For approximate inference in high-dimensional generalized linear models (GLMs), the performance of an estimator may significantly degrade when mismatch exists between the postulated model and the ground truth. In mismatched GLMs with rotation-invariant measurement matrices, Kabashima et al. proved vector approximate message passing (VAMP) computes exactly the optimal estimator if the replica symmetry (RS) ansatz is valid, but it becomes inappropriate if RS breaking (RSB) appears. Although the one-step RSB (1RSB) saddle point equations were given for the optimal estimator, the question remains: how to achieve the 1RSB prediction? This paper answers the question by proposing a new algorithm, vector approximate survey propagation (VASP). VASP derives from a reformulation of Kabashima's extremum conditions, which later links the theoretical equations to survey propagation in vector form and finally the algorithm. VASP has a complexity as low as VAMP, while embracing VAMP as a special case. The SE derived for VASP can capture precisely the per-iteration behavior of the simulated algorithm, and the SE's fixed point equations perfectly match Kabashima's 1RSB prediction, which indicates VASP can achieve the optimal performance even in a model-mismatched setting with 1RSB. Simulation results confirm VASP outperforms many state-of-the-art algorithms.

翻译：在高维广义线性模型（GLM）的近似推断中，当假设模型与真实模型存在失配时，估计器的性能可能显著下降。对于具有旋转不变测量矩阵的失配GLM，Kabashima等人证明，若复制对称（RS）假设成立，向量近似消息传递（VAMP）能精确计算最优估计器；但当出现RS破缺（RSB）时，该算法将不再适用。尽管已有针对最优估计器的一步RSB（1RSB）鞍点方程，但如何实现1RSB预测仍是一个未解问题。本文通过提出新算法——向量近似调查传播（VASP）回答了该问题。VASP源于对Kabashima极值条件的重新表述，该表述随后建立了理论方程与向量形式调查传播之间的联系，最终导出算法。VASP的复杂度与VAMP相当，同时将VAMP作为特例包含在内。为VASP推导的SE可精确捕捉模拟算法的逐次迭代行为，且SE的固定点方程完美匹配Kabashima的1RSB预测，表明VASP即使在存在1RSB的模型失配场景中也能实现最优性能。仿真结果证实VASP优于多种最先进算法。