Lasso¶

Model¶

For a matrix \(\mathsf{A \in \mathbb{R}^{m\times n}}\), a vector \(\mathsf{b \in \mathbb{R}^m}\), and a scalar \(\mathsf{\lambda > 0}\), the model is

\[ \mathsf{\underset{x \in \mathbb{R}^n }{min} \ |Ax - b|_2^2 + \lambda |x|_1. } \]

Overview¶

The Least Absolute Shrinkage and Selection Operator (Lasso) function is commonly used in statistics and machine learning for variable selection and regularization. Introduced by Tibshirani¹, it is primarily used in linear regression models, but its principles can be extended to other models as well. The key idea of the Lasso function is to add a penalty term to least squares regression that is the sum of absolute values of the coefficients.

Property
Convex	✅
Strongly Convex	🟡
Unbiased Estimator²	✅
Feasible Estimator	🟡

Code¶

CVXPYSCIPGurobiCPLEX

#include <iostream>

int main(void) {
  std::cout << "Hello world!" << std::endl;
  return 0;
}

#include <stdio.h>

int main(void) {
  printf("Hello world!\n");
  return 0;
}

#include <iostream>

int main(void) {
  std::cout << "Hello world!" << std::endl;
  return 0;
}

#include <iostream>

int main(void) {
  std::cout << "Hello world!" << std::endl;
  return 0;
}

Applications¶

Statistics...
Compressed sensing...

Lasso¶

Model¶

Overview¶

Code¶

Applications¶

See Also¶