Contents
What is the adaptive lasso?
Adaptive lasso is a weighted 1 penalization method for simultaneous estimation and model selection. It has oracle properties of asymptotic normality with optimal convergence rate and model selection consistency.
What is adaptive lasso regression?
The lasso is a popular technique for simultaneous estimation and variable selection. We then propose a new version of the lasso, called the adaptive lasso, where adaptive weights are used for penalizing different coefficients in the l1 penalty.
What is the Oracle property?
The oracle property means that the penalized estimator is asymptotically equivalent to the oracle estimator that is the ideal estimator obtained only with signal variables without penalization. Many noncovex penalties such as the bridge and SCAD. penalties possess the oracle property.
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What is an Oracle estimator?
The oracle property is that the asymptotic distribution of the estimator is the same as the asymptotic distribution of the MLE on only the true support. That is, the estimator adapts to knowing the true support without paying a price (in terms of the asymptotic distribution.)
When to use Lasso regression to fit a model?
Lasso regression is a method we can use to fit a regression model when multicollinearity is present in the data. In a nutshell, least squares regression tries to find coefficient estimates that minimize the sum of squared residuals (RSS): where j ranges from 1 to p predictor variables and λ ≥ 0.
How big is the difference between adaptive lasso and lasso?
We see that the adaptive lasso error is almost 8 times smaller than the lasso error (1.4 from lasso compared to 11.8 from lasso). And in terms of variable selection, while lasso only selected correctly 13% of the 200 variables, the adaptive lasso selected correctly 100% of the variables.
Which is an example of an adaptive lasso estimator?
We can use, for example, an adaptive lasso estimator. This estimator was proposed initially by Zou (2006), and the idea behind it is pretty straightforward: add some weights w that corrects the bias in lasso. If a variable is important, it should have a small weight. This way it is lightly penalized and remains in the model.
Why do we need an adaptive lasso in Python?
Imagine you are working with a dataset in which you know that only a few of the variables are truly related with the response variable but you do not know which ones. Maybe you are dealing with a high dimensional dataset with more variables than observations, in which a simple linear regression model cannot be solved.