Jackknife variance estimates for random forest

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In statistics, jackknife variance estimates for random forest are a way to estimate the variance in random forest models, in order to eliminate the bootstrap effects.

Jackknife variance estimates[edit]

The sampling variance of bagged learners is:

Jackknife estimates can be considered to eliminate the bootstrap effects. The jackknife variance estimator is defined as:[1]

In some classification problems, when random forest is used to fit models, jackknife estimated variance is defined as:

Here, denotes a decision tree after training, denotes the result based on samples without observation.

Examples[edit]

E-mail spam problem is a common classification problem, in this problem, 57 features are used to classify spam e-mail and non-spam e-mail. Applying IJ-U variance formula to evaluate the accuracy of models with m=15,19 and 57. The results shows in paper( Confidence Intervals for Random Forests: The jackknife and the Infinitesimal Jackknife ) that m = 57 random forest appears to be quite unstable, while predictions made by m=5 random forest appear to be quite stable, this results is corresponding to the evaluation made by error percentage, in which the accuracy of model with m=5 is high and m=57 is low.

Here, accuracy is measured by error rate, which is defined as:

Here N is also the number of samples, M is the number of classes, is the indicator function which equals 1 when observation is in class j, equals 0 when in other classes. No probability is considered here. There is another method which is similar to error rate to measure accuracy:

Here N is the number of samples, M is the number of classes, is the indicator function which equals 1 when observation is in class j, equals 0 when in other classes. is the predicted probability of observation in class .This method is used in Kaggle[2] These two methods are very similar.

Modification for bias[edit]

When using Monte Carlo MSEs for estimating and , a problem about the Monte Carlo bias should be considered, especially when n is large, the bias is getting large:

To eliminate this influence, bias-corrected modifications are suggested:

References[edit]

  1. ^ Wager, Stefan; Hastie, Trevor; Efron, Bradley (2014-05-14). "Confidence Intervals for Random Forests: The Jackknife and the Infinitesimal Jackknife". Journal of Machine Learning Research. arXiv:1311.4555. Bibcode:2013arXiv1311.4555W.
  2. ^ Kaggle https://www.kaggle.com/c/otto-group-product-classification-challenge/details/evaluation. Retrieved 2015. Check date values in: |accessdate= (help); Missing or empty |title= (help)