the minimax detection of a small submatrix of elevated mean in a large matrix contaminated by additive Gaussian noise. To investigate the tradeoff between statistical performance and computational cost from a complexity-theoretic perspective, we consider a sequence of discretized models which are asymptotically equivalent to the Gaussian model. Under the hypothesis that the planted clique detection problem cannot be solved in randomized polynomial time…

非参数回归函数的自适应置信带AI 解读

A new formulation for the construction of adaptive confidence bands in non-parametric function estimation problems is proposed. Confidence bands are constructed which have size that adapts to the smoothness of the function while guaranteeing that both the relative excess mass of the function lying outside the band and the measure of the set of points where the function lies outside the band are small. It is shown that the bands adapt over a maximum range of Lipschitz…

稀疏主成分分析：最优收敛率与自适应估计AI 解读

Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. This paper considers both minimax and adaptive estimation of the principal subspace in the high dimensional setting. Under mild technical conditions, we first establish the optimal rates of convergence for estimating the principal subspace which are sharp with respect to all the parameters, thus providing a complete characterization of the difficulty…

稀疏主成分分析与迭代阈值化AI 解读

Principal component analysis (PCA) is a classical dimension reduction method which projects data onto the principal subspace spanned by the leading eigenvectors of the covariance matrix. However, it behaves poorly when the number of features $p$ is comparable to, or even much larger than, the sample size $n$. In this paper, we propose a new iterative thresholding approach for estimating principal subspaces in the setting where the leading eigenvectors are sparse. Under a…

分布依赖的可折叠性AI 解读

Summary Cox and Wermuth proposed that the partial derivative of the conditional distribution function of a random variable Y given another X is used for measuring association between two variables with arbitrary distributions. The paper presents a necessary and sufficient condition for uniform collapsibility of this association measure over a third variable W.