The Johnson-Lindenstrauss lemma is a mathematical result that states that a set of points in a high-dimensional space can be embedded into a space of much lower dimension while preserving distances between the points. It has applications in compressed sensing, manifold learning, dimensionality reduction, and graph embedding, and is useful for reducing the dimensionality of data while preserving its relevant structure. The lemma is tight up to a constant factor, meaning there exists a set of points that needs a certain dimension to preserve distances within a certain factor.
Stanford University
Fall 2022
This course dives into the use of randomness in algorithms and data structures, emphasizing the theoretical foundations of probabilistic analysis. Topics range from tail bounds, Markov chains, to randomized algorithms. The concepts are applied to machine learning, networking, and systems. Prerequisites indicate intermediate-level understanding required.
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