We introduce PPBoot: a bootstrap-based method for prediction-powered
inference. PPBoot is applicable to arbitrary estimation problems and is very
simple to implement, essentially only requiring one application of the
bootstrap. Through a series of examples, we demonstrate that PPBoot often
performs nearly identically to (and sometimes better than) the earlier PPI(++)
method based on asymptotic normality$\unicode{x2013}$when the latter is
applicable$\unicode{x2013}$without requiring any asymptotic characterizations.
Given its versatility, PPBoot could simplify and expand the scope of
application of prediction-powered inference to problems where central limit
theorems are hard to prove.

PPBoot is a bootstrap-based method that simplifies and expands the scope of prediction-powered inference to estimation problems without requiring asymptotic characterizations.

关于预测强化引导的自助法注释

A Note on the Prediction-Powered Bootstrap

We consider the problem of estimating a signal from measurements obtained via
a generalized linear model. We focus on estimators based on approximate message
passing (AMP), a family of iterative algorithms with many appealing features:
the performance of AMP in the high-dimensional limit can be succinctly
characterized under suitable model assumptions; AMP can also be tailored to the
empirical distribution of the signal entries, and for a wide class of
estimation problems, AMP is conjectured to be optimal among all polynomial-time
algorithms.
However, a major issue of AMP is that in many models (such as phase
retrieval), it requires an initialization correlated with the ground-truth
signal and independent from the measurement matrix. Assuming that such an
initialization is available is typically not realistic. In this paper, we solve
this problem by proposing an AMP algorithm initialized with a spectral
estimator. With such an initialization, the standard AMP analysis fails since
the spectral estimator depends in a complicated way on the design matrix. Our
main contribution is a rigorous characterization of the performance of AMP with
spectral initialization in the high-dimensional limit. The key technical idea
is to define and analyze a two-phase artificial AMP algorithm that first
produces the spectral estimator, and then closely approximates the iterates of
the true AMP. We also provide numerical results that demonstrate the validity
of the proposed approach.

本文章研究了使用广义线性模型的估计问题并探讨了使用近似消息传递算法的表现，提出使用谱估计器作为初始化方法以解决一些模型中初始化时的相关性和独立性问题，并通过两阶段人工消息传递算法进行分析和模拟实验验证了该方法。

广义线性模型的谱初始化近似消息传递

Approximate Message Passing with Spectral Initialization for Generalized  Linear Models

There has been definite progress recently in proving the variational
single-letter formula given by the heuristic replica method for various
estimation problems. In particular, the replica formula for the mutual
information in the case of noisy linear estimation with random i.i.d. matrices,
a problem with applications ranging from compressed sensing to statistics, has
been proven rigorously. In this contribution we go beyond the restrictive
i.i.d. matrix assumption and discuss the formula proposed by Takeda, Uda,
Kabashima and later by Tulino, Verdu, Caire and Shamai who used the replica
method. Using the recently introduced adaptive interpolation method and random
matrix theory, we prove this formula for a relevant large sub-class of
rotationally invariant matrices.

本文通过自适应插值方法和随机矩阵理论证明了 Takeda，Uda，Kabashima 和 Tulino，Verdu，Caire 和 Shamai 使用复制方法提出的公式适用于一类具有旋转不变性质的矩阵，进而超越了原有广泛应用于压缩感知和统计学的噪声线性估计问题中的 i.i.d. 矩阵假设。