Efficient and Parsimonious Modeling with Tensor Envelopes
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Abstract: In the form of multidimensional arrays, tensor data have become increasingly common in scientific studies and applications such as computational biology, brain imaging analysis, and process monitoring system. High-dimensionality, multidimensional structures, and high correlations intrinsically embedded in these data sets cause new challenges in analyzing them. Estimation and inferential techniques become inefficient or inconsistent if they ignore the high correlations among variables, heterogeneity caused by latent clusters, and intrinsic structural information in tensors. There is a pressing need to develop easy-to-interpret and parsimonious statistical models and methods to face these new challenges. This talk will introduce an intuitive construct called Tensor Envelopes, which aims to increase tensorial parameter estimation efficiency and improve prediction and inference. To demonstrate the versatility of tensor envelopes, we will discuss examples of tensor envelope models in regression, discriminant analysis, and clustering.
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