Traffic matrix measurement is fundamental for datacenter operations, but obtaining complete traffic matrices at scale remains challenging due to the prohibitive cost of global fine-grained measurement and partial observations resulting from network faults. Although existing matrix completion methods (reduce cost) achieve satisfactory performance in specific scenarios, their reliance on restrictive assumptions or black-box mappings results in a lack of interpretability and an inability to characterize uncertainty. In this paper, we propose Utimac, an uncertainty-aware traffic matrix completion for data center networks. Our analysis shows that, within a locally stationary window, log-domain traffic can be decomposed into a principal statistical component and a sparse deviation component. Based on this insight, we formulate traffic matrix completion as a parameter inference problem: multiple partially observed frames within a window are used to infer shared parameters and recover missing entries. To avoid the intractability and boundary degeneracy of the original integral-form marginal likelihood, we construct a regularized surrogate objective and solve the resulting joint optimization problem with block coordinate descent. Utimac consistently outperforms all baselines on data center networks datasets in both overall and burst scenarios, with its advantage becoming more pronounced as observations grow sparser. All code is publicly available in an anonymous repository: https://anonymous.4open.science/r/Utimac-0551/

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