Tensor Graphical Model: Non-Convex Optimization and Statistical Inference
نویسندگان
چکیده
منابع مشابه
Non-convex Statistical Optimization for Sparse Tensor Graphical Model
We consider the estimation of sparse graphical models that characterize the dependency structure of high-dimensional tensor-valued data. To facilitate the estimation of the precision matrix corresponding to each way of the tensor, we assume the data follow a tensor normal distribution whose covariance has a Kronecker product structure. The penalized maximum likelihood estimation of this model i...
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1. Introduction. We thank all the discussants for their careful reading of our paper, and for their insightful critiques. We would also like to thank the editors for organizing this discussion. Our paper contributes to the area of high-dimensional statistics which has received much attention over the past several years across the statistics, machine learning and signal processing communities. I...
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1. Matrix perturbation bounds. Given a low-rank matrix we consider what happens to the invariant subspaces when the matrix is perturbed by a small amount. We assume without loss of generality that the matrix under consideration is square and symmetric, and our methods can be extended to the general non-symmetric non-square case. We refer the interested reader to [1, 3] for more details, as the ...
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We wish to congratulate the authors for their innovative contribution, which is bound to inspire much further research. We find latent variable model selection to be a fantastic application of matrix decomposition methods, namely, the superposition of low-rank and sparse elements. Clearly, the methodology introduced in this paper is of potential interest across many disciplines. In the followin...
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ژورنال
عنوان ژورنال: IEEE Transactions on Pattern Analysis and Machine Intelligence
سال: 2020
ISSN: 0162-8828,2160-9292,1939-3539
DOI: 10.1109/tpami.2019.2907679