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Bordino 与 Klopp 对《流形假说的统计探索》的讨论AI 解读

We congratulate the authors on an insightful, practice-grounded contribution showing how manifold-like structure can arise naturally from a broad latent metric space (LMS) model. We especially commend the ‘practice-first’ perspective: beginning with pipelines common among practitioners (e.g. PCA to moderate dimension, then t-SNE/UMAP), and then developing theory that explains why such workflows succeed. We shall now comment on a point where practitioners may require further…

通过逐次投影为文档分配主题AI 解读

Topic models provide a useful tool to organize and understand the structure of large corpora of text documents, in particular, to discover hidden thematic structure. Clustering documents from big unstructured corpora into topics is an important task in various fields, such as image analysis, e-commerce, social networks and population genetics. Since the number of topics is typically substantially smaller than the size of the corpus and of the dictionary, the methods of topic…

混合与不完整数据表中的主效应和交互作用AI 解读

A mixed data frame (MDF) is a table collecting categorical, numerical, and count observations. The use of MDF is widespread in statistics and the applications are numerous from abundance data in ecology to recommender systems. In many cases, an MDF exhibits simultaneously main effects, such as row, column, or group effects and interactions, for which a low-rank model has often been suggested. Although the literature on low-rank approximations is very substantial, with few…

网络模型的预言不等式与稀疏 graphon 估计AI 解读

Inhomogeneous random graph models encompass many network models such as stochastic block models and latent position models. We consider the problem of statistical estimation of the matrix of connection probabilities based on the observations of the adjacency matrix of the network. Taking the stochastic block model as an approximation, we construct estimators of network connection probabilities—the ordinary block constant least squares estimator, and its restricted version.…

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…