Multi-Omics Factor Analysis, Explained (MOFA+)

Your phone logs your week in half a dozen different languages at once — hours of sleep, whether you worked out, texts sent, minutes of music, money spent. They look like six separate diaries. But underneath, a few hidden states — a stretch of stress, a social burst, a cold coming on — quietly drive all of them together. Finding those hidden states, written into several very different data types at once, is exactly what MOFA+ does. MOFA+ (Multi-Omics Factor Analysis) is an unsupervised, multi-view factor model: it explains many heterogeneous data tables with a small set of shared latent factors, learns which factors are shared across views versus specific to one (via automatic relevance determination), extends that to structured groups (the “+”), and hands you a variance-decomposition grid you can read shared-vs-specific structure straight off of. In ML terms it's the multi-view, mixed-likelihood, sparsity-regularized Bayesian cousin of PCA / factor analysis / CCA — group factor analysis, fit by variational inference. With a quantified-self metaphor as our guide — one week, read off a few hidden states — we build MOFA+ from intuition up and connect it to its whole family across statistics and machine learning. What we cover • The core factor model Y⁽ᵐ⁾ ≈ Z W⁽ᵐ⁾ᵀ — shared latent factors, a per-view loading matrix, and per-view noise • Mixed likelihoods — Gaussian, Bernoulli, and Poisson views sharing one model, with missing data handled naturally • Automatic relevance determination (ARD): how the model learns which factors are shared across views vs specific to one — and prunes the rest • Spike-and-slab feature sparsity for interpretable loadings • The MOFA+ “+”: group-wise ARD, so a factor can be active in one group of samples and silent in another • Variance decomposition (R² per factor per view) — the payoff, and how to read shared vs specific off the grid • The honest ceiling: factors are linear directions of shared covariance — correlational, not causal — fit to a local variational optimum, with K and the factor names chosen by you • The family tree: PCA / PPCA, factor analysis, canonical correlation analysis (CCA), group factor analysis (GFA), and modern multimodal / multi-omics latent-variable models (MOFA+, MEFISTO) Where it's used: multi-omics integration (transcriptomics, methylation, proteomics, genomics across patient groups), single-cell multimodal data, and more broadly any quantitative-systems-pharmacology or systems-biology setting where several incommensurable measurement modalities need one shared, interpretable latent representation. Chapters 0:00 — A week your phone quietly remembers 0:44 — Six logs, six different data types 1:12 — A factor model + mixed likelihoods (Y ≈ Z Wᵀ) 2:31 — A hidden state that hides in some logs 2:51 — View×factor ARD — shared vs specific 3:51 — Weekdays aren't weekends — the “+” 4:13 — Group×factor ARD — what MOFA+ adds 5:17 — The panel that explains your week 5:32 — Variance decomposition (R²) — and the ceiling 6:57 — When to use MOFA — and when to use PCA 7:26 — One model, many faces (PCA · FA · CCA · GFA · multi-omics VI) 8:26 — Recap: seven threads, one week 8:58 — Your week in six dialects Topics: multi-omics factor analysis (MOFA, MOFA+), factor analysis, principal component analysis (PCA), probabilistic PCA, canonical correlation analysis (CCA), group factor analysis (GFA), latent variable models, unsupervised learning, dimensionality reduction, variational inference, Bayesian machine learning, automatic relevance determination (ARD), spike-and-slab sparsity, variance decomposition, multi-view / multimodal learning, data integration, single-cell multi-omics, MEFISTO, quantitative systems pharmacology (QSP), systems biology, bioinformatics, pharmacometrics. New here? QSPplus makes cinematic explainers on pharmacometrics, statistics, and machine learning — one hard idea, one honest metaphor at a time. Subscribe for more. #MachineLearning #Bioinformatics #Pharmacometrics