7 papers
Sharper Bounds for Chebyshev Moment Matching, with Applications
Cameron Musco, Christopher Musco, Lucas Rosenblatt +1
We study the problem of approximately recovering a probability distribution given noisy measurements of its Chebyshev polynomial moments. This problem arises broadly across algorit…
Distance Adaptive Beam Search for Provably Accurate Graph-Based Nearest Neighbor Search
Yousef Al-Jazzazi, Haya Diwan, Jinrui Gou +3
Nearest neighbor search is central in machine learning, information retrieval, and databases. For high-dimensional datasets, graph-based methods such as HNSW, DiskANN, and NSG have…
Navigable Graphs for High-Dimensional Nearest Neighbor Search: Constructions and Limits
Haya Diwan, Jinrui Gou, Cameron Musco +2
There has been significant recent interest in graph-based nearest neighbor search methods, many of which are centered on the construction of navigable graphs over high-dimensional…
Improved Spectral Density Estimation via Explicit and Implicit Deflation
Rajarshi Bhattacharjee, Rajesh Jayaram, Cameron Musco +2
We study algorithms for approximating the spectral density of a symmetric matrix that is accessed through matrix-vector product queries. By combining a previously studied Cheby…
Stability of the Lanczos Method for Matrix Function Approximation
Cameron Musco, Christopher Musco, Aaron Sidford
The ubiquitous Lanczos method can approximate for any symmetric matrix , vector , and function . In exact arithmetic, the method's error after ite…
Nearly Optimal Approximation of Matrix Functions by the Lanczos Method
Noah Amsel, Tyler Chen, Anne Greenbaum +2
Approximating the action of a matrix function on a vector is an increasingly important primitive in machine learning, data science, and statistics, wit…