发表机构
Center for Computational Mathematics, Flatiron Institute; Center for Computational Biology, Flatiron Institute; Yale University（计算数学中心，Flatiron研究所; 计算生物学中心，Flatiron研究所; 耶鲁大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究探讨逆问题中对象空间离散化对冷冻电镜构象频率估计的影响，分析其统计性质与期望最大化算法特性，为相关实践提供理论指导。
AI 中文摘要
在许多逆问题中，研究目标是从间接的含噪声观测中恢复潜在（或对象状态）空间上的概率分布。当观测可被建模为混合潜在分布的含噪声样本时，该恢复问题就是概率测度空间上的反卷积问题。一种常用策略是固定一组有限的候选点并为每个点估计权重，将问题转化为单纯形上的有限维凹极大似然问题。我们在冷冻电镜（cryo-EM）背景下研究这种离散化与噪声的综合效应，其中候选点为生物分子构象，权重描述各构象的相对频率。我们的结果涉及该估计量的统计与算法两方面：在候选状态及其似然已知的权重恢复问题中，一对邻近候选点会形成近零方向；更一般地，即使在无限数据下，网格与噪声水平也会对观测密度间可实现的Kullback-Leibler散度施加统一下界。当有限网格估计量的总体目标处于单纯形内部时，它渐近正态；在边界目标处，其极限为锥投影高斯分布。最后，期望最大化（Expectation--Maximization）的精确近端形式，无需 basin 假设或递推线性化，即可在高噪声下对早期迭代与KL惩罚似然进行全局比较。对Hsp90分子合成图像的测试验证了理论发现，并转化为解释重加权集合的实用指南。
英文摘要
In many inverse problems, the aim is to recover a probability distribution on a latent (or object state) space from indirect, noisy observations. When the observations can be modelled as noisy samples from the mixing latent distribution, the recovery problem is a deconvolution problem on the space of probability measures. A common strategy is to fix a finite set of candidate points and estimate a weight for each, turning the problem into a finite-dimensional concave maximum likelihood problem on the simplex. We study the combined effect of this discretization and of the noise in the context of cryo-electron microscopy (cryo-EM), where the candidate points are biomolecular conformations and the weights describe the relative frequency of each conformation. Our results pertain to both statistical and algorithmic aspects of the estimator. We analyze the weight-recovery problem in which the candidate states and their likelihoods are known. A nearby pair of candidates forces a near-null direction. More generally, the grid and the noise level impose a uniform lower bound on the achievable Kullback--Leibler divergence between observation densities, even with infinite data. The finite-grid estimator is asymptotically normal when its population target is in the interior of the simplex; at a boundary target, its limit is a cone-projected Gaussian. Finally, the exact proximal form of Expectation--Maximization leads to a global high-noise comparison between an early iterate and a KL-penalized likelihood, without a basin assumption or a linearization of the recursion. Tests on synthetic images of the Hsp90 molecule illustrate the theoretical findings and translate them into practical guidelines for interpreting reweighted ensembles.
