Verifying the Lasso Irrepresentable Condition without knowing true signals

Develop practical methods to verify or circumvent the Irrepresentable Condition (IRC) for Lasso variable selection when the identity of the true signal covariates within the active set is unknown, so that selection consistency can be assessed in high-dimensional forecasting models.

Background

The Lasso’s variable selection consistency relies on the Irrepresentable Condition, which restricts correlations between true signals and other covariates. The condition is central in determining whether Lasso will correctly identify the relevant predictors.

In practice, the true signals are not known ex ante, making it impossible to directly test whether the IRC holds. This practical limitation creates a methodological gap in validating Lasso-based selection in empirical applications.