• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Information Theory, IEEE Transactions on >Robust 1-bit Compressed Sensing and Sparse Logistic Regression: A Convex Programming Approach
【24h】

Robust 1-bit Compressed Sensing and Sparse Logistic Regression: A Convex Programming Approach

机译：鲁棒的1位压缩感知和稀疏Logistic回归：一种凸编程方法

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

This paper develops theoretical results regarding noisy 1-bit compressed sensing and sparse binomial regression. We demonstrate that a single convex program gives an accurate estimate of the signal, or coefficient vector, for both of these models. We show that an $s$-sparse signal in $BBR^{n}$ can be accurately estimated from $m = O(slog (n/s))$ single-bit measurements using a simple convex program. This remains true even if each measurement bit is flipped with probability nearly 1/2. Worst-case (adversarial) noise can also be accounted for, and uniform results that hold for all sparse inputs are derived as well. In the terminology of sparse logistic regression, we show that $O(s log (2n/s))$ Bernoulli trials are sufficient to estimate a coefficient vector in $BBR^{n}$ which is approximately $s$-sparse. Moreover, the same convex program works for virtually all generalized linear models, in which the link function may be unknown. To our knowledge, these are the first results that tie together the theory of sparse logistic regression to 1-bit compressed sensing. Our results apply to general signal structures aside from sparsity; one only needs to know the size of the set $K$ where signals reside. The size is given by the mean width of $K$, a computable quantity whose square serves as a robust extension of the dimension.
机译：本文提出了有关噪声1位压缩感知和稀疏二项式回归的理论结果。我们证明了单个凸程序可以为这两个模型提供信号或系数矢量的准确估计。我们显示，可以使用简单的凸程序从$ m = O（slog（n / s））$单个位测量值准确估算$ BBR ^ {n} $中的$ s $稀疏信号。即使每个测量位以接近1/2的概率翻转，也是如此。还可以考虑最坏情况（对抗性）的噪声，并得出适用于所有稀疏输入的统一结果。在稀疏逻辑回归的术语中，我们表明$ O（s log（2n / s））$ Bernoulli试验足以估计$ BBR ^ {n} $中的系数向量，其近似为$ s $-稀疏。此外，同一个凸程序实际上适用于所有广义线性模型，其中链接函数可能是未知的。据我们所知，这是将稀疏逻辑回归理论与1位压缩感测联系在一起的第一批结果。我们的结果适用于稀疏性之外的一般信号结构；只需知道信号所驻留的集合$ K $的大小即可。大小由$ K $的平均宽度给出，$ K $是一个可计算的数量，其平方可作为维的可靠扩展。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号