Multidimensional scaling is widely used to reconstruct a map with the points' coordinates in a low-dimensional space from the original high-dimensional space while preserving the pairwise distances. In a Bayesian framework, the current approach using Markov chain Monte Carlo algorithms has limitations in terms of model generalization and performance comparison. To address these limitations, a general framework that incorporates non-Gaussian errors and robustness to fit different types of dissimilarities is developed. Then, an adaptive inference method using annealed Sequential Monte Carlo algorithm for Bayesian multidimensional scaling is proposed. This algorithm performs inference sequentially in time and provides an approximate posterior distribution over the points' coordinates in a low-dimensional space and an unbiased estimator for the marginal likelihood. In this study, we compare the performance of different models based on marginal likelihoods, which are produced as a byproduct of the adaptive annealed Sequential Monte Carlo algorithm. Using synthetic and real data, we demonstrate the effectiveness of the proposed algorithm. Our results show that the proposed algorithm outperforms other benchmark algorithms under the same computational budget based on common metrics used in the literature. The implementation of our proposed method and applications are available at https://github.com/nunujiarui/GBMDS.

翻译：多维缩放被广泛用于从原始高维空间中重构低维空间中的点坐标映射，同时保持成对距离。在贝叶斯框架下，当前基于马尔可夫链蒙特卡洛算法的方法在模型泛化能力和性能比较方面存在局限性。为克服这些局限，本文提出了一种通用框架，该框架包含非高斯误差项并对不同类型相异性度量具有鲁棒性。随后，我们提出了一种基于退火顺序蒙特卡洛算法的自适应贝叶斯多维缩放推理方法。该算法可随时间顺序执行推理，并给出低维空间点坐标的近似后验分布以及边际似然的无偏估计量。本研究基于作为自适应退火顺序蒙特卡洛算法副产物生成的边际似然值，比较了不同模型的性能。通过合成数据与真实数据的实验，我们验证了所提算法的有效性。结果表明：在相同计算预算下，基于文献常用评价指标，所提算法优于其他基准算法。本文方法的实现及应用代码已发布于 https://github.com/nunujiarui/GBMDS。