Fig. 1: Problem description and overview of LEOPARD architecture.

a An example of a missing view in a longitudinal multi-omics dataset. Here, some views at Timepoint T are absent. The observed views may contain additional missing data points. b An example of data density calculated from a variable in observed data (Timepoint 1 and Timepoint T) and imputed data. The data density indicates a distribution shift across the two timepoints. Imputation methods developed for cross-sectional data cannot account for the temporal changes within the data, and their imputation models built with data from one timepoint, such as Timepoint 1, might not be appropriate for inferring data from another timepoint, such as Timepoint T. c Compared to Raw data, data of Imputation 1 may exhibit lower MSE than data of Imputation 2, but Imputation 1 potentially lose biological variations present in the data. d The architecture of LEOPARD. Omics data from multiple timepoints are disentangled into omics-specific content representation and timepoint-specific temporal knowledge by the content and temporal encoders. The generator learns mappings between two views, while temporal knowledge is injected into content representation via the AdaIN operation. The multi-task discriminator encourages the distributions of reconstructed data to align more closely with the actual distribution. Contrastive loss enhances the representation learning process. Reconstruction loss measures the MSE between the input and reconstructed data. Representation loss stabilizes the training process by minimizing the MSE between the representations factorized from the reconstructed and actual data. Adversarial loss is incorporated to alleviate the element-wise averaging issue of the MSE loss. e the performance of LEOPARD is evaluated with percent bias and UMAP. The central line in the box plot represents the median. The box spans the interquartile range (IQR), and whiskers extend to values within 1.5 times the IQR. Data points outside this range are plotted as outliers. The two-sided paired Wilcoxon test is used to compare percent bias across methods. P-values are Bonferroni-adjusted, with significance denoted as: ns (not significant), * ( < 0.05), ** ( < 0.01), *** ( < 0.001). f several case studies, including both regression and classification analyses are performed to evaluate if biological information is preserved in the imputed data.