Data-oblivious measurements play an important role in low-rank data compression and recovery techniques, frequently used in streaming settings and within iterative algorithms. Typically, linear data-oblivious measurements involve some version of a random sketch that preserves the geometric properties of the data. When data is tensorial, a special challenge is to create a sketch with a structure that reflects tensor structure: this way, it can work similarly to a dense unstructured random matrix but can be applied faster and stored much more efficiently. I will discuss our recent work on developing flexible and provable modewise sketches for tensor data processing, including compressed CP rank fitting, modewise tensor iterative hard thresholding and direct recovery from leave-one-out modewise measurements for low Tucker rank tensors.
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