gradient_epsilon.rst

gradient_epsilon

• Available in: GLM, GAM
• Hyperparameter: no

Description

GLM and GAM include three criteria outside of max_iterations that define and check for convergence during logistic regression:

• beta_epsilon: Converge if the beta change is less than this value (or if beta stops changing). This is used by solvers.
• gradient_epsilon: Converge if the gradient value change is less than this value (using L-infinity norm). This is used when solver=L-BFGS.
• objective_epsilon: Converge if the relative objective value changes (for example, (old_val - new_val)/old_val). This is used by all solvers.

The default for these options is based on a heurisitic:

• beta_epsilon: The default for beta_epsilon is 1e-4.
• gradient_epsilon: If lambda_search is set to False and lambda is equal to zero, the default value of gradient_epsilon is equal to .000001; otherwise the default value is .0001. If lambda_search is set to True, then the conditional values above are 1E-8 and 1E-6 respectively.
• objective_epsilon: If lambda_search=True, then the default value of objective_epsilon is .0001. If lambda_search=False and lambda is equal to zero, then the default value of objective_epsilon is .000001. For any other value of lambda, the default value of objective_epsilon is set to .0001.

Related Parameters

• beta_epsilon
• max_iterations
• objective_epsilon
• solver

Example

.. tabs::
   .. code-tab:: r R

                library(h2o)
                h2o.init()

                # import the boston dataset:
                # this dataset looks at features of the boston suburbs and predicts median housing prices
                # the original dataset can be found at https://archive.ics.uci.edu/ml/datasets/Housing
                boston <- h2o.importFile("https://s3.amazonaws.com/h2o-public-test-data/smalldata/gbm_test/BostonHousing.csv")

                # set the predictor names and the response column name
                predictors <- colnames(boston)[1:13]
                # set the response column to "medv", the median value of owner-occupied homes in $1000's
                response <- "medv"

                # convert the chas column to a factor (chas = Charles River dummy variable (= 1 if tract bounds river; 0 otherwise))
                boston["chas"] <- as.factor(boston["chas"])

                # split into train and validation sets
                boston_splits <- h2o.splitFrame(data =  boston, ratios = 0.8)
                train <- boston_splits[[1]]
                valid <- boston_splits[[2]]

                # try using the `gradient_epsilon` parameter:
                # train your model, where you specify gradient_epsilon
                boston_glm <- h2o.glm(x = predictors, y = response, training_frame = train,
                                      validation_frame = valid,
                                      gradient_epsilon = 1e-3)

                # print the mse for the validation data
                print(h2o.mse(boston_glm, valid = TRUE))

   .. code-tab:: python

                import h2o
                from h2o.estimators.glm import H2OGeneralizedLinearEstimator
                h2o.init()

                # import the boston dataset:
                # this dataset looks at features of the boston suburbs and predicts median housing prices
                # the original dataset can be found at https://archive.ics.uci.edu/ml/datasets/Housing
                boston = h2o.import_file("https://s3.amazonaws.com/h2o-public-test-data/smalldata/gbm_test/BostonHousing.csv")

                # set the predictor names and the response column name
                predictors = boston.columns[:-1]
                # set the response column to "medv", the median value of owner-occupied homes in $1000's
                response = "medv"

                # convert the chas column to a factor (chas = Charles River dummy variable (= 1 if tract bounds river; 0 otherwise))
                boston['chas'] = boston['chas'].asfactor()

                # split into train and validation sets
                train, valid = boston.split_frame(ratios = [.8])

                # try using the `gradient_epsilon` parameter:
                # initialize the estimator then train the model
                boston_glm = H2OGeneralizedLinearEstimator(gradient_epsilon = 1e-3)
                boston_glm.train(x = predictors, y = response, training_frame = train, validation_frame = valid)

                # print the mse for validation set
                print(boston_glm.mse(valid=True))