family

  • Available in: GLM, GAM, HGLM

  • Hyperparameter: no

Description

GLM and GAM problems consist of three main components:

  • A random component \(f\) for the dependent variable \(y\): The density function \(f(y;\theta,\phi)\) has a probability distribution from the exponential family parametrized by \(\theta\) and \(\phi\). This removes the restriction on the distribution of the error and allows for non-homogeneity of the variance with respect to the mean vector.

  • A systematic component (linear model) \(\eta\): \(\eta = X\beta\), where \(X\) is the matrix of all observation vectors \(x_i\).

  • A link function \(g\): \(E(y) = \mu = {g^-1}(\eta)\) relates the expected value of the response \(\mu\) to the linear component \(\eta\). The link function can be any monotonic differentiable function. This relaxes the constraints on the additivity of the covariates, and it allows the response to belong to a restricted range of values depending on the chosen transformation \(g\).

Accordingly, in order to specify a GLM problem, you must choose a family function \(f\), link function \(g\), and any parameters needed to train the model.

You can specify one of the following family options based on the response column type:

  • gaussian: The data must be numeric (Real or Int). This is the default family.

  • binomial: The data must be categorical 2 levels/classes or binary (Enum or Int).

  • If the family is fractionalbinomial, the response must be a numeric between 0 and 1.

  • ordinal: The data must be categorical with at least 3 levels.

  • quasibinomial: The data must be numeric.

  • multinomial: The data can be categorical with more than two levels/classes (Enum).

  • poisson: The data must be numeric and non-negative (Int).

  • gamma: The data must be numeric and continuous and positive (Real or Int).

  • tweedie: The data must be numeric and continuous (Real) and non-negative.

  • negativebinomial: The data must be numeric and non-negative (Int).

  • AUTO: The family can fall into three cases based on the response:

    • If the data is Enum with cardinality = 2, then the family is automatically determined as binomial.

    • If the data is Enum with cardinality > 2, then the family is automatically determined as multinomial.

    • If the data is numeric (Real or Int), then the family is automatically determined as gaussian.

Refer to the Families section for detailed information about each family option.

Note: If your response column is binomial, then you must convert that column to a categorical (.asfactor() in Python and as.factor() in R) and set family = binomial. The following configurations can lead to unexpected results.

  • If you DO convert the response column to categorical and DO NOT to set family=binomial, then you will receive an error message.

  • If you DO NOT convert response column to categorical and DO NOT set the family, then the algorithm will assume the 0s and 1s are numbers and will provide a Gaussian solution to a regression problem.

Example

R

Python

library(h2o)
h2o.init()

# import the cars dataset:
# this dataset is used to classify whether or not a car is economical based on
# the car's displacement, power, weight, and acceleration, and the year it was made
cars <- h2o.importFile("https://s3.amazonaws.com/h2o-public-test-data/smalldata/junit/cars_20mpg.csv")

# convert response column to a factor
cars["economy_20mpg"] <- as.factor(cars["economy_20mpg"])

# set the predictor names and the response column name
predictors <- c("displacement", "power", "weight", "acceleration", "year")
response <- "economy_20mpg"

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

# try using the `family` parameter:
car_glm <- h2o.glm(x = predictors, y = response, family = 'binomial', training_frame = train,
                   validation_frame = valid)

# print the auc for your validation data
print(h2o.auc(car_glm, valid = TRUE))

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

# import the cars dataset:
# this dataset is used to classify whether or not a car is economical based on
# the car's displacement, power, weight, and acceleration, and the year it was made
cars = h2o.import_file("https://s3.amazonaws.com/h2o-public-test-data/smalldata/junit/cars_20mpg.csv")

# convert response column to a factor
cars["economy_20mpg"] = cars["economy_20mpg"].asfactor()

# set the predictor names and the response column name
predictors = ["displacement","power","weight","acceleration","year"]
response = "economy_20mpg"

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

# try using the `family` parameter:
# Initialize and train a GLM
cars_glm = H2OGeneralizedLinearEstimator(family = 'binomial')
cars_glm.train(x = predictors, y = response, training_frame = train, validation_frame = valid)

# print the auc for the validation data
cars_glm.auc(valid = True)