Glossary

Session 2 : Creating Multi-Omics Profiles

Global concepts across all parts

Term	Definition
Omic / omics layer	One molecular data type profiled on the same patients — transcriptomics (RNA-seq), proteomics, or methylation.
Subtype	The supervised prediction target — the breast cancer subtype label (e.g., Basal, LumA, LumB, Her2, Normal) for each patient in TCGA-BRCA.
Patient ID / index	The identifier used to align rows (patients) consistently across all omics matrices and the label vector.
Feature	A single measured variable within an omic (e.g., one gene’s expression, one protein level, one methylation probe).
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Train/test split	A single, patient-level split shared across all omics views, ensuring a patient’s data isn’t split across train and test in different views.
Out-of-fold (OOF) probabilities	Predicted probabilities for training patients generated via cross-validation, so that a meta-learner (stacking) is trained on predictions the base model didn’t get to “cheat” on — avoiding information leakage.
Cross-validation (cross_val_predict)	The technique used to generate out-of-fold predictions on the training set for building the stacking meta-learner.
Data leakage	When information from the test set inadvertently influences model training (e.g. fitting a scaler on all data instead of just training data), leading to overly optimistic performance estimates.
Standardization / scaling	Rescaling features (via StandardScaler) to comparable ranges before fitting; done inside the pipeline so scaling parameters are learned only from training data, not test data.
Label encoding	Converting categorical class labels (e.g. cancer subtypes) into integer codes that a model can work with.
Held-out test set	The patients not used in training, used only to evaluate final model performance.
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Balanced accuracy	The primary comparison metric — the average of per-class recall, which avoids favoring predictions on larger subtype classes.
Macro-F1	The unweighted average F1 score across all subtype classes.
Classification report	Per-class precision, recall, and F1-score summary for a model’s predictions.
Confusion matrix	A table cross-tabulating true vs. predicted subtypes
PCA (Principal Component Analysis)	Used only as a quick, exploratory 2D visualization of each omic (not fed into the classifiers) to see whether different omics separate patients/subtypes differently.

Part 1: Linear Methods for Multi-Omic Integration

Linear integration strategies

Term	Meaning in this notebook
Early integration (concatenation)	Combining all omics (transcriptomics, proteomics, methylation) into one wide feature matrix before training a single classifier. Simple and often strong, but increases dimensionality and doesn’t distinguish shared, redundant, or omic-specific signal.
Late integration (prediction averaging)	Training one classifier per omic, then combining their predicted class probabilities (by default, an equal-weighted average) into a final prediction. Keeps each omic’s model separate and interpretable.
Stacking (learned combiner / meta-learner)	A more adaptive form of late integration: instead of a fixed averaging rule, a second (“meta”) model is trained on the per-omic predicted probabilities to learn how much each omic should contribute, potentially differently per class.
Single-omic baseline	A classifier trained on just one omics layer, used as a reference point to judge whether any integration strategy actually improves over using the best individual omic alone.
Fusion rule	The rule used to combine modality-specific outputs — e.g., fixed equal-weight averaging (late integration) versus a learned rule (stacking).

Part 2: Correlation-Based / Factor-Based Multi-Omic Integration with MOFA

Core MOFA concepts

Term	Definition
MOFA (Multi-Omics Factor Analysis)	An unsupervised, intermediate-integration method that keeps omics views separate but learns one shared patient-level latent representation across them.
Intermediate integration (latent-factor integration)	An integration strategy that is neither early integration (concatenating all omics into one table) nor late integration (training separate models per view and combining results at the end); MOFA instead learns shared latent factors directly from multiple views.
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Sample	One patient. Each row in the omics matrices is a patient.
View	One omics layer measured on the same patients (e.g., transcriptomics, proteomics, methylation).
Group	A cohort or batch of samples; here a single group, TCGA-BRCA.
Feature	One measured variable within a view — a gene, protein, or methylation probe.
Factor	A hidden (“latent”) axis of variation learned by MOFA. May reflect a biological process, technical effect, subtype gradient, or other source of covariance across views. Factors are not automatically biological pathways — they must be interpreted after fitting.
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Factor value	The coordinate of one patient on one factor — how strongly that factor is active in that patient. Collected in the factor matrix Z.
Weight / loading	The contribution of one feature to one factor — which molecular features define the factor. Collected in the weight matrix W (one per view).
Variance explained (R2)	A summary (as a %) of how much of a view’s variance is reconstructed by a given factor. Read from the fitted model via mofax.
Factor activity	A factor’s value in a given patient (or the average factor value within a group, e.g., a subtype), used to describe how “on” or “off” that latent axis is.
Variable feature selection	Reducing high-dimensional views (transcriptomics, methylation) to their most variable features, computed on training patients only

MOFA definitions, structure, and math

Term	Definition
X_view / Y(v)	One molecular table (e.g., transcriptomics) — the observed omics data for view v.
Z (factor matrix)	Patients × factors matrix of factor values, shared across all views.
W(v) (weight/loading matrix)	Features × factors matrix for view v, giving each feature’s contribution to each factor.
Reconstruction	The approximation of each input matrix as X_view ≈ Z × W(v) + noise; conceptually similar to PCA but extended to multiple omics views simultaneously.
Sign ambiguity	The direction (positive/negative) of a factor and its weights is arbitrary — multiplying both by −1 describes the same pattern. Only relative differences between patients/features matter.
ARD (Automatic Relevance Determination)	A model mechanism (ard_factors, ard_weights) that automatically shrinks/down-weights factors or features that explain little signal, letting a compact model discover how many factors are actually needed.
Spike-and-slab prior	A sparsity-inducing prior (spikeslab_weights) that lets individual feature weights be effectively zero, making factors easier to interpret by concentrating on a smaller set of strong features.
Variational inference	The optimization approach MOFA uses to fit its probabilistic model — searching for factors and weights that best reconstruct the omics data while accounting for noise.
Eta-squared (η²)	An ANOVA-based statistic estimating the proportion of a factor’s total variation explained by subtype-group differences; used to rank factors by subtype association.
Active factors	The subset of the initialized (upper-bound) factors that are kept for interpretation, selected by summing each factor’s R2 across views and keeping those above a chosen cutoff (MIN_TOTAL_R2).
Projection	Estimating factor values for new (e.g., held-out test) patients by keeping the learned MOFA weights fixed and computing where those patients fall on the existing factors, without refitting the model.

Part 3: Deep Learning Integration Methods Methods

Core Deep-Learning Concepts

Term	Definition
Neural network	A model made of layers of connected “neurons” (weighted sums followed by a non-linear activation) that learns to map inputs to outputs by adjusting weights during training.
Multi-layer perceptron (MLP)	A basic type of neural network consisting of one or more fully-connected (Linear) layers stacked with non-linear activations in between.
Multi-modal encoder	A fusion strategy that trains a separate encoder for each data view first, then combines (concatenates) the resulting embeddings before a shared classifier.
Integrated Gradients	A gradient-based feature-attribution method that estimates each input feature’s contribution to a model’s prediction by integrating gradients along a path from a baseline input to the actual input.
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Encoder	The part of a neural network that compresses raw input features into a lower-dimensional internal representation (an embedding).
Embedding	A dense, lower-dimensional numeric vector that represents an input (e.g. a patient’s omics profile) in a way that preserves useful structure for downstream tasks.
Linear layer	A neural network layer that applies a weighted sum plus a bias to its inputs (y = Wx + b); the basic building block of an MLP.
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ReLU (Rectified Linear Unit)	A non-linear activation function, f(x) = max(0, x), applied after linear layers so the network can learn non-linear relationships.
Dropout	A regularisation technique that randomly “switches off” a fraction of neurons during training to reduce overfitting.
Batch / mini-batch	A small subset of training samples processed together in one forward/backward pass, rather than using the whole dataset at once.
Epoch	One complete pass through the entire training dataset during model training.
DataLoader	A PyTorch utility that wraps a dataset and serves it in shuffled mini-batches during training/evaluation.
Cross-entropy loss	A loss function commonly used for multi-class classification; it measures how well the predicted class probabilities match the true labels.
Adam optimiser	An adaptive gradient-descent algorithm commonly used to update neural network weights during training.
Weight decay (L2 regularisation)	A penalty added during training that discourages large weight values, helping to reduce overfitting.
Gradient descent	An optimisation method that iteratively adjusts model parameters in the direction that reduces the loss function.