Fast Fourier Sparsity Testing over the Boolean Hypercube Grigory Yaroslavtsev Joint with Andrew Arnold (Waterloo), Arturs Backurs (MIT),

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Presentation transcript:

Fast Fourier Sparsity Testing over the Boolean Hypercube Grigory Yaroslavtsev Joint with Andrew Arnold (Waterloo), Arturs Backurs (MIT), Eric Blais (Waterloo) and Krzysztof Onak (IBM).

Fourier Analysis

PAC-style learning

Fourier Analysis and Learning

k- sparse NO Property Tester Don’t care Tolerant Property Tester Don’t care NO k- sparse

Previous work under Hamming

Pairwise Independent Hashing

Pairwise Fourier Hashing [FGKP’09]

Testing k-sparsity [GOSSW’11] #

Our Algorithm

Analysis Two main challenges – Top-k coefficients may collide – Noise from non top-k coefficients

Analysis: Large coefficients

Analysis: Small coefficients

Analysis: Putting it together

Other results + Open Problems