lambda ---------- - Available in: GLM - Hyperparameter: yes Description ~~~~~~~~~~~ To get the best possible model, GLM needs to find the optimal values of the regularization parameters :math:\alpha and :math:\lambda. When performing regularization, penalties are introduced to the model buidling process to avoid overfitting, to reduce variance of the prediction error, and to handle correlated predictors. The two most common penalized models are ridge regression and LASSO (least absolute shrinkage and selection operator). The elastic net combines both penalties. These types of penalties are described in greater detail in the Regularization <../glm.html#regularization>__ section in GLM for more information. The lambda parameter controls the amount of regularization applied to the model. A non-negative value represents a shrinkage parameter, which multiplies :math:P(\alpha, \beta) in the objective. The larger lambda is, the more the coefficients are shrunk toward zero (and each other). When the value is 0, regularization is disabled, and ordinary generalized liner models are fit. The default value for lambda is calculated by H2O using a heuristic based on the training data. This option also works closely with the alpha __ parameter, which controls the distribution between the :math:\ell_1 (LASSO) and :math:\ell_2 (ridge regression) penalties. The following table describes the type of penalized model that results based on the values specifed for the lambda and alpha options. +------------------+-----------------------+------------------------------------------+ | lambda value | alpha value | Result | +==================+=======================+==========================================+ | lambda == 0 | alpha = any value | No regularization. alpha is ignored. | +------------------+-----------------------+------------------------------------------+ | lambda > 0 | alpha == 0 | Ridge Regression | +------------------+-----------------------+------------------------------------------+ | lambda > 0 | alpha == 1 | LASSO | +------------------+-----------------------+------------------------------------------+ | lambda > 0 | 0 < alpha < 1 | Elastic Net Penalty | +------------------+-----------------------+------------------------------------------+ Related Parameters ~~~~~~~~~~~~~~~~~~ - alpha __ - lambda_min_ratio __ - lambda_search __ - nlambdas __ Example ~~~~~~~ .. example-code:: .. code-block:: r library(h2o) h2o.init() # import the airlines dataset: # This dataset is used to classify whether a flight will be delayed 'YES' or not "NO" # original data can be found at http://www.transtats.bts.gov/ airlines <- h2o.importFile("http://s3.amazonaws.com/h2o-public-test-data/smalldata/airlines/allyears2k_headers.zip") # convert columns to factors airlines["Year"] <- as.factor(airlines["Year"]) airlines["Month"] <- as.factor(airlines["Month"]) airlines["DayOfWeek"] <- as.factor(airlines["DayOfWeek"]) airlines["Cancelled"] <- as.factor(airlines["Cancelled"]) airlines['FlightNum'] <- as.factor(airlines['FlightNum']) # set the predictor names and the response column name predictors <- c("Origin", "Dest", "Year", "UniqueCarrier", "DayOfWeek", "Month", "Distance", "FlightNum") response <- "IsDepDelayed" # split into train and validation airlines.splits <- h2o.splitFrame(data = airlines, ratios = .8) train <- airlines.splits[[1]] valid <- airlines.splits[[2]] # try using the lambda parameter: airlines.glm <- h2o.glm(family = 'binomial', x = predictors, y = response, training_frame = train, validation_frame = valid, lambda =.0001) # print the AUC for the validation data print(h2o.auc(airlines.glm, valid = TRUE)) # Example of values to grid over for lambda hyper_params <- list( lambda = c(1, 0.5, 0.1, 0.01, 0.001, 0.0001, 0.00001, 0) ) # 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: list(strategy = "RandomDiscrete") grid <- h2o.grid(x = predictors, y = response, family = 'binomial', training_frame = train, validation_frame = valid, algorithm = "glm", grid_id = "air_grid", hyper_params = hyper_params, search_criteria = list(strategy = "Cartesian")) ## Sort the grid models by AUC sortedGrid <- h2o.getGrid("air_grid", sort_by = "auc", decreasing = TRUE) sortedGrid .. code-block:: python import h2o from h2o.estimators.glm import H2OGeneralizedLinearEstimator h2o.init() # import the airlines dataset: # This dataset is used to classify whether a flight will be delayed 'YES' or not "NO" # original data can be found at http://www.transtats.bts.gov/ airlines= h2o.import_file("https://s3.amazonaws.com/h2o-public-test-data/smalldata/airlines/allyears2k_headers.zip") # convert columns to factors airlines["Year"]= airlines["Year"].asfactor() airlines["Month"]= airlines["Month"].asfactor() airlines["DayOfWeek"] = airlines["DayOfWeek"].asfactor() airlines["Cancelled"] = airlines["Cancelled"].asfactor() airlines['FlightNum'] = airlines['FlightNum'].asfactor() # set the predictor names and the response column name predictors = ["Origin", "Dest", "Year", "UniqueCarrier", "DayOfWeek", "Month", "Distance", "FlightNum"] response = "IsDepDelayed" # split into train and validation sets train, valid= airlines.split_frame(ratios = [.8]) # try using the lambda_ parameter: # initialize your estimator airlines_glm = H2OGeneralizedLinearEstimator(family = 'binomial', lambda_ = .0001) # then train your model airlines_glm.train(x = predictors, y = response, training_frame = train, validation_frame = valid) # print the auc for the validation data print(airlines_glm.auc(valid=True)) # Example of values to grid over for lambda # import Grid Search from h2o.grid.grid_search import H2OGridSearch # select the values for lambda_ to grid over hyper_params = {'lambda': [1, 0.5, 0.1, 0.01, 0.001, 0.0001, 0.00001, 0]} # 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 airlines_glm_2 = H2OGeneralizedLinearEstimator(family = 'binomial') # build grid search with previously made GLM and hyperparameters grid = H2OGridSearch(model = airlines_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 decreasing AUC sorted_grid = grid.get_grid(sort_by = 'auc', decreasing = True) print(sorted_grid)