``tweedie_link_power``
----------------------
- Available in: GLM
- Hyperparameter: yes
Description
~~~~~~~~~~~
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. When ``family=tweedie``, the ``tweedie_link_power`` option can be used to specify the power for the tweedie link function. The link functions :math:`g(\cdot)` are of the form :math:`g(\eta) = \eta^{link.power}`.
This option defaults to 1.
The following describes the values that can be specified for this option:
- A value of 0 specifies a logarithm link (log-link) function. This is typically used for a count of occurrences in a fixed amount of time/space and is defined as **X**:math:`\beta = ln(\mu)`
- A value of 1 - vpow (1 minus the variance power) specifies a canonical link function.
- A value of 1 specifies an identity link function. This is typically used for linear-response data and is defined as **X**:math:`\beta = \mu`
- A value of 2 specifies an inverse link function. This is defined as **X**:math:`\beta = \mu^{-2}`
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 |
+------------------+------------------------+--------------------+
| Inverse-Gaussian | 3 | 1, 1-vpow |
+------------------+------------------------+--------------------+
Related Parameters
~~~~~~~~~~~~~~~~~~
- `family <family.html>`__
- `link <link.html>`__
- `tweedie_variance_power <tweedie_variance_power.html>`__
Example
~~~~~~~
.. example-code::
.. code-block:: r
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 $1000s)
response <- "y"
# split into train and validation sets
auto.splits <- h2o.splitFrame(data = auto, ratios = .8)
train <- auto.splits[[1]]
valid <- auto.splits[[2]]
# try using the `tweedie_link_power` parameter:
# train your model, where you specify tweedie_link_power
auto_glm <- h2o.glm(x = predictors, y = response, training_frame = train,
validation_frame = valid,
family = 'tweedie',
tweedie_link_power = 1)
# print the mse for validation set
print(h2o.mse(auto_glm, valid=TRUE))
# look at several values of `tweedie_link_power`
# use the tweedie_variance_power (vp) with the tweedie_link_power to create the canonical link function
vp_list = list(0, 1, 1.1, 1.2,1.3,1.4,1.5,1.6,1.7,1.8,1.9,2,
2.1, 2.2,2.3,2.4,2.5,2.6,2.7,2.8,2.9,3, 5, 7)
# create a dataframe with the tweedie_variance_power, tweedie_link_power, and corresponding mse
model_results <-lapply(vp_list, function(vp) {
auto_glm_2 <- h2o.glm(x = predictors, y = response, training_frame = train,
validation_frame = valid,
family = 'tweedie', tweedie_variance_power = vp,
tweedie_link_power = 1.0 - vp)
temp_df <- data.frame(vp, 1.0 - vp, h2o.mse(auto_glm_2, valid = TRUE))
names(temp_df) <- c("variance_power","link_power","mse")
return(temp_df)})
results = do.call('rbind',model_results)
# print results
results[order(results$mse),]
.. code-block:: python
import pandas as pd
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_link_power` parameter:
# initialize the estimator then train the model
auto_glm = H2OGeneralizedLinearEstimator(family = 'tweedie', tweedie_link_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))
# look at several values of `tweedie_link_power`
# use the tweedie_variance_power (vp) with the tweedie_link_power to create the canonical link function
vp_list = [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]
# loop though the values and append values to the list 'results'
results = []
for vp in vp_list:
auto_glm_2 = H2OGeneralizedLinearEstimator(family = 'tweedie',
tweedie_variance_power = vp,
tweedie_link_power = 1.0 - vp)
auto_glm_2.train(x = predictors, y = response, training_frame = train, validation_frame = valid)
results.append((vp, 1-vp, auto_glm_2.mse(valid=True)))
# create a pandas dataframe that has the tweedie_variance_power,tweedie_link_power, and corresponding mse
pd.DataFrame(sorted(results, key=lambda triple: triple[2]), columns=['variance_power', 'link_power', 'mse'])