Determining critical parameters using a high-dimensional variable selection model

A system comprising:

• a high-dimensional variable selection unit that includes a processor and electronic storage device in electronic communication with the input unit, wherein the high-dimensional variable selection unit is configured to:
• receive a plurality of sensor data and parametric tool measurements from a semiconductor manufacturing tool;
• determine a list of critical parameters from the plurality of sensor data and parametric tool measurements, wherein the high-dimensional variable selection unit is configured to analyze the plurality of sensor data and parametric tool measurements using a high-dimensional variable selection model, and wherein the high-dimensional variable selection model includes a formula (min(Y−BX))2+λ(∥X∥+∥X∥2), wherein Y is a performance measurement of the semiconductor manufacturing tool, X is a vector of input parameter, B is a vector of coefficient to estimate, and λ controls a degree that parameter coefficients are penalized;
• and
• re-parameterize the high-dimensional variable selection model in a hierarchical manner, wherein a hierarchy for re-parameterization is decided based on a weight of the input parameter.