Package 'rfinterval'

Beijing PM2.5 Air Pollution Data

Description

This hourly data set contains the PM2.5 data of US Embassy in Beijing. Meanwhile, meteorological data from Beijing Capital International Airport are also included.

Usage

BeijingPM25

Format

A data frame with 8661 rows and 11 variables:

pm2.5

PM2.5 concentration (ug/m^3)

month

month of observation

day

day of observation

hour

hour of observation

DEWP

dew point

TEMP

temperature

PRES

air pressure

cbwd

combined wind direction

Iws

cumulated wind speed

Is

cumulated hours of snow

Ir

cumulated hours of rain

Source

Liang, X., Zou, T., Guo, B., Li, S., Zhang, H., Zhang, S., Huang, H. and Chen, S. X. (2015). Assessing Beijing's PM2.5 pollution: severity, weather impact, APEC and winter heating. Proceedings of the Royal Society A, 471, 20150257.

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Prediction Intervals for Random forests

Description

The rfinterval constructs prediction intervals for random forest predictions using a fast implementation package 'ranger'.

Usage

rfinterval(formula = NULL, train_data = NULL, test_data = NULL,
  method = c("oob", "split-conformal", "quantreg"), alpha = 0.1,
  symmetry = TRUE, seed = NULL, params_ranger = NULL)

Arguments

formula	Object of class formula or character describing the model to fit. Interaction terms supported only for numerical variables.
train_data	Training data of class data.frame, matrix, or dgCMatrix (Matrix).
test_data	Test data of class data.frame, matrix, or dgCMatrix (Matrix).
method	Method for constructing prediction interval. If method = "oob", compute the out-of-bag prediction intervals; if method = "split-conformal", compute the split conformal prediction interval; if method = "quantreg", use quantile regression forest to compute prediction intervals.
alpha	Confidence level. alpha = 0.05 for the 95% prediction interval.
symmetry	True if constructing symmetric out-of-bag prediction intervals, False otherwise. Only for method = "oob"
seed	Seed (only for method = "split-conformal")
params_ranger	List of further parameters that should be passed to ranger. See ranger for possible parameters.

Value

oob_interval	Out-of-bag prediction intervals
sc_interval	Split-conformal prediction intervals
quantreg_interval	Quantile regression forest prediction intervals
alpha	Confidence level for prediction intervals
testPred	Random forest prediction for test set
train_data	Training data
test_data	Test data

References

Haozhe Zhang, Joshua Zimmerman, Dan Nettleton, and Dan Nordman. (2019). "Random Forest Prediction Intervals." The American Statistician. Doi: 10.1080/00031305.2019.1585288.

Haozhe Zhang. (2019). "Topics in Functional Data Analysis and Machine Learning Predictive Inference." Ph.D. Dissertations. Iowa State University Digital Repository. 17929.

Lei, J., Max G’Sell, Alessandro Rinaldo, Ryan J. Tibshirani, and Larry Wasserman. "Distribution-free predictive inference for regression." Journal of the American Statistical Association 113, no. 523 (2018): 1094-1111.

Meinshausen, Nicolai. "Quantile regression forests." Journal of Machine Learning Research 7 (2006): 983-999.

Leo Breiman. (2001). Random Forests. Machine Learning 45(1), 5-32.

Examples

train_data <- sim_data(n = 500, p = 8)
test_data <- sim_data(n = 500, p = 8)
output <- rfinterval(y~., train_data = train_data, test_data = test_data,
                     method = c("oob", "split-conformal", "quantreg"),
                     symmetry = TRUE,alpha = 0.1)
y <- test_data$y
mean(output$oob_interval$lo < y & output$oob_interval$up > y)
mean(output$sc_interval$lo < y & output$sc_interval$up > y)
mean(output$quantreg_interval$lo < y & output$quantreg_interval$up > y)

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Simulate data

Description

Simulate data for illustrate the performance of prediction intervals for random forests

Usage

sim_data(n = 500, p = 10, rho = 0.6, predictor_dist = "correlated",
  mean_function = "nonlinear-interaction",
  error_dist = "homoscedastic")

Arguments

n	Sample size
p	Number of features
rho	Correlation between predictors
predictor_dist	Distribution of predictor: "uncorrelated", and "correlated"
mean_function	Mean function: "linear", "nonlinear", and "nonlinear-interaction"
error_dist	Distribution of error: "homoscedastic", "heteroscedastic", and "heavy-tailed"

Value

a data.frame of simulated data

Examples

train_data <- sim_data(n = 500, p = 10)
test_data <- sim_data(n = 500, p = 10)

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