We consider the estimation of an n-dimensional vector s from the noisy element-wise measurements of $\mathbf{s}\mathbf{s}^T$, a generic problem that arises in statistics and machine learning. We study a mismatched Bayesian inference setting, where some of the parameters are not known to the statistician. We derive the full exact analytic expression of the asymptotic mean squared error (MSE) in the large system size limit for the particular case of Gaussian priors and additive noise. From our formulas, we see that estimation is still possible in the mismatched case; and also that the minimum MSE (MMSE) can be achieved if the statistician chooses suitable parameters. Our technique relies on the asymptotics of the spherical integrals and can be applied as long as the statistician chooses a rotationally invariant prior.

翻译：我们认为,从对$\mathbf{s ⁇ mathb{s{s{mathbf{s ⁇ T$的噪音元素测算中估算正维矢量,这是一个在统计和机器学习中产生的通用问题。我们研究了一种不匹配的贝叶斯推论设置,统计师不知道其中的一些参数。我们从对高斯前科和添加剂噪声的特定案例的大规模系统规模限制中得出了无症状平均正方形错误(MSE)的完全精确的分析表达。我们从我们的公式中看到,在不匹配的案例中,估计仍然是可能的;如果统计师选择了合适的参数,最低的MSE(MSE)是可以实现的。我们的技术依赖于球体整体的无症状,只要统计师在之前选择旋转变量,就可以应用。