Aaai:uncorrelated Lasso

Si-bao Chen, Chris Ding, Bin Luo and Ying Xie. Uncorrelated Lasso. AAAI, 2013.

The first author is an associate professor of Chen Sibao Anhui University.

The second author, Chris Ding, is a professor at the University of Texas at Arlington, which he cited more than 15,700 times on Google scholar.

This article considers the correlation between features when Lasso does feature selection, so that the selected features are as irrelevant as possible to reduce redundancy.

The optimization form is a convex term that joins a correlation coefficient matrix (squared) after the original Lasso, such as:

Where Matrix C is the matrix of the square of correlation coefficient, it is symmetric semi-definite.

When λ2=0, degenerate into the general Lasso;

When C is a unit array, it is degraded to elastic-net.

The three parts of this optimization form are convex, so this is a convex problem with a unique global optimal solution.

This paper gives an iterative algorithm:

Convergence of the algorithm: it is proved that the objective function is non-increasing (non-increasing), that is, L (α (t+1)) ≤l (α (t)).

The first two lemma were proved.

The first lemma defines an auxiliary function

and proved that G (β (t+1)) ≤g (β (t)).

The second lemma proves L (β (t+1))-L (β (T)) ≤g (β (t+1))-G (β (t)).

Combined with two lemma, it is concluded that L (β (t+1))-L (β (t)) ≤0.

Finally, the experiment was on two genetic data (Colon Cancer and leukemia datasets).

Aaai:uncorrelated Lasso