A1763
Title: Configuration recovery for distance-based latent space models
Authors: Yinghang Chen - Southern University of Science and Technology (China)
Yunxiao Chen - London School of Economics and Political Science (United Kingdom)
Haoran Zhang - Southern University of Science and Technology (China) [presenting]
Abstract: Multidimensional Unfolding (MDU) is a fundamental tool for visualizing joint embeddings of distinct object sets, such as respondents and items, based on their similarities. However, existing MDU methods often lack rigorous statistical guarantees and are also computationally intensive when applied to high-dimensional, noisy data. A Generalized Multidimensional Unfolding (GMDU) framework is proposed that handles continuous, binary, and count data within a unified statistical model. A three-stage estimation procedure is further developed, which includes matrix denoising, singular space refinement, and configuration retrieval. The matrix denoising step employs a truncated singular value thresholding algorithm to recover the underlying drifted distance matrix with average Frobenius-norm consistency guarantee, followed by a refinement step that upgrades the initial estimator to achieve entry-wise uniform consistency. The final step consists of a low-dimensional optimization to recover the configuration by resolving rotation and translation ambiguities. Non-asymptotic error bounds are established for the estimators under mild conditions. Extensive simulations and an application to the 2020 Cooperative Election Study (CES) reveal a primary ideological spectrum and an orthogonal institutional dimension, providing clear visualization of geopolitical and ideological structures.
