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作者：Lyu, Zhongyuan; Xia, Dong
作者单位：Hong Kong University of Science & Technology
摘要：This article investigates the computational and statistical limits in clustering matrix-valued observations. We propose a low-rank mixture model (LrMM), adapted from the classical Gaussian mixture model (GMM), to handle matrix-valued observations, assuming low-rankness for population centre matrices. A computationally efficient clustering method is designed by integrating Lloyd's algorithm and low-rank approximation. Once well-initialized, the algorithm converges fast and achieves an exponenti...
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作者：Dong, Pinjun; Han, Ruijian; Jiang, Binyan; Xu, Yiming
作者单位：Zhejiang University; Hong Kong Polytechnic University; University of Kentucky
摘要：We introduce a general covariate-assisted statistical ranking model within the Plackett-Luce framework. Unlike previous studies that focus on individual effects with fixed covariates, our model allows covariates to vary across comparisons. This added flexibility enhances model fitting but also brings significant challenges in analysis. This article addresses these challenges in the context of maximum likelihood estimation (MLE). We first provide necessary and sufficient conditions for both mod...
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作者：Luedtke, Alex
作者单位：University of Washington; University of Washington Seattle
摘要：We introduce an algorithm that simplifies the construction of efficient estimators, making them accessible to a broader audience. 'Dimple' takes as input computer code representing a parameter of interest and outputs an efficient estimator. Unlike standard approaches, it does not require users to derive a functional derivative known as the efficient influence function. Dimple avoids this task by applying automatic differentiation to the statistical functional of interest. Doing so requires exp...
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作者：Wang, Fan; Li, Wanshan; Madrid Padilla, Oscar Hernan; Yu, Yi; Rinaldo, Alessandro
作者单位：University of Warwick; University of California System; University of California Los Angeles; University of Texas System; University of Texas Austin
摘要：We study the multilayer random dot product graph (MRDPG) model, a generalization of the random dot product graph model to multilayer networks. To estimate the edge probabilities, we deploy a tensor-based methodology and demonstrate its superiority over existing approaches. Moving to dynamic MRDPGs, we formulate and analyse an online change point detection framework, where, at each time point, we observe a realization from an MRDPG. Across layers, we assume fixed shared common node sets and lat...
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作者：Song, Shanshan; Wang, Tong; Shen, Guohao; Lin, Yuanyuan; Huang, Jian
作者单位：Tongji University; Tongji University; Chinese University of Hong Kong; Hong Kong Polytechnic University; Hong Kong Polytechnic University; Hong Kong Polytechnic University
摘要：In this paper, we propose a new and unified approach for nonparametric regression and conditional distribution learning. Our approach simultaneously estimates a regression function and a conditional generator using a generative learning framework, where a conditional generator is a function that can generate samples from a conditional distribution. The main idea is to estimate a conditional generator satisfying the constraint that it produces a good regression function estimator. We use deep n...
