MOFA+ Multi-Omics Factor Analysis

Overview

MOFA+ (Multi-Omics Factor Analysis v2) is an unsupervised statistical framework that jointly decomposes multiple omics datasets into a small set of latent factors. Each factor captures an independent source of variation (e.g., cell cycle, a disease phenotype, a technical batch) and is associated with feature weights (loadings) that reveal which genes, peaks, or proteins drive it. The Python package mofapy2 produces an HDF5 model file compatible with downstream analysis in both Python and R. MOFA+ extends the original MOFA to support multi-group settings where samples belong to distinct cohorts or conditions.

When to Use

• Integrating two or more omics layers from the same set of cells or samples (e.g., scRNA-seq + scATAC-seq, RNA + proteomics, methylation + RNA)
• Identifying shared and view-specific sources of variation across omics modalities without supervised labels
• Comparing how latent factors differ between patient groups, treatment conditions, or time points in a multi-group analysis
• Reducing multi-omics dimensionality before clustering, trajectory inference, or survival modeling
• Discovering which genomic features (genes, peaks, proteins) drive each factor via sparse loadings
• Annotating latent factors by correlating factor scores with sample metadata (age, stage, treatment response)
• Use omics-plotting SKILL after training for publication-quality factor scatter and loading heatmaps
• Use scVI / MultiVI (scverse) instead when you need deep generative batch correction across modalities with explicit latent space inference and VAE architecture
• Use LIGER instead when your primary goal is integrating datasets across technologies (e.g., snRNA-seq + snATAC-seq) with shared and dataset-specific factors via iNMF

Prerequisites

• Python packages: mofapy2>=0.7, anndata>=0.10, numpy>=1.24, pandas>=2.0, scipy>=1.11, matplotlib>=3.7, seaborn>=0.13, muon (optional, for MuData integration)
• Data requirements: One AnnData object per omics view (cells/samples x features). All views must share the same obs (cell/sample) index. Missing samples per group are supported.
• Environment: Python 3.9+; trained model is saved as HDF5 and can be analyzed in R via the MOFA2 Bioconductor package

pip install mofapy2 anndata muon matplotlib seaborn

Pre-flight Interview

Settle these with the user before writing any analysis code.

decisions:
  - id: D1
    param: views
    kind: required
    source: data
    ask: "Which omics layers go into the model, and do they share the same samples?"
    default: null

  - id: D2
    param: likelihoods
    kind: required
    source: data
    depends_on: [D1]
    ask: "For each layer, is the data continuous and normalized, binary, or raw counts?"
    default: null

  - id: D3
    param: scaleViews
    kind: required
    source: user
    depends_on: [D1]
    ask: "Should layers be rescaled so the one with the largest variance does not dominate every factor?"
    default: "rescaled"

  - id: D4
    param: numFactors
    kind: required
    source: user
    ask: "How many latent factors should the model start from? Unused ones are pruned automatically."
    default: 15

  - id: D5
    param: groups
    kind: optional
    source: data
    ask: "Should samples be split into groups so the model can compare variance across them?"
    default: "one group"

  - id: D6
    param: convergence
    kind: optional
    source: user
    ask: "Stop early for a quick look, or run to a tight tolerance for the final model?"
    default: "medium tolerance, up to 1000 iterations"

  - id: D7
    param: factorDropThreshold
    kind: optional
    source: user
    ask: "Drop factors that explain almost no variance in any layer?"
    default: "drop below 1% variance explained"

  - id: D8
    param: sparsityPriors
    kind: optional
    source: user
    ask: "Should MOFA retain spike-and-slab weights and per-view relevance priors for sparse, interpretable factors?"
    default: "both enabled"

D2 hangs on D1 and is the decision that breaks models quietly: handing raw counts to a layer declared gaussian fits the model to sequencing depth, and the factors that come back are depth, not biology.

Quick Start

import numpy as np
import pandas as pd
import anndata as ad
from mofapy2.run.entry_point import entry_point

# Simulate two omics views, 200 cells, 500 RNA genes, 300 ATAC peaks
np.random.seed(42)
n_cells, n_rna, n_atac = 200, 500, 300

adata_rna  = ad.AnnData(np.abs(np.random.randn(n_cells, n_rna)),
                         obs=pd.DataFrame(index=[f"cell_{i}" for i in range(n_cells)]))
adata_atac = ad.AnnData(np.abs(np.random.randn(n_cells, n_atac)),
                         obs=adata_rna.obs.copy())

ent = entry_point()
ent.set_data_options(scale_groups=False, scale_views=True)
ent.set_data_matrix([[adata_rna.X, adata_atac.X]],
                    likelihoods=["gaussian", "gaussian"],
                    views_names=["RNA", "ATAC"],
                    groups_names=["all_cells"],
                    samples_names=[list(adata_rna.obs_names)])
ent.set_model_options(factors=10)
ent.set_train_options(iter=500, convergence_mode="fast", seed=42)
ent.build()
ent.run()
ent.save("mofa_model.hdf5")
print("Model saved to mofa_model.hdf5")

Workflow

Step 1: Load and Prepare Multi-Omics Data

Each omics layer is represented as an AnnData object. Align cell indices across modalities, log-normalize RNA counts, and binarize or normalize ATAC/methylation data as appropriate.

import numpy as np
import pandas as pd
import anndata as ad
import scipy.sparse as sp

# --- RNA-seq: 200 cells x 2000 highly variable genes ---
np.random.seed(42)
n_cells = 200
cell_ids = [f"cell_{i:03d}" for i in range(n_cells)]

# Simulate log-normalized counts (in practice: load from h5ad after Scanpy preprocessing)
rna_counts = np.abs(np.random.randn(n_cells, 2000) * 2)
adata_rna = ad.AnnData(
    X=rna_counts,
    obs=pd.DataFrame(
        {"condition": ["A"] * 100 + ["B"] * 100,
         "patient": [f"P{i % 10}" for i in range(n_cells)]},
        index=cell_ids
    ),
    var=pd.DataFrame(index=[f"Gene_{i}" for i in range(2000)])
)

# --- ATAC-seq: same cells x 1000 peaks ---
atac_matrix = (np.random.rand(n_cells, 1000) > 0.8).astype(float)
adata_atac = ad.AnnData(
    X=atac_matrix,
    obs=adata_rna.obs.copy(),
    var=pd.DataFrame(index=[f"Peak_{i}" for i in range(1000)])
)

# Confirm alignment
assert list(adata_rna.obs_names) == list(adata_atac.obs_names), "Cell indices must match"
print(f"RNA: {adata_rna.shape}, ATAC: {adata_atac.shape}")
print(f"Conditions: {adata_rna.obs['condition'].value_counts().to_dict()}")

Step 2: Create the MOFA+ Model Object

Instantiate the entry_point and register all data views. Views are provided as a list-of-lists: data[groups][views]. Assign meaningful view and group names for interpretability.

from mofapy2.run.entry_point import entry_point

ent = entry_point()

# Configure data options before setting data
ent.set_data_options(
    scale_groups=False,   # Do not rescale variance between groups
    scale_views=True,     # Rescale each view to unit variance (recommended when views differ in scale)
)

# Provide data as list-of-lists: [groups][views]
# Single group → wrap each view in a list
ent.set_data_matrix(
    data=[[adata_rna.X, adata_atac.X]],       # outer list = groups, inner = views
    likelihoods=["gaussian", "bernoulli"],      # gaussian for continuous, bernoulli for binary ATAC
    views_names=["RNA", "ATAC"],
    groups_names=["all_cells"],
    samples_names=[list(adata_rna.obs_names)]  # one list per group
)

print("Data registered. Views: RNA, ATAC | Groups: all_cells")

Step 3: Set Model and Training Options

Configure the number of factors and training hyperparameters. More factors capture finer variation but increase computation and risk overfitting; convergence_mode="medium" balances speed and accuracy.

# Model options
ent.set_model_options(
    factors=15,          # Number of latent factors (start with 15; prune inactive ones automatically)
    spikeslab_weights=True,  # Sparse weight prior (ARD+spike-slab); recommended for feature selection
    ard_factors=True,    # Automatic relevance determination per factor per view
    ard_weights=True,    # ARD per feature weight; enables pruning of irrelevant features
)

# Training options
ent.set_train_options(
    iter=1000,                     # Maximum EM iterations
    convergence_mode="medium",     # "fast" (<1000 iter), "medium" (default), "slow" (>5000 iter)
    startELBO=1,                   # Start computing ELBO from iteration 1
    freqELBO=5,                    # Compute ELBO every 5 iterations
    dropR2=0.01,                   # Drop factors explaining < 1% variance (set to None to disable)
    seed=42,
    verbose=False
)

print("Model and training options set")

Step 4: Build and Train the Model

Build the internal data structures, then run variational inference. Training produces a fitted model where each factor's weights and scores are optimized to maximize the evidence lower bound (ELBO).

# Build internal model structure
ent.build()

# Run training (EM algorithm with variational Bayes updates)
ent.run()

# Save trained model to HDF5 — required for downstream analysis
output_path = "mofa_model.hdf5"
ent.save(output_path, overwrite=True)
print(f"Model trained and saved to {output_path}")

Step 5: Load Trained Model and Inspect Variance Explained

Load the HDF5 model and inspect how much variance each factor explains per view. Factors explaining less than ~1-2% total variance are typically noise.

import h5py
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns

def load_mofa_r2(model_path):
    """Extract variance explained (R2) per factor per view from MOFA+ HDF5."""
    with h5py.File(model_path, "r") as f:
        r2 = f["variance_explained"]["r2_per_factor"]
        views = [v.decode() for v in f["views"]["views"][:]]
        groups = [g.decode() for g in f["groups"]["groups"][:]]

        # r2_per_factor: shape (n_groups, n_views, n_factors)
        r2_array = np.stack([r2[g][:] for g in groups], axis=0)  # (groups, views, factors)

    # Average across groups; shape → (n_views, n_factors)
    r2_mean = r2_array.mean(axis=0)
    n_factors = r2_mean.shape[1]
    df = pd.DataFrame(r2_mean * 100,
                      index=views,
                      columns=[f"Factor{i+1}" for i in range(n_factors)])
    return df

r2_df = load_mofa_r2("mofa_model.hdf5")
print("Variance explained (%) per factor per view:")
print(r2_df.round(2))

# Heatmap of variance explained
fig, ax = plt.subplots(figsize=(max(8, r2_df.shape[1] * 0.6), 3))
sns.heatmap(r2_df, annot=True, fmt=".1f", cmap="YlOrRd",
            linewidths=0.5, ax=ax, vmin=0)
ax.set_title("MOFA+ Variance Explained (%) per Factor per View")
ax.set_xlabel("Factor")
ax.set_ylabel("Omics View")
plt.tight_layout()
plt.savefig("mofa_variance_explained.png", dpi=200)
print("Saved mofa_variance_explained.png")

Step 6: Extract Factor Scores and Correlate with Metadata

Factor scores (Z matrix) are the per-sample coordinates in factor space. Correlate scores with continuous or categorical metadata to biologically annotate each factor.

import scipy.stats as stats

def load_mofa_factors(model_path):
    """Load factor scores (Z) from MOFA+ HDF5. Returns DataFrame (samples x factors)."""
    with h5py.File(model_path, "r") as f:
        groups = [g.decode() for g in f["groups"]["groups"][:]]
        factors_list = []
        for g in groups:
            z = f["expectations"]["Z"][g][:]   # shape: (n_factors, n_samples)
            samples = [s.decode() for s in f["samples"][g][:]]
            n_factors = z.shape[0]
            df = pd.DataFrame(z.T, index=samples,
                              columns=[f"Factor{i+1}" for i in range(n_factors)])
            factors_list.append(df)
    return pd.concat(factors_list, axis=0)

factors_df = load_mofa_factors("mofa_model.hdf5")
print(f"Factor scores: {factors_df.shape} (cells x factors)")

# Merge with metadata
meta = adata_rna.obs[["condition", "patient"]].copy()
factors_meta = factors_df.join(meta)

# Point-biserial correlation: factor score vs binary metadata
factor_cols = [c for c in factors_meta.columns if c.startswith("Factor")]
print("\nFactor–Condition correlation (eta-squared approximation):")
for fc in factor_cols[:5]:
    groups_vals = [factors_meta.loc[factors_meta["condition"] == g, fc].values
                   for g in factors_meta["condition"].unique()]
    stat, pval = stats.f_oneway(*groups_vals)
    print(f"  {fc}: F={stat:.2f}, p={pval:.3f}")

Step 7: Visualize Factors — Scatter Plots and Feature Heatmaps

Extract the feature weights (loadings) per factor here, then read skills/data-visualization/omics-plotting/SKILL.md and follow its recipes so figures share one consistent style: factors_meta (from Step 6) → factor scatter (→ figures/mofa_factor_scatter.png); weights_rna → expression heatmap of the top ± loadings (→ figures/mofa_rna_weights_heatmap.png).

def load_mofa_weights(model_path, view_name):
    """Load feature weights (W) for a specific view. Returns DataFrame (features x factors)."""
    with h5py.File(model_path, "r") as f:
        w = f["expectations"]["W"][view_name][:]   # (n_factors, n_features)
        features = [ft.decode() for ft in f["features"][view_name][:]]
        n_factors = w.shape[0]
        df = pd.DataFrame(w.T, index=features,
                          columns=[f"Factor{i+1}" for i in range(n_factors)])
    return df

weights_rna = load_mofa_weights("mofa_model.hdf5", "RNA")
print(f"RNA weights: {weights_rna.shape} (features x factors)")

# Plot inputs are ready; use the omics-plotting SKILL (`skills/data-visualization/omics-plotting/SKILL.md`) to render:
#   factors_meta -> "factor scatter"  -> figures/mofa_factor_scatter.png
#   weights_rna  -> loading heatmap   -> figures/mofa_rna_weights_heatmap.png

Step 8: Downstream — Cluster Cells by Factor Scores and Enrichment

Use factor scores as a low-dimensional embedding for clustering, and extract top-weighted genes per factor for pathway enrichment.

from sklearn.cluster import KMeans
from sklearn.preprocessing import StandardScaler
import warnings

# --- Cluster cells using factor scores ---
factor_cols = [c for c in factors_df.columns if c.startswith("Factor")]
X_factors = StandardScaler().fit_transform(factors_df[factor_cols].values)

kmeans = KMeans(n_clusters=4, random_state=42, n_init=10)
with warnings.catch_warnings():
    warnings.simplefilter("ignore")
    cluster_labels = kmeans.fit_predict(X_factors)

factors_df["mofa_cluster"] = cluster_labels.astype(str)
print(f"K-means clusters (k=4):\n{pd.Series(cluster_labels).value_counts().sort_index()}")

# --- Extract top-weighted genes per factor for enrichment input ---
weights_rna = load_mofa_weights("mofa_model.hdf5", "RNA")

enrichment_inputs = {}
for fc in [f"Factor{i+1}" for i in range(min(5, weights_rna.shape[1]))]:
    # Positive weights: top activating genes; negative: top repressing genes
    top_pos = weights_rna[fc].nlargest(100).index.tolist()
    top_neg = weights_rna[fc].nsmallest(100).index.tolist()
    enrichment_inputs[f"{fc}_positive"] = top_pos
    enrichment_inputs[f"{fc}_negative"] = top_neg

# Save gene lists for external enrichment (e.g., gseapy Enrichr)
for name, genes in list(enrichment_inputs.items())[:2]:
    print(f"\n{name} — top 10: {genes[:10]}")

# Example: run ORA with gseapy (install separately)
# import gseapy
# enr = gseapy.enrichr(gene_list=enrichment_inputs["Factor1_positive"],
#                       gene_sets="GO_Biological_Process_2023",
#                       organism="human", outdir=None)
# print(enr.results.head(5)[["Term", "Adjusted P-value", "Genes"]])

factors_df.to_csv("mofa_factor_scores.csv")
print("\nFactor scores with cluster labels saved to mofa_factor_scores.csv")

Key Parameters

Parameter	Default	Range / Options	Effect
factors	15	5–50	Number of latent factors to infer; inactive ones pruned by ARD
likelihoods	(required)	"gaussian", "bernoulli", "poisson"	Per-view likelihood; gaussian for normalized continuous, bernoulli for binary ATAC, poisson for raw counts
scale_views	True	True/False	Rescale each view to unit variance; recommended when views differ in scale or unit
scale_groups	False	True/False	Rescale variance across groups; set True if groups have very different total variances
spikeslab_weights	True	True/False	Spike-and-slab sparsity prior on weights; enables feature selection via near-zero weights
ard_factors	True	True/False	Automatic relevance determination per factor per view; prunes factors not used in a view
iter	1000	200–5000	Maximum EM iterations; convergence usually reached in 200–800
convergence_mode	"medium"	"fast", "medium", "slow"	ELBO convergence tolerance: fast = 1e-4, medium = 1e-6, slow = 1e-8
dropR2	0.01	None, 0.001–0.05	Drop factors explaining less than this fraction of variance; None keeps all
startELBO	1	1–100	Iteration to start ELBO monitoring; set higher to skip initial instability

Key Concepts

Latent Factors and Loadings

Each latent factor Z_k (a vector of length n_samples) represents a source of variation. The corresponding weight matrix W_k (a vector of length n_features per view) contains the loading of each feature on that factor. Factors with spike-and-slab priors produce sparse loadings: most weights are shrunk to near zero, leaving a small set of features that meaningfully drive the factor. A positive weight means higher factor score correlates with higher feature expression.

Multi-Group vs Single-Group

A "group" in MOFA+ is a set of samples that share the same factor weight matrices W but have independent factor score distributions Z. Use multi-group analysis when:

• Samples come from distinct cohorts with batch-level differences (patients, datasets)
• You want to compare how much each factor explains within vs between groups
• You expect the same biological programs to operate differently across conditions

Single-group analysis (all samples in one group) is appropriate when samples are from a single experiment with no major batch structure.

Variance Explained Heatmap Interpretation

The R2 heatmap (views x factors) is the primary diagnostic output. Factors should show:

• View-specific R2: a factor driving only RNA captures transcriptional programs; one driving both RNA and ATAC captures chromatin-accessibility-coupled gene expression
• Declining R2: Factor 1 explains the most variance; factors should be inspected in order
• Factors with <1% R2 in all views can generally be ignored

Common Recipes

Recipe: Multi-Group Analysis Across Conditions

Use when comparing two or more patient groups or experimental conditions, where you want to identify condition-specific vs shared factors.

from mofapy2.run.entry_point import entry_point
import numpy as np
import pandas as pd
import anndata as ad

# Simulate two groups: condition A (100 cells) and condition B (100 cells)
np.random.seed(0)
n_per_group, n_genes, n_peaks = 100, 1000, 500
groups = {"condA": {}, "condB": {}}

for g in groups:
    groups[g]["rna"] = np.abs(np.random.randn(n_per_group, n_genes))
    groups[g]["atac"] = (np.random.rand(n_per_group, n_peaks) > 0.75).astype(float)

sample_ids_A = [f"A_cell_{i}" for i in range(n_per_group)]
sample_ids_B = [f"B_cell_{i}" for i in range(n_per_group)]

ent = entry_point()
ent.set_data_options(scale_groups=False, scale_views=True)

# Multi-group: data[groups][views] — two groups, each with RNA and ATAC
ent.set_data_matrix(
    data=[[groups["condA"]["rna"], groups["condA"]["atac"]],
          [groups["condB"]["rna"], groups["condB"]["atac"]]],
    likelihoods=["gaussian", "bernoulli"],
    views_names=["RNA", "ATAC"],
    groups_names=["condA", "condB"],
    samples_names=[sample_ids_A, sample_ids_B]
)

ent.set_model_options(factors=10, spikeslab_weights=True, ard_factors=True)
ent.set_train_options(iter=500, convergence_mode="fast", seed=0, verbose=False)
ent.build()
ent.run()
ent.save("mofa_multigroup.hdf5", overwrite=True)

# Compare factor scores between groups
factors_all = load_mofa_factors("mofa_multigroup.hdf5")
factors_all["group"] = ["condA"] * n_per_group + ["condB"] * n_per_group
print(f"Multi-group model trained. Factor scores: {factors_all.shape}")
print(factors_all.groupby("group")[["Factor1", "Factor2"]].mean().round(3))

Recipe: Identify and Annotate Factors by Top-Weighted Genes

Retrieve the top positive and negative loading genes per factor and print a summary table for biological annotation.

import pandas as pd

def annotate_factors(model_path, view_name="RNA", top_n=20, n_factors=5):
    """
    Summarize top-loading features per factor to assist biological annotation.

    Returns a DataFrame with factor names, top positive genes, top negative genes,
    and the absolute weight range (an activity proxy).
    """
    weights = load_mofa_weights(model_path, view_name)
    factor_cols = [f"Factor{i+1}" for i in range(min(n_factors, weights.shape[1]))]

    rows = []
    for fc in factor_cols:
        w = weights[fc]
        top_pos = w.nlargest(top_n).index.tolist()
        top_neg = w.nsmallest(top_n).index.tolist()
        rows.append({
            "Factor": fc,
            "Max_weight": round(w.max(), 4),
            "Min_weight": round(w.min(), 4),
            "Top_positive": ", ".join(top_pos[:5]),
            "Top_negative": ", ".join(top_neg[:5]),
        })

    summary = pd.DataFrame(rows)
    return summary

summary_df = annotate_factors("mofa_model.hdf5", view_name="RNA", top_n=20, n_factors=5)
print("\nFactor annotation summary (RNA view):")
print(summary_df.to_string(index=False))
summary_df.to_csv("mofa_factor_annotation.csv", index=False)
print("\nSaved mofa_factor_annotation.csv")

Expected Outputs

Output	Description
mofa_model.hdf5	Trained MOFA+ model — factor scores, weights, ELBO trace, variance explained
mofa_variance_explained.png	Heatmap of R2 (%) per factor per view; primary diagnostic for factor selection
figures/mofa_factor_scatter.png	Scatter plots of Factor1 vs Factor2/3 colored by metadata (condition, patient); via omics-plotting
figures/mofa_rna_weights_heatmap.png	Heatmap of top RNA feature weights across the first 5 factors; via omics-plotting
mofa_factor_scores.csv	Table of per-cell factor scores (cells x factors) with cluster labels
mofa_factor_annotation.csv	Factor annotation table: top positive/negative genes per factor
Per-factor gene lists	Input for gseapy Enrichr or GSEA to identify enriched pathways per factor

Troubleshooting

Problem	Cause	Solution
KeyError in set_data_matrix	Mismatched number of groups, views, or sample list dimensions	Ensure data, likelihoods, views_names, groups_names, samples_names all have consistent lengths
All factors show near-zero variance explained	Data not preprocessed or scale mismatch across views	Normalize each view before input; set scale_views=True; verify non-zero variance in input matrices
Model trains but factor scores are NaN	Convergence failure due to extreme values or near-singular data	Check for Inf/NaN in input matrices; reduce iter; try convergence_mode="fast" first
Too many factors pruned (only 1-2 remain)	dropR2 threshold too aggressive or insufficient variation in data	Set dropR2=0.001 or dropR2=None; increase data diversity or reduce noise
HDF5 file cannot be read	File truncated due to crash during training	Re-run training; check disk space; use overwrite=True in ent.save()
Factor scores identical across all samples	Single-sample group or zero-variance input view	Confirm at least 2 distinct samples per group; check input matrix is not all zeros
Very slow training (>1 hr)	Large feature space (>10k features per view) or many factors	Pre-filter to top HVGs (2000-5000) per view; reduce factors to 10-15; enable verbose=False
ELBO not converging (oscillates)	Learning rate instability or poorly scaled data	Increase startELBO; standardize each view independently; use convergence_mode="slow"
Weights all near zero for one view	Bernoulli likelihood on continuous data or vice versa	Verify likelihoods list matches view data types; use "gaussian" for normalized RNA
ModuleNotFoundError: mofapy2	Package not installed	pip install mofapy2

References

• MOFA2 GitHub repository — Source code for mofapy2 (Python) and MOFA2 R package
• MOFA2 documentation and tutorials — Official documentation with vignettes for Python and R
• Argelaguet et al. (2020) — "MOFA+: a statistical framework for comprehensive integration of multi-modal single-cell data", Genome Biology
• Argelaguet et al. (2018) — Original MOFA paper, Molecular Systems Biology
• mofapy2 PyPI package — Installation and version history