Poster
Local Density Estimation in High Dimensions
Xian Wu · Moses Charikar · Vishnu Natchu

Thu Jul 12th 06:15 -- 09:00 PM @ Hall B #158

An important question that arises in the study of high dimensional vector representations learned from data is: given a set D of vectors and a query q, estimate the number of points within a specified distance threshold of q. Our algorithm uses locality sensitive hashing to preprocess the data to accurately and efficiently estimate the answers to such questions via an unbiased estimator that uses importance sampling. A key innovation is the ability to maintain a small number of hash tables via preprocessing data structures and algorithms that sample from multiple buckets in each hash table. We give bounds on the space requirements and query complexity of our scheme, and demonstrate the effectiveness of our algorithm by experiments on a standard word embedding dataset.

Author Information

Xian Wu (Stanford University)
Moses Charikar (Stanford University)
Vishnu Natchu

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