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`laplace`

  • Available in: Naïve-Bayes
  • Hyperparameter: yes

Description​

This option specifies a value for the Laplace smoothing factor, which sets the conditional probability of a predictor. If the Laplace smoothing parameter is disabled (laplace = 0), then Naive Bayes will predict a probability of 0 for any row in the test set that contains a previously unseen categorical level. However, if the Laplace smoothing parameter is used (for example, laplace = 1), then the model can make predictions for rows that include previously unseen categorical level.

Laplace smoothing adjusts the maximum likelihood estimates by adding 1 to the numerator and kk to the denominator to allow for new categorical levels in the training set:

ϕj∣y=1=Σi=1m1(xj(i) = 1 ⋂y(i) = 1) + 1Σi=1m1(y(i) = 1) + k\phi_{j|y=1}= \frac{\Sigma_{i=1}^m 1(x_{j}^{(i)} \ = \ 1 \ \bigcap y^{(i)} \ = \ 1) \ + \ 1}{\Sigma_{i=1}^{m}1(y^{(i)} \ = \ 1) \ + \ k}

ϕj∣y=0=Σi=1m1(xj(i) = 1 ⋂y(i) = 0) + 1Σi = 1m1(y(i) = 0) + k\phi_{j|y=0}= \frac{\Sigma_{i=1}^m 1(x_{j}^{(i)} \ = \ 1 \ \bigcap y^{(i)} \ = \ 0) \ + \ 1}{\Sigma_{i \ = \ 1}^{m}1(y^{(i)} \ = \ 0) \ + \ k}

x(i)x^{(i)} represents features, y(i)y^{(i)} represents the response column, and kk represents the addition of each new categorical level. (kk functions to balance the added 1 in the numerator.)

Laplace smoothing should be used with care; it is generally intended to allow for predictions in rare events. As prediction data becomes increasingly distinct from training data, new models should be trained when possible to account for a broader set of possible feature values.

This value must be >=0 and defaults to 0.

  • None

Example​

library(h2o)
h2o.init()

# import the cars dataset:
prostate <- h2o.importFile("http://s3.amazonaws.com/h2o-public-test-data/smalldata/prostate/prostate.csv.zip")

# Converting CAPSULE, RACE, DCAPS, and DPROS to categorical
prostate$CAPSULE <- as.factor(prostate$CAPSULE)
prostate$RACE <- as.factor(prostate$RACE)
prostate$DCAPS <- as.factor(prostate$DCAPS)
prostate$DPROS <- as.factor(prostate$DPROS)

# Compare with Naive Bayes when x = 3:9, y = 2, and use laplace smoothing
prostate_nb <- h2o.naiveBayes(x = 3:9, y = 2, training_frame = prostate, laplace = 1)
print(prostate_nb)

# Predict on training data
prostate_pred <- predict(prostate_nb, prostate)
print(head(prostate_pred))
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