# tweedie_variance_power¶

• Available in: GLM, GAM

• Hyperparameter: yes

## Description¶

When family=tweedie, this option can be used to specify the power for the tweedie variance. This option defaults to 0.

Tweedie distributions are a family of distributions that include gamma, normal, Poisson and their combinations. This distribution is especially useful for modeling positive continuous variables with exact zeros. The variance of the Tweedie distribution is proportional to the $$p$$-th power of the mean $$var(y_i) = \phi\mu{^p_i}$$.

The Tweedie distribution is parametrized by variance power $$p$$. It is defined for all $$p$$ values except in the (0,1) interval and has the following distributions as special cases:

• $$p = 0$$: Normal

• $$p = 1$$: Poisson

• $$p \in (1,2)$$: Compound Poisson, non-negative with mass at zero

• $$p = 2$$: Gamma

• $$p = 3$$: Gaussian

• $$p > 2$$: Stable, with support on the positive reals

The following table shows the acceptable relationships between family functions, tweedie variance powers, and tweedie link powers.

Family Function

Tweedie Variance Power

Tweedie Link Power

Poisson

1

0, 1-vpow, 1

Gamma

2

0, 1-vpow, 2

Gaussian

3

1, 1-vpow

## Example¶

library(h2o)
h2o.init()

# import the auto dataset:
# this dataset looks at features of motor insurance policies and predicts the aggregate claim loss
# the original dataset can be found at https://cran.r-project.org/web/packages/HDtweedie/HDtweedie.pdf
auto <- h2o.importFile("https://s3.amazonaws.com/h2o-public-test-data/smalldata/glm_test/auto.csv")

# set the predictor names and the response column name
predictors <- colnames(auto)[-1]
# The  response is aggregate claim loss (in $1000s) response <- "y" # split into train and validation sets auto_splits <- h2o.splitFrame(data = auto, ratios = 0.8) train <- auto_splits[] valid <- auto_splits[] # try using the tweedie_variance_power parameter: # train your model, where you specify tweedie_variance_power auto_glm <- h2o.glm(x = predictors, y = response, training_frame = train, validation_frame = valid, family = 'tweedie', tweedie_variance_power = 1) # print the mse for validation set print(h2o.mse(auto_glm, valid = TRUE)) # grid over tweedie_variance_power # select the values for tweedie_variance_power to grid over hyper_params <- list( tweedie_variance_power = c(0, 1, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 3, 5, 7) ) # this example uses cartesian grid search because the search space is small # and we want to see the performance of all models. For a larger search space use # random grid search instead: {'strategy': "RandomDiscrete"} # build grid search with previously selected hyperparameters grid <- h2o.grid(x = predictors, y = response, training_frame = train, validation_frame = valid, family = 'tweedie', algorithm = "glm", grid_id = "auto_grid", hyper_params = hyper_params, search_criteria = list(strategy = "Cartesian")) # Sort the grid models by mse sorted_grid <- h2o.getGrid("auto_grid", sort_by = "mse", decreasing = FALSE) sorted_grid # print the mse for the validation data print(h2o.mse(auto_glm, valid = TRUE))  import h2o from h2o.estimators.glm import H2OGeneralizedLinearEstimator h2o.init() # import the auto dataset: # this dataset looks at features of motor insurance policies and predicts the aggregate claim loss # the original dataset can be found at https://cran.r-project.org/web/packages/HDtweedie/HDtweedie.pdf auto = h2o.import_file("https://s3.amazonaws.com/h2o-public-test-data/smalldata/glm_test/auto.csv") # set the predictor names and the response column name predictors = auto.names predictors.remove('y') # The response is aggregate claim loss (in$1000s)
response = "y"

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

# try using the tweedie_variance_power parameter:
# initialize the estimator then train the model
auto_glm = H2OGeneralizedLinearEstimator(family = 'tweedie', tweedie_variance_power = 1)
auto_glm.train(x = predictors, y = response, training_frame = train, validation_frame = valid)

# print the mse for the validation data
print(auto_glm.mse(valid=True))

# grid over tweedie_variance_power
# import Grid Search
from h2o.grid.grid_search import H2OGridSearch

# select the values for tweedie_variance_power to grid over
hyper_params = {'tweedie_variance_power': [0, 1, 1.1, 1.2,1.3,1.4,1.5,1.6,1.7,1.8,1.9,2,
2.1, 2.2,2.3,2.4,2.5,2.6,2.7,2.8,2.9,3, 5, 7]}

# this example uses cartesian grid search because the search space is small
# and we want to see the performance of all models. For a larger search space use
# random grid search instead: {'strategy': "RandomDiscrete"}
# initialize the GLM estimator
auto_glm_2 = H2OGeneralizedLinearEstimator(family = 'tweedie')

# build grid search with previously made GLM and hyperparameters
grid = H2OGridSearch(model = auto_glm_2, hyper_params = hyper_params,
search_criteria = {'strategy': "Cartesian"})

# train using the grid
grid.train(x = predictors, y = response, training_frame = train, validation_frame = valid)

# sort the grid models by mse
sorted_grid = grid.get_grid(sort_by='mse', decreasing=False)
print(sorted_grid)