Cross-Validation¶

How Cross-Validation is Calculated¶

In general, for all algos that support the nfolds parameter, H2O’s cross-validation works as follows:

For example, for nfolds=5, 6 models are built. The first 5 models (cross-validation models) are built on 80% of the training data, and a different 20% is held out for each of the 5 models. Then the main model is built on 100% of the training data. This main model is the model you get back from H2O in R, Python and Flow.

This main model contains training metrics and cross-validation metrics (and optionally, validation metrics if a validation frame was provided). The main model also contains pointers to the 5 cross-validation models for further inspection.

All 5 cross-validation models contain training metrics (from the 80% training data) and validation metrics (from their 20% holdout/validation data). To compute their individual validation metrics, each of the 5 cross-validation models had to make predictions on their 20% of of rows of the original training frame, and score against the true labels of the 20% holdout.

For the main model, this is how the cross-validation metrics are computed: The 5 holdout predictions are combined into one prediction for the full training dataset (i.e., predictions for every row of the training data, but the model making the prediction for a particular row has not seen that row during training). This “holdout prediction” is then scored against the true labels, and the overall cross-validation metrics are computed.

This approach has some implications. Scoring the holdout predictions freshly can result in different metrics than taking the average of the 5 validation metrics of the cross-validation models. For example, if the sizes of the holdout folds differ a lot (e.g., when a user-given fold_column is used), then the average should probably be replaced with a weighted average. Also, if the cross-validation models map to slightly different probability spaces, which can happen for small DL models that converge to different local minima, then the confused rank ordering of the combined predictions would lead to a significantly different AUC than the average.

library(h2o)
h2o.init()
df <- h2o.importFile("http://s3.amazonaws.com/h2o-public-test-data/smalldata/prostate/prostate.csv.zip")
df$CAPSULE <- as.factor(df$CAPSULE)
model_fit <- h2o.gbm(3:8,2,df,nfolds=5,seed=1234)

# Default: AUC of holdout predictions
h2o.auc(model_fit,xval=TRUE)

# Optional: Average the holdout AUCs
cvAUCs <- sapply(sapply(model_fit@model$cross_validation_models, `[[`, "name"), function(x) { h2o.auc(h2o.getModel(x), valid=TRUE) })
print(cvAUCs)
mean(cvAUCs)

Using Cross-Validated Predictions¶

With cross-validated model building, H2O builds N+1 models: N cross-validated model and 1 overarching model over all of the training data.

Each cv-model produces a prediction frame pertaining to its fold. It can be saved and probed from the various clients if keep_cross_validation_predictions parameter is set in the model constructor.

These holdout predictions have some interesting properties. First they have names like:

prediction_GBM_model_1452035702801_1_cv_1

and they contain, unsurprisingly, predictions for the data held out in the fold. They also have the same number of rows as the entire input training frame with 0s filled in for all rows that are not in the hold out.

Let’s look at an example.

Here is a snippet of a three-class classification dataset (last column is the response column), with a 3-fold identification column appended to the end:

Each cross-validated model produces a prediction frame

prediction_GBM_model_1452035702801_1_cv_1
prediction_GBM_model_1452035702801_1_cv_2
prediction_GBM_model_1452035702801_1_cv_3

and each one has the following shape (for example the first one):

prediction_GBM_model_1452035702801_1_cv_1

The training rows receive a prediction of 0 (more on this below) as well as 0 for all class probabilities. Each of these holdout predictions has the same number of rows as the input frame.

Combining Holdout Predictions¶

The frame of cross-validated predictions is simply the superposition of the individual predictions. Here’s an example from R:

library(h2o)
h2o.init()

# H2O Cross-validated K-means example
prosPath <- system.file("extdata", "prostate.csv", package="h2o")
prostate.hex <- h2o.uploadFile(path = prosPath)
fit <- h2o.kmeans(training_frame = prostate.hex,
                  k = 10,
                  x = c("AGE", "RACE", "VOL", "GLEASON"),
                  nfolds = 5,  #If you want to specify folds directly, then use "fold_column" arg
                  keep_cross_validation_predictions = TRUE)

# This is where cv preds are stored:
fit@model$cross_validation_predictions$name


# Compress the CV preds into a single H2O Frame:
# Each fold's preds are stored in a N x 1 col, where the row values for non-active folds are set to zero
# So we will compress this into a single 1-col H2O Frame (easier to digest)

nfolds <- fit@parameters$nfolds
predlist <- sapply(1:nfolds, function(v) h2o.getFrame(fit@model$cross_validation_predictions[[v]]$name)$predict, simplify = FALSE)
cvpred_sparse <- h2o.cbind(predlist)  # N x V Hdf with rows that are all zeros, except corresponding to the v^th fold if that rows is associated with v
pred <- apply(cvpred_sparse, 1, sum)  # These are the cross-validated predicted cluster IDs for each of the 1:N observations

This can be extended to other family types as well (multinomial, binomial, regression):

# helper function
.compress_to_cvpreds <- function(h2omodel, family) {
  # return the frame_id of the resulting 1-col Hdf of cvpreds for learner l
  V <- h2omodel@allparameters$nfolds
  if (family %in% c("bernoulli", "binomial")) {
    predlist <- sapply(1:V, function(v) h2o.getFrame(h2omodel@model$cross_validation_predictions[[v]]$name)[,3], simplify = FALSE)
  } else {
    predlist <- sapply(1:V, function(v) h2o.getFrame(h2omodel@model$cross_validation_predictions[[v]]$name)$predict, simplify = FALSE)
  }
  cvpred_sparse <- h2o.cbind(predlist)  # N x V Hdf with rows that are all zeros, except corresponding to the v^th fold if that rows is associated with v
  cvpred_col <- apply(cvpred_sparse, 1, sum)
  return(cvpred_col)
}


# Extract cross-validated predicted values (in order of original rows)
h2o.cvpreds <- function(object) {

  # Need to extract family from model object
  if (class(object) == "H2OBinomialModel") family <- "binomial"
  if (class(object) == "H2OMulticlassModel") family <- "multinomial"
  if (class(object) == "H2ORegressionModel") family <- "gaussian"

  cvpreds <- .compress_to_cvpreds(h2omodel = object, family = family)
  return(cvpreds)
}