具有隐稀疏正则化的有效张量回归

Ko-Shin Chen, Tingyang Xu, Guannan Liang, Qianqian Tong, Minghu Song, J. Bi
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引用次数: 1

摘要

随着数据采集技术的进步,纵向分析面临着从高维数据中探索复杂特征模式和建模特征对响应的潜在时间滞后效应的挑战。我们提出了一种基于张量的多维数据分析模型。它同时发现特征中的模式,并揭示在过去时间点观察到的特征是否对当前结果有影响。模型系数,一个k模张量,被分解成k个相同维度张量的总和。我们引入了一个所谓的潜在F-1范数,它可以应用于系数张量来进行特征的结构化选择。具体来说,将沿着张量的每个模式选择特征。该模型通过采用基于张量的二次推理函数考虑了主体内的相关性。渐近分析表明,当样本量接近无穷大时,我们的模型可以识别出真正的支持。为了解决相应的优化问题,我们提出了一种线性化的块坐标下降算法,并证明了它在固定样本量下的收敛性。在合成数据集和真实的fMRI和EEG数据集上的计算结果表明,该方法优于现有技术。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
An Effective Tensor Regression with Latent Sparse Regularization
As data acquisition technologies advance, longitudinal analysis is facing challenges of exploring complex feature patterns from high-dimensional data and modeling potential temporally lagged effects of features on a response. We propose a tensor-based model to analyze multidimensional data. It simultaneously discovers patterns in features and reveals whether features observed at past time points have impact on current outcomes. The model coefficient, a k-mode tensor, is decomposed into a summation of k tensors of the same dimension. We introduce a so-called latent F-1 norm that can be applied to the coefficient tensor to performed structured selection of features. Specifically, features will be selected along each mode of the tensor. The proposed model takes into account within-subject correlations by employing a tensor-based quadratic inference function. An asymptotic analysis shows that our model can identify true support when the sample size approaches to infinity. To solve the corresponding optimization problem, we develop a linearized block coordinate descent algorithm and prove its convergence for a fixed sample size. Computational results on synthetic datasets and real-life fMRI and EEG datasets demonstrate the superior performance of the proposed approach over existing techniques.
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