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 __ - link __ - tweedie_variance_power __ 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'])