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Physical Sciences and Mathematics Commons

Open Access. Powered by Scholars. Published by Universities.®

Mathematics

CMC Faculty Publications and Research

2016

Numerical analysis

Articles 1 - 2 of 2

Full-Text Articles in Physical Sciences and Mathematics

Batched Stochastic Gradient Descent With Weighted Sampling, Deanna Needell, Rachel Ward Aug 2016

Batched Stochastic Gradient Descent With Weighted Sampling, Deanna Needell, Rachel Ward

CMC Faculty Publications and Research

We analyze a batched variant of Stochastic Gradient Descent (SGD) with weighted sampling distribution for smooth and non-smooth objective functions. We show that by distributing the batches computationally, a significant speedup in the convergence rate is provably possible compared to either batched sampling or weighted sampling alone. We propose several computationally efficient schemes to approximate the optimal weights, and compute proposed sampling distributions explicitly for the least squares and hinge loss problems. We show both analytically and experimentally that substantial gains can be obtained


Methods For Quantized Compressed Sensing, Hao-Jun Michael Shi, Mindy Case, Xiaoyi Gu, Shenyinying Tu, Deanna Needell Jan 2016

Methods For Quantized Compressed Sensing, Hao-Jun Michael Shi, Mindy Case, Xiaoyi Gu, Shenyinying Tu, Deanna Needell

CMC Faculty Publications and Research

In this paper, we compare and catalog the performance of various greedy quantized compressed sensing algorithms that reconstruct sparse signals from quantized compressed measurements. We also introduce two new greedy approaches for reconstruction: Quantized Compressed Sampling Matching Pursuit (QCoSaMP) and Adaptive Outlier Pursuit for Quantized Iterative Hard Thresholding (AOP-QIHT). We compare the performance of greedy quantized compressed sensing algorithms for a given bit-depth, sparsity, and noise level.