Regularization

Any modification to an estimator that deliberately adds bias to reduce variance, improving generalization when data are scarce or noisy. In BCI decoders the canonical forms are L2 / ridge (penalize squared weights, shrinking all weights smoothly and staying stable under correlated features), L1 / lasso (penalize absolute weights, driving some exactly to zero for embedded feature selection), and elastic net (a mix of the two). Covariance shrinkage is regularization of a covariance estimate; early stopping and dropout regularize neural networks.

The regularization strength is a hyperparameter that must be chosen by validation that never touches the test data. Because neural features are high-dimensional while calibration data are only minutes long, some regularization is almost always necessary; the practical question is which prior (smooth weights, sparse weights, filters that are smooth in time or space) best matches the signal.