Least Absolute Shrinkage and Selection Operator (LASSO)

LASSO adds a penalty equal to the absolute value of the magnitude of coefficients (L1 norm) to the loss function. This constraint shrinks less important feature coefficients to exactly zero, effectively removing them from the model. Unlike Ridge regression (L2), which only shrinks coefficients toward zero, LASSO produces sparse models that are inherently interpretable—critical in radiomics where identifying a small subset of predictive features from thousands of candidates is the primary goal.

In high-dimensional radiomic datasets where the number of features (p) often exceeds the number of patients (n), LASSO performs embedded feature selection during model training. The optimization process simultaneously:

• Minimizes prediction error on the training data
• Penalizes model complexity through the L1 constraint
• Eliminates redundant or noisy radiomic features This eliminates the need for separate filter or wrapper selection methods, reducing computational overhead and preventing information leakage between feature selection and model evaluation steps.

The tuning parameter λ (lambda) controls the strength of regularization. As λ increases:

• More coefficients are driven to exactly zero
• Model variance decreases but bias increases
• The optimal λ is typically selected via k-fold cross-validation The standard approach uses 1-standard-error rule: selecting the largest λ within one standard error of the minimum cross-validation error, yielding the most parsimonious model with predictive performance indistinguishable from the best model.

When radiomic features are highly correlated (e.g., multiple texture descriptors capturing similar patterns), LASSO tends to arbitrarily select one feature from the correlated group and zero out the others. This behavior:

• Produces simpler, more interpretable radiomic signatures
• Can lead to instability in feature selection across different data splits
• Is often addressed by stability selection or elastic net (which combines L1 and L2 penalties) Understanding this property is essential when validating radiomic biomarkers across multiple scanner vendors and acquisition protocols.

LASSO is typically solved using coordinate descent, an iterative algorithm that optimizes one coefficient at a time while holding others fixed. The soft-thresholding operator provides a closed-form update:

• If the partial residual is below the penalty threshold, the coefficient is set to exactly zero
• Otherwise, the coefficient is shrunk by the penalty amount This computational efficiency makes LASSO tractable for radiomic datasets with thousands of candidate features, fitting in seconds rather than the hours required by subset selection methods.

LASSO is the dominant method for building radiomic signatures—composite biomarkers combining multiple quantitative imaging features. The typical workflow:

• Extract 1,000+ radiomic features from segmented tumor volumes
• Apply Z-score normalization to standardize feature scales
• Fit LASSO-Cox or LASSO-logistic regression with 10-fold cross-validation
• The resulting model typically retains 5-20 features from thousands
• These selected features form a parsimonious, clinically deployable signature validated on independent external cohorts.