Signal Recovery by Stochastic Optimization
Signal Recovery by Stochastic Optimization
复制标题
通过随机优化恢复信号
DOI：
10.1134/s0005117919100084
复制
发表时间：
2019
影响因子：
0.7
通讯作者：
A. S. Nemirovsky
中科院分区：
文献类型：
--
作者：
A. Juditsky;A. S. Nemirovsky
本文讨论了广义线性模型（GLM）中信号恢复的一种方法，将信号估计问题归结为求解随机单调变分不等式（VI）的问题。随机VI的解可以以计算有效的方式找到，并且在VI是强单调的情况下，我们推导出随着观察数K的增长，期望误差以O（1/K）的速率收敛到0的有限时间上界。我们的结构假设基本上是弱于那些必要的，以确保凸性的最大似然估计的优化问题。事后看来，我们推广的方法可以直接追溯到Rosenblatt感知器算法背后的思想。
We discuss an approach to signal recovery in Generalized Linear Models (GLM) in which the signal estimation problem is reduced to the problem of solving a stochastic monotone Variational Inequality (VI). The solution to the stochastic VI can be found in a computationally efficient way, and in the case when the VI is strongly monotone we derive finite-time upper bounds on the expected ‖ · ‖22 error converging to 0 at the rate O(1/K) as the number K of observation grows. Our structural assumptions are essentially weaker than those necessary to ensure convexity of the optimization problem resulting from Maximum Likelihood estimation. In hindsight, the approach we promote can be traced back directly to the ideas behind the Rosenblatt’s perceptron algorithm.