FINDING STRUCTURE WITH RANDOMNESS : PROBABILISTIC ALGORITHMS FOR CONSTRUCTING

By Long Chen. 2016

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In Optimization & Training

Citations in the corpus

Rethinking LDA: Moment Matching for Discrete ICA (2015, methodology): “e when N = 50,000. Each algorithm was run 5times, so the times in the table display the minimum (min), mean, and maximum (max) time. Another option is using a stochastic eigendecomposition(see, e.g., [33]) to approximate the whitening matrix. Variational inference. For variational inference, we used”
Tensor decompositions for learning latent variable models (2012, positive): “As shown by Hsu and Kakade (2013), M1 = ∑k i=1wiσ 2 i μi.”
On Hyperparameter Optimization of Machine Learning Algorithms: Theory and Practice (2020, methodology): “In some cases, people may want to fine-tune the ML model by considering other less important hyper-parameters, like the distance metric of KNN and the SVD solver type of PCA; so BO-TPE, GA, or PSO could be chosen for these situations.”
Methods of Moments for Learning Stochastic Languages: Unified Presentation and Empirical Comparison (2014, unknown): “Given a matrix M we write ‖M‖F for its Frobenius norm and ‖M‖∗ for its trace/nuclear norm.”
Revisiting the Nystrom Method for Improved Large-scale Machine Learning (2013, methodology): “A large part of the recent body of work on randomized matrix algorithms has been summarized in the recent monograph of Mahoney (Mahoney, 2011) and the recent review of Halko, Martinsson, and Tropp (Halko et al., 2011).”
Vector Approximate Message Passing (2019, methodology): “In the case that SVD complexity may be an issue, we note that it costs O(M N R) flops by classical methods or O(M N log R) by modern approaches [22].”
Sketchy Decisions: Convex Low-Rank Matrix Optimization with Optimal Storage (2017, methodology): “, compute an update direction via Lanczos or via randomized SVD [17]:”
Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overview (2018, methodology): “Lanczos algorithm) [101] or the randomized linear algebra algorithms [112].”
Tighter Low-rank Approximation via Sampling the Leveraged Element (2014, methodology): “[21, 19] have provided guarantees on error in spectral norm which are later improved in [13, 3].”
Subspace Inference for Bayesian Deep Learning (2019, methodology): “For example, using standard hardware (a Dell XPS-15 laptop, with Intel core i7, 16Gb RAM), it takes 4 minutes to perform exact SVD on our largest model, WideResNet on CIFAR-100, with 36 million parameters.”
Watch Your Step: Learning Node Embeddings via Graph Attention (2017, background): “Furthermore, the SVD can be approximated in time linear to the number of non-zero entries [16].”
Multidimensional simultaneous random plus erratic noise attenuation and interpolation for seismic data by joint low-rank and sparse inversion (2015, methodology): “…methods use random projections to uncover a lower dimensional subspace capturing most of the action of a matrix and are competitive in speed and accuracy with Krylov methods while being conceptually simple, robust, and easily parallelizable on multiprocessor architectures (Halko et al., 2011).”