Valid knockoffs for binary two-level designs with fixed margins

Construct valid knockoffs for binary two-level designs while preserving fixed margins, so that the knockoff filter and its Model-X extension can be applied to supersaturated screening with binary factor settings.

Background

The paper discusses stability selection and knockoff-based variable-selection methods as related screening approaches. It states that the knockoff filter and Model-X knockoffs do not directly apply to the binary two-level designs used in the study.

The unresolved technical issue is the construction of valid knockoffs that preserve the fixed margins of binary two-level designs. Solving this problem would make knockoff-based error-control methods applicable in this experimental-design setting.