Have you ever wondered how missing data can reveal valuable insights?

Imagine you have three notebooks: one for math, one for history, and one for science. If some pages are blank, the data are “missing”. In scientific work this is called “blockwise missingness” (BM). At the same time, getting precise gold‑standard labels is expensive, so most samples stay unlabeled – the “semi‑supervised” (SS) problem. The new DEFUSE method tackles both issues. It starts with an estimator that uses only the primary notebook, then gradually incorporates the missing data and the unlabeled samples, cutting error without introducing bias. A screening step removes data sources that are not aligned with the primary source, preventing violations of the missing‑at‑random assumption. Thanks to an adaptive control variate, DEFUSE handles missing data efficiently even when distributions shift across sources. Moreover, it shows that unlabeled samples play a crucial role in missing‑data regression, boosting estimation accuracy. The result is a more reliable estimate, backed by simulations and two real‑world biomedical applications. In practice, DEFUSE turns incomplete datasets into valuable resources, saving time and enabling discoveries across medicine, climate science, and beyond. This flexibility lets scientists use huge, heterogeneous datasets without manual cleaning, making research faster and more inclusive. It also supports applications in environmental monitoring and health analytics, showing its broad impact.

The DEFUSE method starts with an initial estimator that uses only the primary dataset, then iteratively incorporates variables with missing values and unlabeled observations. A screening algorithm identifies and discards data sources that are not synchronized with the primary source, preventing violations of the missing‑at‑random assumption. An adaptive control variate reduces estimator variance, maintaining efficiency even when distributional shifts occur. Empirical tests on synthetic simulations and real biomedical applications show that DEFUSE lowers standard error without introducing bias, improving prediction accuracy. These findings suggest that DEFUSE can be extended to complex data fusion scenarios, supporting more robust analyses in research, health, and environmental sustainability.