Package 'RLT'

survival time

The censoring indicator if survival model is used

the predicted value for each subject

A fitted RLT object.

The dataset for prediction. This calculates an $n_1 \times n_1$ kernel matrix of X1.

The dataset for reference/training. If X2 is supplied, then calculate an $n_1 \times n_2$ kernel matrix. If vs.train is used, then this must be the original training data.

To calculate the kernel weights with respect to the training data. This is slightly different than supplying the training data to X2 due to re-samplings of the training process. To use this feature, you must specify resample.track = TRUE in param.control when fitting the forest

Whether fitting should be printed.

... Additional arguments.

A fitted RLT object

the tree number, starting from 1 to ntrees.

...

A RLT prediction object. This must be an object calculated from a forest with var.ready = TRUE.

Observation number in the prediction. Default to calculate all ($i = 0$)

alpha level for interval $(\alpha/2, 1 - \alpha/2)$

What approach is used to calculate the confidence band. Can be

• naive-mc: positive-definite projection of the covariance matrix. the confidence band is non-smooth

• smoothed-mc: use a smoothed marginal variance to perform the Monte Carlo approximation of the critical value. This is only recommended for large number of time points.

• smoothed-lr: use a smoothed low-rank approximation of the covariance matrix and apply an adaptive Bonferroni correction to derive the critical values. Note that this approach relies on the assumption of the smoothness and low rank of the covariance matrix.

number of simulations for estimating the Monte Carlo critical value. Set this to be a large number. Default is 1000.

maximum number of ranks used in the smoothed-lr approximation. Usually 5 is enough for approximating the covariance matrix due to smoothness.

...

n

other arguments

A fitted RLT object

The testing samples, must have the same structure as the training samples

Whether to estimate the variance of each testing data. The original forest must be fitted with var.ready = TRUE. For survival forests, calculates the covariance matrix over all observed time points and calculates critical value for the confidence band.

whether to keep the prediction from all trees. Warning: this can occupy a large storage space, especially in survival model

number of cores

print additional information

...

Prediction

if var.est = TRUE and the fitted object is var.ready = TRUE

predicted hazard functions

predicted cumulative hazard function

predicted survival function

if keep.all = TRUE, the predicted hazard function for each observation and each tree

if keep.all = TRUE, the predicted cumulative hazard function for each observation and each tree

if var.est = TRUE and the fitted object is var.ready = TRUE. For each test subject, a matrix of size NFail$\times$NFail where NFail is the number of observed failure times in the training data

if var.est = TRUE and the fitted object is var.ready = TRUE. Marginal variance for each subject

ordered observed failure times from the training data

if var.est = TRUE and the fitted object is var.ready = TRUE. Marginal variance for each subject from the Cov matrix projected to the nearest positive definite matrix

if var.est = TRUE and the fitted object is var.ready = TRUE. Marginal variance for each subject from the Cov matrix projected to the nearest positive definite matrix and then smoothed using Gaussian kernel smoothing

if var.est = TRUE and the fitted object is var.ready = TRUE. Critical values to calculate confidence bands around cumulative hazard predictions at several confidence levels. Calculated using MarginalVar

if var.est = TRUE and the fitted object is var.ready = TRUE. Critical values to calculate confidence bands around cumulative hazard predictions at several confidence levels. Calculated using MarginalVarSmooth

A fitted RLT object

...

A matrix or data.frame of features. If x is a data.frame, then all factors are treated as categorical variables, which will go through an exhaustive search of splitting criteria.

Response variable. a numeric/factor vector.

Censoring indicator if survival model is used.

The model type: "regression", "classification", "quantile", "survival" or "graph".

Number of trees, ntrees = 100 if reinforcement is used and ntrees = 1000 otherwise.

Number of randomly selected variables used at each internal node.

Terminal node size. Splitting will stop when the internal node size is less equal to nmin.

How the cutting points are generated: "random", "rank" or "best". If minimum child node size is enforced (alpha $> 0$), then "rank" and "best" should be used.

Number of random cutting points to compare for each variable at an internal node.

Whether the in-bag samples are obtained with replacement.

Proportion of in-bag samples.

A pre-specified matrix for in-bag data indicator/count matrix. It must be an $n \times$ ntrees matrix with integer entries. Positive number indicates the number of copies of that observation (row) in the corresponding tree (column); zero indicates out-of-bag; negative values indicates not being used in either. Extremely large counts should be avoided. The sum of each column should not exceed $n$.

Observation weights. The weights will be used for calculating the splitting scores, such as a weighted variance reduction or weighted gini index. But they will not be used for sampling observations. In that case, one can pre-specify resample.preset instead for balanced sampling, etc. For survival analysis, observation weights are not implemented in the "logrank" or "suplogrank" tests, due to the difficulty of calculating the variance of test statistic. However, it is used in the "coxgrad" splitting rule. For other models, this feature is currently not available.

Variable weights. If this is supplied, the default is to perform weighted sampling of mtry variables. For other usage, see the details of split.rule in param.control.

Whether to calculate variable importance measures. When set to "TRUE" (or "permute"), the calculation follows Breiman's original permutation strategy. If set to "distribute", then it sends the oob data to both child nodes with weights proportional to their sample sizes. Hence the final prediction is a weighted average of all possible terminal nodes that a perturbed observation could fall into. This feature is currently only available in regression and classification models.

Should reinforcement splitting rule be used. Default is "FALSE", i.e., regular random forests with marginal search of splitting variable. When it is activated, an embedded model is fitted to find the best splitting variable or a linear combination of them, if linear.comb $> 1$. They can also be specified in param.control.

A list of additional parameters. This can be used to specify other features in a random forest or set embedded model parameters for reinforcement splitting rules. Using reinforcement = TRUE will automatically generate some default tuning for the embedded model. This mode is currently only available in regression. They are not necessarily optimized.

• embed.ntrees: number of trees in the embedded model

• embed.mtry: number or proportion of variables

• embed.nmin: terminal node size

• embed.split.gen random cutting point search method ("random", "rank" or "best")

• embed.nsplit number of random cutting points

• embed.resample.replace whether to sample with replacement

• embed.resample.prob: proportion of samples (of the internal node) in the embedded model

• embed.mute muting rate

• embed.protect number of protected variables

• embed.threshold threshold, as a fraction of the best VI, for being included in the protected set at an internal node.

                   \code{linear.comb} is a separate feature that can be 
                   activated with or without using reinforcement. It creates 
                   linear combination of features as the splitting rule. 
                   Currently only available for regression. 
                   \itemize{
                   \item In reinforcement mode, a linear combination is created 
                         using the top continuous variables from the embedded 
                         model. If a categorical variable is the best, then 
                         a regular split will be used. The splitting point 
                         will be searched based on \code{split.rule} of the
                         model. 
                   \item In non-reinforcement mode, a marginal screening 
                         is performed and the top features are used to construct 
                         the linear combination. This is an experimental feature. 
                   }
                   
                   \code{split.rule} is used to specify the criteria used 
                   to compare different splittings. Here are the available 
                   choices. The first one is the default:
                   \itemize{
                   \item Regression: `"var"` (variance reduction); `"pca"` 
                         and `"sir"` can be used for linear combination splits
                   \item Classification: `"gini"` (gini index)
                   \item Survival: `"logrank"` (log-rank test), `"suplogrank"`, 
                         `"coxgrad"`.
                   \item Quantile: `"ks"` (Kolmogorov-Smirnov test)
                   \item Graph: `"spectral"` (spectral embedding with variance 
                   reduction)
                   }
                   
                   \code{resample.track} indicates whether to keep track 
                   of the observations used in each tree.
                   
                   \code{var.ready} this is a feature to allow calculating variance 
                   (hence confidence intervals) of the random forest prediction. 
                   Currently only available for regression (Xu, Zhu & Shao, 2023) 
                   and confidence band in survival models (Formentini, Liang & Zhu, 2023). 
                   Please note that this only perpares the model fitting 
                   so that it is ready for the calculation. To obtain the 
                   confidence intervals, please see the prediction function. 
                   Specifying \code{var.ready = TRUE} has the following effect 
                   if these parameters are not already provided. For details 
                   of their restrictions, please see the orignal paper.
                   \itemize{
                   \item \code{resample.preset} is constructed automatically
                   \item \code{resample.replace} is set to `FALSE`
                   \item \code{resample.prob} is set to \eqn{n / 2}
                   \item \code{resample.track} is set to `TRUE`
                   }
                   
                   It is recommended to use a very large \code{ntrees}, 
                   e.g, 10000 or larger. For \code{resample.prob} greater 
                   than \eqn{n / 2}, one should consider the bootstrap 
                   approach in Xu, Zhu & Shao (2023).
                   
                   \code{alpha} force a minimum proportion of samples 
                   (of the parent node) in each child node.
                   
                   \code{failcount} specifies the unique number of failure 
                   time points used in survival model. By default, all failure 
                   time points will be used. A smaller number may speed up 
                   the computation. The time points will be chosen uniformly 
                   on the quantiles of failure times, while must include the 
                   minimum and the maximum.

Number of CPU logical cores. Default is 0 (using all available cores).

Whether info should be printed.

Random seed number to replicate a previously fitted forest. Internally, the ⁠xoshiro256++⁠ generator is used. If not specified, a seed will be generated automatically and recorded.

Additional arguments.