Universal ε-approximators for integrals

By Michael Langberg, Leonard J. Schulman. ACM-SIAM Symposium on Discrete Algorithms, 2010

134 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/25e4a63d958bd891554201c3fc7671139c1bd57c

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Citations in the corpus

Practical Coreset Constructions for Machine Learning (2017, background): “Langberg and Schulman [2010] show that it is suﬃ-cient to consider the worst-case query Q ∈ Q for each point x ∈ X .”
Coresets for Nonparametric Estimation - the Case of DP-Means (2015, methodology): “…authors’ knowledge, all previous work on coresets was focused exclusively on parametric models such as K-Means (Har-Peled & Mazumdar, 2004; Har-Peled & Kushal, 2005; Feldman et al., 2007; Chen, 2009; Langberg & Schulman, 2010; Feldman & Langberg, 2011) and Gaussian mixtures (Feldman et al., 2011).”
Training Mixture Models at Scale via Coresets (2017, methodology): “It can be shown that sampling proportionally to the sensitivity — the worst case impact of each point – guarantees that the cost estimated on the coreset φ(C | θ) is an unbiased estimator of φ(X | θ) with bounded variance (Langberg and Schulman, 2010).”
Data-Dependent Coresets for Compressing Neural Networks with Applications to Generalization Bounds (2018, methodology): “[32] Michael Langberg and Leonard J Schulman.”
Training Gaussian Mixture Models at Scale via Coresets (2017, background): “While the exact sensitivity is hard to compute, Langberg and Schulman (2010) show that any uniform upper bound s C ( x ) to σ C ( x ) can be used.”
A unified framework for approximating and clustering data (2011, background): “This improves on previous results in [27, 10, 31], where the construction of ε -coresets of size O ( k , is respectively presented.”
Automated Scalable Bayesian Inference via Hilbert Coresets (2017, background): “However, their construction cannot be easily automated, as it requires computing the sensitivity (Langberg and Schulman, 2010) of each data point, a model-specific task that involves significant technical expertise.”
k-Means for Streaming and Distributed Big Sparse Data (2015, background): “An improved version of size O(dk(2)/ε(2)) was suggested in [17] which is a special case of the algorithms in [11].”