Weighted Lasso estimates for sparse logistic regression: non-asymptotic properties with measurement errors

For high-dimensional models with a focus on classification performance, the ℓ₁-penalized logistic regression is becoming important and popular. However, the Lasso estimates could be problematic when penalties of different coefficients are all the same and not related to the data. We propose two types of weighted Lasso estimates, depending upon covariates determined by the McDiarmid inequality. Given sample size n and a dimension of covariates p, the finite sample behavior of our proposed method with a diverging number of predictors is illustrated by non-asymptotic oracle inequalities such as the ℓ₁-estimation error and the squared prediction error of the unknown parameters. We compare the performance of our method with that of former weighted estimates on simulated data, then apply it to do real data analysis.