Unified imputation of missing data modalities and features in multi-omic data via shared representation learning

Multi-omic studies promise a more comprehensive view of biological systems by jointly measuring multiple molecular layers. In practice, however, such datasets are rarely complete: entire molecular modalities may be missing for many samples, and observed modalities often contain substantial feature-level missingness. Existing imputation approaches typically address only one of these two problems, relying either on feature-level imputation within a single modality or on pairwise translation models that cannot accommodate arbitrary combinations of missing modalities. As a result, there is, to our knowledge, no unified framework for reconstructing both missing data modalities and missing values within those modalities. We present MIMIR, a deep learning framework for unified multi-omic imputation that addresses both missing modalities and missing values through shared representation learning. MIMIR first learns modality-specific representations using masked autoencoders and then projects these representations into a common latent space, enabling reconstruction from any subset of observed modalities. Evaluated on pan-cancer multi-omic data from The Cancer Genome Atlas, MIMIR consistently outperforms baseline methods across a range of missing-modality and missing-value scenarios, including missing completely at random and missing not at random settings. Analysis of the learned shared space reveals structured cross-modal dependencies that explain modality-specific differences in imputation accuracy, with transcriptional and epigenetic modalities forming a strongly aligned core and copy number variation contributing more distinct signal. Together, these results demonstrate that shared representation learning provides an effective and flexible foundation for multi-omic imputation under heterogeneous missingness.