In Generalized Linear Estimation (GLE) problems, we seek to estimate a signal that is observed through a linear transform followed by a component-wise, possibly nonlinear and noisy, channel. In the Bayesian optimal setting, Generalized Approximate Message Passing (GAMP) is known to achieve optimal performance for GLE. However, its performance can significantly degrade whenever there is a mismatch between the assumed and the true generative model, a situation frequently encountered in practice. In this paper, we propose a new algorithm, named Generalized Approximate Survey Propagation (GASP), for solving GLE in the presence of prior or model mis-specifications. As a prototypical example, we consider the phase retrieval problem, where we show that GASP outperforms the corresponding GAMP, reducing the reconstruction threshold and, for certain choices of its parameters, approaching Bayesian optimal performance. Furthermore, we present a set of State Evolution equations that exactly characterize the dynamics of GASP in the high-dimensional limit.

中文翻译：

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用于高维估计的广义近似调查传播 *

在广义线性估计 (GLE) 问题中，我们试图估计通过线性变换观察到的信号，然后是组件方式，可能是非线性和有噪声的通道。在贝叶斯最优设置中，已知广义近似消息传递 (GAMP) 可实现 GLE 的最佳性能。然而，只要假设和真实的生成模型之间存在不匹配，它的性能就会显着降低，这种情况在实践中经常遇到。在本文中，我们提出了一种名为广义近似调查传播 (GASP) 的新算法，用于在存在先验或模型错误规范的情况下解决 GLE。作为一个典型的例子，我们考虑相位检索问题，我们证明 GASP 优于相应的 GAMP，降低了重建阈值，并且，对于其参数的某些选择，接近贝叶斯最优性能。此外，我们提出了一组状态演化方程，它们准确地表征了高维极限下 GASP 的动力学。