The problem. When a study measures several modalities across several groups of cells, you want the major axes of variation that structure the whole dataset — and, crucially, to know which modality each axis is driven by. Analysing each layer separately misses shared structure; naïve concatenation loses the ability to attribute variation to its source.

The idea. MOFA+ is an unsupervised factor-analysis framework: it infers a small set of latent factors that explain variation across all modalities and sample groups, with per-modality weight matrices that make each factor interpretable — you can read off whether a factor is expressed in the RNA layer, the protein layer, or shared. It scales to large single-cell datasets and handles missing modalities gracefully.

Why it matters. This is the linear, interpretable end of the dimensionality-reduction spectrum that runs through the reading — the same reduce-to-latent-factors instinct as PCA, t-SNE, UMAP, and the scVI latent space, but designed to attribute variance across data types. Interpretability is the selling point: for translational work like the STU’s, knowing which layer a signal lives in is often the finding, not a footnote.

Verdict. A widely-used, interpretable integration method; being essentially linear, it can miss the nonlinear structure deep models capture, and factor interpretation still needs care. Read it as the interpretable factor decomposition of a multi-omics dataset.