How to require prediction mean = y mean for deep learning

[nateschor]

Hi,

I was wondering if there is an argument to h2o.deeplearning() that would require $mean(\hat{y}) = mean(y)$?

In the example below, the mean of mpg is 0 while the mean of the predicted value is .06. For comparison, the nnet package predicts a mean of 0.

Please let me know if there is any other information I can provide you with. Thank you!

if (!requireNamespace("nnet", quietly = TRUE)) install.packages("nnet")
if (!requireNamespace("h2o", quietly = TRUE)) install.packages("h2o")

suppressPackageStartupMessages({
  library(nnet)
  library(h2o)
})

scaled_mtcars <- scale(mtcars)

mpg_scaled_mean <- mean(scaled_mtcars[, "mpg"])

set.seed(1234)

nnet_model <- nnet(mpg ~ ., data = as.data.frame(scaled_mtcars), size = 5, linout = TRUE, maxit = 200, trace = FALSE)
nnet_predictions <- predict(nnet_model, as.data.frame(scaled_mtcars))

nnet_mean <- mean(nnet_predictions)

invisible(capture.output(suppressWarnings(h2o.init())))
h2o.no_progress()

mtcars_h2o <- as.h2o(scaled_mtcars)

predictors <- setdiff(names(mtcars), "mpg")
response <- "mpg"

h2o_model <- h2o.deeplearning(
  x = predictors,
  y = response,
  training_frame = mtcars_h2o,
  hidden = 5,
  epochs = 200,
  activation = "Rectifier",
  rate = .0001,
  adaptive_rate = FALSE,
  standardize = TRUE,
  seed = 1234,
  reproducible = TRUE
)

h2o_predictions <- h2o.predict(h2o_model, mtcars_h2o)

h2o_mean <- mean(h2o_predictions$predict)

h2o.shutdown(prompt = FALSE)

data.frame(
  scaled_mgp_mean = mpg_scaled_mean,
  nnet_predicted_value_mean = nnet_mean,
  h2o_predicted_value_mean = h2o_mean
)
#>   scaled_mgp_mean nnet_predicted_value_mean h2o_predicted_value_mean
#> 1    7.112366e-17             -8.120994e-06               0.06660721

^{Created on 2024-10-13 with reprex v2.1.1}

Session info

sessioninfo::session_info()
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