"LinearRegression" (Machine Learning Method)
- Method for Predict .
- Predict values using a linear combination of features.
Details & Suboptions
- The linear regression predicts the numerical output y using a linear combination of numerical features . The conditional probability is modeled according to , with .
- The estimation of the parameter vector θ is done by minimizing the loss function 1/2sum_(i=1)^m(y_i-f(theta,x_i))^2+lambda_1sum_(i=1)^nTemplateBox[{{theta, _, i}}, Abs]+(lambda_2)/2 sum_(i=1)^ntheta_i^2, where m is the number of examples and n is the number of numerical features.
- The following suboptions can be given:
- Possible settings for the "OptimizationMethod" option include:
-
"NormalEquation" linear algebra method"StochasticGradientDescent" stochastic gradient method"OrthantWiseQuasiNewton" orthant-wise quasi-Newton method
- For this method, Information [PredictorFunction […],"Function"] gives a simple expression to compute the predicted value from the features.
Examples
open allclose allBasic Examples (2)
Train a predictor on labeled examples:
Look at the Information :
Predict a new example:
Generate two-dimensional data:
Train a predictor function on it:
Compare the data with the predicted values and look at the standard deviation:
Options (5)
"L1Regularization" (2)
Use the "L1Regularization" option to train a predictor:
Generate a training set and visualize it:
Train two predictors by using different values of the "L1Regularization" option:
Look at the predictor function to see how the larger L1 regularization has forced one parameter to be zero:
"L2Regularization" (2)
Use the "L2Regularization" option to train a predictor:
Generate a training set and visualize it:
Train two predictors by using different values of the "L2Regularization" option:
Look at the predictor functions to see how the L2 regularization has reduced the norm of the parameter vector:
"OptimizationMethod" (1)
Generate a large training set:
Train predictors with different optimization methods and compare their training times: