Scalable Training of Mixture Models via Coresets

By Dan Feldman, Matthew Faulkner, Andreas Krause. 2011

170 citations recorded by the source corpus.

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Citations in the corpus

Variance Reduced Stochastic Gradient Descent with Neighbors (2015, methodology): “ere k2o(n), most drastically k2O(1). The simplest way to do this is via uniform subsampling of kpoints from the training data. More reﬁned methods are available from the literature on core sets, e.g. [4]. How will decrease with kremains data set dependent though. (ii) We can use locality-sensitive h”
Coresets for Scalable Bayesian Logistic Regression (2016, methodology): “[10], who developed a coreset algorithm for Gaussian mixture models.”
Automated Scalable Bayesian Inference via Hilbert Coresets (2017, background): “The concept of a coreset originated in computational geometry and optimization (Agarwal et al., 2005; Feldman and Langberg, 2011; Feldman et al., 2013; Bachem et al., 2015; Lucic et al., 2016; Bachem et al., 2016; Feldman et al., 2011; Han et al., 2016).”
Training Gaussian Mixture Models at Scale via Coresets (2017, result): “ As a by-product of our analysis, we also answer an open question on the pseudo-dimension (generalization of the VC dimension) of arbitrary mixtures of Gaussians. This paper is an extended version of Feldman et al. (2011) and provides several improvements over the original work. The theoretical anal”
k-Means for Streaming and Distributed Big Sparse Data (2015, methodology): “This problem is solved in theory using rough approximation algorithms or bi-criteria approximations [28, 12] that replaces the optimal solution, or using the merge-and-reduce tree that apply the coreset constuction only on small sets.”
Core‐sets: An updated survey (2019, methodology): “Here, See for example, Braverman et al. (2016), Chen (2009), Feldman, Krause, and Faulkner (2011) and Langberg and Schulman (2010).”
Turning big data into tiny data: Constant-size coresets for k-means, PCA and projective clustering (2013, unknown): “For example, when we choose C to be the family of all j-dimensional subspaces of Rd we obtain the j-subspace problem or when C is the family of sets of k centers we obtain the k-means problem.”
Towards Total Recall in Industrial Anomaly Detection (2021, background): “Coresets have seen longstanding usage in fundamental kNN and kMeans approaches [22] or mixture models [19] by ﬁnding subsets that best approximate the structure of some available set and allow for approximate solution ﬁnding with notably reduced cost [1,9].”
Gradient-based training of Gaussian Mixture Models in High-Dimensional Spaces (2019, background): “Apart from these works, some authors avoid the issue of massive datasets altogether by determining smaller “core sets” of representative samples and performing vanilla EM on them (Feldman et al., 2011).”
Training Mixture Models at Scale via Coresets (2017, unknown): “This paper is an extended version of Feldman et al. (2011) and provides several improvements over the original work.”
Practical Coreset Constructions for Machine Learning (2017, methodology): “In fact, for a sequence of ( k, ε )-coresets C ε we have that Based on the framework presented in Chapter 2, the sensitivity can be bounded by O (cid:0) kλ − 4 and the pseudo-dimension of the associated function family is O (cid:0) (cid:1) Feldman et al., 2011, Lucic et al., 2017].”
Submodularity in Data Subset Selection and Active Learning (2015, background): “Many machine learning problems including SVMs, k-means clustering , k-median clustering, and Gaussian mixtures (Tsang et al., 2005; Har-Peled & Mazumdar, 2004; Feldman et al., 2011) can be approximately solved on a coreset.”
DataComp: In search of the next generation of multimodal datasets (2023, background): “[42] Dan Feldman, Matthew Faulkner, and Andreas Krause.”