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Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
Batched Stochastic Gradient Descent With Weighted Sampling, Deanna Needell, Rachel Ward
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
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.
A Note On Practical Approximate Projection Schemes In Signal Space Methods, Xiaoyi Gu, Deanna Needell, Shenyinying Tu
A Note On Practical Approximate Projection Schemes In Signal Space Methods, Xiaoyi Gu, Deanna Needell, Shenyinying Tu
CMC Faculty Publications and Research
Compressive sensing (CS) is a new technology which allows the acquisition of signals directly in compressed form, using far fewer measurements than traditional theory dictates. Recently, many socalled signal space methods have been developed to extend this body of work to signals sparse in arbitrary dictionaries rather than orthonormal bases. In doing so, CS can be utilized in a much broader array of practical settings. Often, such approaches often rely on the ability to optimally project a signal onto a small number of dictionary atoms. Such optimal, or even approximate, projections have been difficult to derive theoretically. Nonetheless, it has …
One-Bit Compressive Sensing With Partial Support, Phillip North, Deanna Needell
One-Bit Compressive Sensing With Partial Support, Phillip North, Deanna Needell
CMC Faculty Publications and Research
The Compressive Sensing framework maintains relevance even when the available measurements are subject to extreme quantization, as is exemplified by the so-called one-bit compressed sensing framework which aims to recover a signal from measurements reduced to only their sign-bit. In applications, it is often the case that we have some knowledge of the structure of the signal beforehand, and thus would like to leverage it to attain more accurate and efficient recovery. This work explores avenues for incorporating such partial support information into the one-bit setting. Experimental results demonstrate that newly proposed methods of this work yield improved signal recovery …