Intel® oneAPI Data Analytics Library Developer Guide and Reference
Developer Guide and Reference
Least Absolute Shrinkage and Selection Operator (LASSO)
Least Absolute Shrinkage and Selection Operator (LASSO) is a method
for modeling relationship between a dependent variable (which may be
a vector) and one or more explanatory variables by fitting
regularized least squares model. Trained LASSO model can produce
sparse coefficients due to the use of regularization
term. LASSO regression is widely used in feature selection tasks. For
example, in the field of compressed sensing it is used to effectively
identify relevant features associated with the dependent variable
from a few observations with a large number of features. LASSO
regression is also used to overcome multicollinearity of feature
vectors in the training data set.
Let be a vector of input variables and be the response.
For each , the LASSO model has the form similar to linear and ridge regression model [Hoerl70],
except that the coefficients are trained by minimizing a regularized by penalty mean squared error (MSE)
Here , are referred to as independent variables,
is referred to as dependent variable or response and .
Let be a set of
training data (for regression task, , and for feature selection could be greater than ).
The matrix of size contains observations , ,
of independent variables.
For each , , the LASSO regression estimates
by minimizing the objective function:
In the equation above, the first term is a mean squared error function and the second one is a regularization term that
penalizes the norm of vector