sklearn.linear model.LassoLarsIC

A sklearn.linear model.LassoLarsIC is an LASSO-LARS Information Criteria System within sklearn.linear_model class.

• Context:
  • Usage:

1) Import LassoLarsIC model from scikit-learn : from sklearn.linear_model import LassoLarsIC

2) Create design matrix X and response vector Y

3) Create LassoLarsIC object: model=LassoLarsIC([criterion=’aic’, fit_intercept=True, verbose=False, normalize=True, precompute=’auto’, max_iter=500, eps=2.2204460492503131e-16, copy_X=True, positive=False, ...])

4) Choose method(s):

• fit(X, y[, copy_X]), fits the model using X, y as training data.
• get_params([deep]), gets parameters for this estimator.
• predict(X), predicts using the linear model
• score(X, y[, sample_weight]), returns the coefficient of determination R^2 of the prediction.
• set_params(**params), sets the parameters of this estimator.

• Example(s):
  • Lasso model selection: Cross-Validation / AIC / BIC
• Counter-Example(s):
  • sklearn.linear model.LinearRegression
  • sklearn.linear_model.Lasso
  • sklearn.linear_model.Ridge.
  • sklearn.linear_model.ARDRegression.
  • sklearn.linear_model.ElasticNet.
  • sklearn.linear_model.HuberRegressor.
  • sklearn.linear_model.Lars.
• See: Regression System, Regressor, Regularization Task, Cross-Validation Task, Akaike Information Criterion, Bayes Information Criterion, Bayesian Analysis.

---

---

References

2017A

• (Scikit-Learn) ⇒ http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LassoLarsIC.html
  • QUOTE: class sklearn.linear_model.LassoLarsIC(criterion=’aic’, fit_intercept=True, verbose=False, normalize=True, precompute=’auto’, max_iter=500, eps=2.2204460492503131e-16, copy_X=True, positive=False)

Lasso model fit with Lars using BIC or AIC for model selection

The optimization objective for Lasso is:

(1 / (2 * n_samples)) * ||y - Xw||^2_2 + alpha * ||w||_1

AIC is the Akaike information criterion and BIC is the Bayes Information criterion. Such criteria are useful to select the value of the regularization parameter by making a trade-off between the goodness of fit and the complexity of the model. A good model should explain well the data while being simple.

2017B

• (Scikit Learn) ⇒ "1.1.8. LARS Lasso" http://scikit-learn.org/stable/modules/linear_model.html#lars-lasso Retrieved:2017-11-05
  • QUOTE: LassoLars is a lasso model implemented using the LARS algorithm, and unlike the implementation based on coordinate_descent, this yields the exact solution, which is piecewise linear as a function of the norm of its coefficients.

(...)

The algorithm is similar to forward stepwise regression, but instead of including variables at each step, the estimated parameters are increased in a direction equiangular to each one’s correlations with the residual.

Instead of giving a vector result, the LARS solution consists of a curve denoting the solution for each value of the L1 norm of the parameter vector. The full coefficients path is stored in the array coef_path_, which has size (n_features, max_features+1). The first column is always zero.

---