scholarly journals Smoothed Coordinate Descent for MAP Inference

2014 ◽  
Keyword(s):  
Coordinate Descent ◽  
Map Inference

scholarly journals Efficient Asynchronous Semi-stochastic Block Coordinate Descent Methods for Large-Scale SVD

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Fanhua Shang ◽  
Zhihui Zhang ◽  
Yuanyuan Liu ◽  
Hongying Liua ◽  
Jing Xu
Keyword(s):  
Large Scale ◽  
Coordinate Descent ◽  
Descent Methods ◽  
Block Coordinate Descent

scholarly journals Differentiable Architecture Search Based on Coordinate Descent

IEEE Access ◽  
2021 ◽  
Vol 9 ◽  
pp. 48544-48554
Author(s):  
Pyunghwan Ahn ◽  
Hyeong Gwon Hong ◽  
Junmo Kim
Keyword(s):  
Coordinate Descent

scholarly journals A Block Coordinate Descent-Based Projected Gradient Algorithm for Orthogonal Non-Negative Matrix Factorization

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 540
Author(s):  
Soodabeh Asadi ◽  
Janez Povh
Keyword(s):  
Matrix Factorization ◽  
Synthetic Data ◽  
Coordinate Descent ◽  
The Other ◽  
Gradient Algorithm ◽  
Block Coordinate Descent ◽  
Projected Gradient Method ◽  
Projected Gradient ◽  
Factorization Problem ◽  
Non Negative Matrix Factorization

This article uses the projected gradient method (PG) for a non-negative matrix factorization problem (NMF), where one or both matrix factors must have orthonormal columns or rows. We penalize the orthonormality constraints and apply the PG method via a block coordinate descent approach. This means that at a certain time one matrix factor is fixed and the other is updated by moving along the steepest descent direction computed from the penalized objective function and projecting onto the space of non-negative matrices. Our method is tested on two sets of synthetic data for various values of penalty parameters. The performance is compared to the well-known multiplicative update (MU) method from Ding (2006), and with a modified global convergent variant of the MU algorithm recently proposed by Mirzal (2014). We provide extensive numerical results coupled with appropriate visualizations, which demonstrate that our method is very competitive and usually outperforms the other two methods.

Coordinate Descent Method for k-means

2021 ◽  
pp. 1-1
Author(s):  
Feiping Nie ◽  
Jingjing Xue ◽  
Danyang Wu ◽  
Rong Wang ◽  
Hui Li ◽  
...  
Keyword(s):  
Descent Method ◽  
Coordinate Descent ◽  
Coordinate Descent Method

scholarly journals High-performance sampling of generic determinantal point processes

2020 ◽  
Vol 378 (2166) ◽  
pp. 20190059 ◽  
Author(s):  
Jack Poulson
Keyword(s):  
Point Process ◽  
Spectral Decomposition ◽  
High Performance ◽  
Point Processes ◽  
Cholesky Factorization ◽  
Determinantal Point Processes ◽  
Determinantal Point Process ◽  
Decomposition Approach ◽  
Map Inference ◽  
Sampling Schemes

Determinantal point processes (DPPs) were introduced by Macchi (Macchi 1975 Adv. Appl. Probab. 7 , 83–122) as a model for repulsive (fermionic) particle distributions. But their recent popularization is largely due to their usefulness for encouraging diversity in the final stage of a recommender system (Kulesza & Taskar 2012 Found. Trends Mach. Learn. 5 , 123–286). The standard sampling scheme for finite DPPs is a spectral decomposition followed by an equivalent of a randomly diagonally pivoted Cholesky factorization of an orthogonal projection, which is only applicable to Hermitian kernels and has an expensive set-up cost. Researchers Launay et al. 2018 ( http://arxiv.org/abs/1802.08429 ); Chen & Zhang 2018 NeurIPS ( https://papers.nips.cc/paper/7805-fast-greedy-map-inference-for-determinantal-point-process-to-improve-recommendation-diversity.pdf ) have begun to connect DPP sampling to LDL H factorizations as a means of avoiding the initial spectral decomposition, but existing approaches have only outperformed the spectral decomposition approach in special circumstances, where the number of kept modes is a small percentage of the ground set size. This article proves that trivial modifications of LU and LDL H factorizations yield efficient direct sampling schemes for non-Hermitian and Hermitian DPP kernels, respectively. Furthermore, it is experimentally shown that even dynamically scheduled, shared-memory parallelizations of high-performance dense and sparse-direct factorizations can be trivially modified to yield DPP sampling schemes with essentially identical performance. The software developed as part of this research, Catamari ( hodgestar.com/catamari ) is released under the Mozilla Public License v.2.0. It contains header-only, C++14 plus OpenMP 4.0 implementations of dense and sparse-direct, Hermitian and non-Hermitian DPP samplers. This article is part of a discussion meeting issue ‘Numerical algorithms for high-performance computational science’.

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