# Is standardizing data necessary for glasso?

I am wondering, if it is necessary to standardize data (mean zero and stddev eq. 1) for glasso. In many papers on glasso this is mentioned to have data with mean=0 and stddev 1, while using covarience matrix of the data for variable selection through glasso. However, in book "Using R! by Gentleman et al (Editors) covarience matrix is converted to correlation matrix and then glasso is applied without standardizing data.

Would appreciate explaination about it i.e. whether starndardization is necessary for glasso and if yes then why.

• I am not sure to follow: using the covariance of standardized variables is the same as using the correlation matrix, no?
– chl
Oct 8 '14 at 14:20
• What you have asked is a different question. My question is do we need to standardize data before glasso. In literature several papers say to have mean zero and covarience matrix sigma before running glasso. Several papers explicitly say to standardize data. However, in other places it is not done. Like in Book "USE R" Thibshirani is one of the authers and they don't normalize data before running glasso. Now I am confused do we need to starndize data or not? Oct 8 '14 at 14:24
• sorry authers are Søren Højsgaard, David Edwards et al and not Thibshirani Oct 8 '14 at 14:34

## 1 Answer

LASSO implements a penalty on the sum of the magnitudes of the coefficients relating predictor variables to the outcome. So unless some type of standardization is done, the variables retained by LASSO will depend on the relative scaling of each of the predictor variables. For example, it might matter whether you express a time variable in minutes versus hours. Transforming a covariance matrix to a correlation matrix is one type of scaling.

• great answer. I was looking for this explaination. In the book I have refered "USE R-Graphical Methods" Søren Højsgaard, David Edwards et al, used raw data to determine covarience but then converted the covarience matrix to correlation matrix before running glasso. I was wondering why didn't they standardize and why did they converted cov. matrix to correlation matrix. Could you comment. whether there will be any difference between standardizing data before determining covarience matrix and running glasso vs using correlation matrix before glasso. Thank You Oct 8 '14 at 14:32
• I don't think so, but I don't have experience specifically with glasso. Try it both ways (on a data subset if there are issues with time/cost of computation) and see if it makes a difference.
– EdM
Oct 8 '14 at 15:53
• Converting covariance to correlation and standardizing are the same thing, it's easy to show.
– Joe
Jul 13 '16 at 21:29