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.

Example

R

Python

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 = .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))

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))