Ahle, Thomas Dybdahl

English

We study five fundemental problems in the field of high dimensional algorithms,similarity search and machine learning. We obtain many new results, including:• Data structures with Las Vegas guarantees for l-Approximate Near Neighbours and Braun Blanquet Approximate Set Similarity Search with performance matching state of the art Monte Carlo algorithms up to factors nο(1).• “Supermajorities:” The first space/time tradeoff for Approximate Set SimilaritySearch, along with a number of lower bounds suggesting that the algorithms are optimal among all Locality Sensitive Hashing (LSH) data structures.• The first lower bounds on approximative data structures based on the Orthogonal Vectors Conjecture (OVC).• Output Sensitive LSH data structures with query time near t + nρ for outputtingt distinct elements, where nρ is the state of the art time to output a single element and tnρ was the previous best for t items.• A Johnson Lindenstrauss embedding with fast multiplication on tensors (a Tensor Sketch), with high probability guarantees for subspace- and nearneighbour-embeddings.We study five fundemental problems in the field of high dimensional algorithms,similarity search and machine learning. We obtain many new results,including:• Data structures with Las Vegas guarantees for `1-Approximate Near Neighboursand Braun Blanquet Approximate Set Similarity Search with performancematching state of the art Monte Carlo algorithms up to factors no(1).• “Supermajorities:” The first space/time tradeoff for Approximate Set SimilaritySearch, along with a number of lower bounds suggesting that thealgorithms are optimal among all Locality Sensitive Hashing (LSH) datastructures.• The first lower bounds on approximative data structures based on the OrthogonalVectors Conjecture (OVC).• Output Sensitive LSH data structures with query time near t + nr for outputtingt distinct elements, where nr is the state of the art time to output asingle element and tnr was the previous best for t items.• A Johnson Lindenstrauss embedding with fast multiplication on tensors (aTensor Sketch), with high probability guarantees for subspace- and nearneighbour-embeddings

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Similarity Search: Algorithms for Sets and other High Dimensional Data

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Similarity Search: Algorithms for Sets and other High Dimensional Data

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