title: One-hot-encoded categorical variables in LASSO, how to compare variable importance?
body: <p>I am working on a regression project in <code>sklearn</code> where I used LASSO regression on a variety of numeric and categorical variables. The categorical variables were transformed using the One-hot-encoder method.</p>
  
  <p>Since the feature matrix was normalized in the beginning, the absolute value of the coefficients in the final LASSO model should be able to represent the relative importance of the model.</p>
  
  <p>However, I cannot figure out the way to compare importance between a numeric variable and a categorical variable. For example (to predict housing price using square footage and household type):</p>
  
  <pre><code>Feature         Coefficient
  sqft             114.35
  type_house       67.11
  type_apartment   -23.97
  type_condo       5.14
  </code></pre>
  
  <p>What should be a reasonable way to compare the importance of sqft and type?</p>