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Abstract:
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The analysis of tensor data has become an active research topic in statistics and data science recently. Many high-order datasets arising from a wide range of modern applications, such as genomics, material science, and neuroimaging analysis, requires modeling with high-dimensional tensors. Tensor methods also provide unique perspectives and solutions to many high-dimensional problems where the observations are not necessarily tensors. High-dimensional tensor problems possess distinct characteristics that pose unprecedented challenges to the statistical community. There is a need to develop novel methods, algorithms, and theories to analyze the high-dimensional tensor data. In this talk, we discuss some recent advances in high-dimensional tensor data analysis through several fundamental topics and their applications in microscopy imaging and neuroimaging. We will also illustrate how we develop new statistically optimal methods, computationally efficient algorithms, and fundamental theories that exploit information from high-dimensional tensor data based on the modern theory of computation, non-convex optimization, applied linear algebra, and high-dimensional statistics.
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