Bayesian Mixed Multidimensional Scaling for Auditory Processing

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.