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Tensor Methods in High Dimensional Data Analysis: Opportunities and Challenges
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Large amount of multidimensional data represented by multiway arrays or tensors are prevalent in modern applications across various fields such as chemometrics, genomics, physics, psychology, and signal processing. The structural complexity of such data provides vast new opportunities for modeling and analysis, but efficiently extracting information content from them, both statistically and computationally, presents unique and fundamental challenges. Addressing these challenges requires an interdisciplinary approach that brings together tools and insights from statistics, optimization and numerical linear algebra among other fields. Despite these hurdles, significant progress has been made in the last decade. This review seeks to examine some of the key advancements and identify common threads among them, under eight different statistical settings.
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Cited by 2 Pith papers
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Large Average Subtensor Problem: Ground-State, Algorithms, and Algorithmic Barriers
For random order-p tensors with large p, the largest average k×...×k subtensor concentrates around sqrt(2p log(N choose k)/k^p), a greedy algorithm achieves a 2√p/(p+1) fraction of it, and an overlap gap property bloc...
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Information-Theoretic Guarantees for Recovering Low-Rank Tensors from Symmetric Rank-One Measurements
Near-optimal sample complexity Θ(rd) is claimed for recovering low symmetric-rank tensors from symmetric rank-one log-concave measurements, with a lower bound of dr^{0.98-o(1)}.
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