The human brain distinguishes speech sound categories by representing acoustic signals in a latent multidimensional auditory-perceptual space. This space can be statistically constructed using multidimensional scaling, a technique that can compute lower-dimensional latent features representing the speech signals in such a way that their pairwise distances in the latent space closely resemble the corresponding distances in the observation space. The inter-individual and inter-population (e.g., native versus non-native listeners) heterogeneity in such representations is however not well understood. These questions have often been examined using joint analyses that ignore individual heterogeneity or using separate analyses that cannot characterize human similarities. Neither extreme, therefore, allows for principled comparisons between populations and individuals. The focus of the current literature has also often been on inference on latent distances between the categories and not on the latent features themselves, which are crucial for our applications, that make up these distances. Motivated by these problems, we develop a novel Bayesian mixed multidimensional scaling method, taking into account the heterogeneity across populations and subjects. We design a Markov chain Monte Carlo algorithm for posterior computation. We then recover the latent features using a post-processing scheme applied to the posterior samples. We evaluate the method's empirical performances through synthetic experiments. Applied to a motivating auditory neuroscience study, the method provides novel insights into how biologically interpretable lower-dimensional latent features reconstruct the observed distances between the stimuli and vary between individuals and their native language experiences.

翻译：人类大脑通过在潜在的多维听觉-感知空间中表征声学信号来区分语音类别。该空间可通过多维尺度分析进行统计构建，该技术能够计算代表语音信号的低维潜在特征，使得这些信号在潜在空间中的成对距离与观测空间中的相应距离高度相似。然而，这种表征在个体间与群体间（例如母语与非母语听众）的异质性尚未被充分理解。以往研究常采用忽略个体异质性的联合分析或无法刻画人类共性的独立分析来探讨这些问题。这两种极端方法均无法对群体与个体进行有原则的比较。现有文献也通常聚焦于语音类别间潜在距离的推断，而非构成这些距离的潜在特征本身——而后者对我们的应用至关重要。针对这些问题，我们提出了一种新型贝叶斯混合多维尺度分析方法，能够兼顾群体与受试者之间的异质性。我们设计了马尔可夫链蒙特卡洛算法进行后验计算，并通过后验样本的后处理方案恢复潜在特征。通过合成实验评估了该方法的实证性能。应用于一项启发性的听觉神经科学研究中，该方法揭示了具有生物学可解释性的低维潜在特征如何重构观测到的刺激间距离，并展现其在不同个体及其母语语言经验中的变异机制，提供了全新见解。