This paper studies the deflation algorithm when applied to estimate a low-rank symmetric spike contained in a large tensor corrupted by additive Gaussian noise. Specifically, we provide a precise characterization of the large-dimensional performance of deflation in terms of the alignments of the vectors obtained by successive rank-1 approximation and of their estimated weights, assuming non-trivial (fixed) correlations among spike components. Our analysis allows an understanding of the deflation mechanism in the presence of noise and can be exploited for designing more efficient signal estimation methods.

翻译：本文研究了将收缩算法应用于估计被加性高斯噪声污染的大规模张量中的低秩对称尖峰问题。具体而言，在假定尖峰分量之间存在非平凡（固定）相关性的条件下，我们精确刻画了收缩算法在大维情形下的性能，包括通过连续秩一近似所得向量的对齐程度及其估计权重。我们的分析有助于理解噪声环境中收缩机制的工作原理，并可用于设计更高效的信号估计方法。