sksurv.ensemble.ComponentwiseGradientBoostingSurvivalAnalysis¶

class
sksurv.ensemble.
ComponentwiseGradientBoostingSurvivalAnalysis
(loss='coxph', learning_rate=0.1, n_estimators=100, subsample=1.0, dropout_rate=0, random_state=None, verbose=0)[source]¶ Gradient boosting with componentwise least squares as base learner.
See the User Guide and 1 for further description.
 Parameters
loss ({'coxph', 'squared', 'ipcwls'}, optional, default: 'coxph') – loss function to be optimized. ‘coxph’ refers to partial likelihood loss of Cox’s proportional hazards model. The loss ‘squared’ minimizes a squared regression loss that ignores predictions beyond the time of censoring, and ‘ipcwls’ refers to inverseprobability of censoring weighted least squares error.
learning_rate (float, optional, default: 0.1) – learning rate shrinks the contribution of each base learner by learning_rate. There is a tradeoff between learning_rate and n_estimators.
n_estimators (int, default: 100) – The number of boosting stages to perform. Gradient boosting is fairly robust to overfitting so a large number usually results in better performance.
subsample (float, optional, default: 1.0) – The fraction of samples to be used for fitting the individual base learners. If smaller than 1.0 this results in Stochastic Gradient Boosting. subsample interacts with the parameter n_estimators. Choosing subsample < 1.0 leads to a reduction of variance and an increase in bias.
dropout_rate (float, optional, default: 0.0) – If larger than zero, the residuals at each iteration are only computed from a random subset of base learners. The value corresponds to the percentage of base learners that are dropped. In each iteration, at least one base learner is dropped. This is an alternative regularization to shrinkage, i.e., setting learning_rate < 1.0.
random_state (int seed, RandomState instance, or None, default: None) – The seed of the pseudo random number generator to use when shuffling the data.
verbose (int, default: 0) – Enable verbose output. If 1 then it prints progress and performance once in a while (the more trees the lower the frequency). If greater than 1 then it prints progress and performance for every tree.

coef\_
The aggregated coefficients. The first element coef_[0] corresponds to the intercept. If loss is coxph, the intercept will always be zero.
 Type
array, shape = (n_features + 1,)

loss_
¶ The concrete
LossFunction
object. Type
LossFunction

estimators_
¶ The collection of fitted subestimators.
 Type
list of base learners

train_score_
¶ The ith score
train_score_[i]
is the deviance (= loss) of the model at iterationi
on the inbag sample. Ifsubsample == 1
this is the deviance on the training data. Type
array, shape = (n_estimators,)

oob_improvement_
¶ The improvement in loss (= deviance) on the outofbag samples relative to the previous iteration.
oob_improvement_[0]
is the improvement in loss of the first stage over theinit
estimator. Type
array, shape = (n_estimators,)
References
 1
Hothorn, T., Bühlmann, P., Dudoit, S., Molinaro, A., van der Laan, M. J., “Survival ensembles”, Biostatistics, 7(3), 35573, 2006

__init__
(loss='coxph', learning_rate=0.1, n_estimators=100, subsample=1.0, dropout_rate=0, random_state=None, verbose=0)[source]¶ Initialize self. See help(type(self)) for accurate signature.
Methods
__init__
([loss, learning_rate, …])Initialize self.
fit
(X, y[, sample_weight])Fit estimator.
predict
(X)Predict risk scores.
Predict cumulative hazard function.
Predict survival function.
score
(X, y)Returns the concordance index of the prediction.
Attributes
Return the aggregated coefficients.
feature_importances_

property
coef_
¶ Return the aggregated coefficients.
 Returns
coef_ – Coefficients of features. The first element denotes the intercept.
 Return type
ndarray, shape = (n_features + 1,)

fit
(X, y, sample_weight=None)[source]¶ Fit estimator.
 Parameters
X (arraylike, shape = (n_samples, n_features)) – Data matrix
y (structured array, shape = (n_samples,)) – A structured array containing the binary event indicator as first field, and time of event or time of censoring as second field.
sample_weight (arraylike, shape = (n_samples,), optional) – Weights given to each sample. If omitted, all samples have weight 1.
 Returns
 Return type
self

predict
(X)[source]¶ Predict risk scores.
If loss=’coxph’, predictions can be interpreted as log hazard ratio corresponding to the linear predictor of a Cox proportional hazards model. If loss=’squared’ or loss=’ipcwls’, predictions are the time to event.
 Parameters
X (arraylike, shape = (n_samples, n_features)) – Data matrix.
 Returns
risk_score – Predicted risk scores.
 Return type
array, shape = (n_samples,)

predict_cumulative_hazard_function
(X)[source]¶ Predict cumulative hazard function.
Only available if
fit()
has been called with loss = “coxph”.The cumulative hazard function for an individual with feature vector \(x\) is defined as
\[H(t \mid x) = \exp(f(x)) H_0(t) ,\]where \(f(\cdot)\) is the additive ensemble of base learners, and \(H_0(t)\) is the baseline hazard function, estimated by Breslow’s estimator.
 Parameters
X (arraylike, shape = (n_samples, n_features)) – Data matrix.
 Returns
cum_hazard – Predicted cumulative hazard functions.
 Return type
ndarray of
sksurv.functions.StepFunction
, shape = (n_samples,)
Examples
>>> import matplotlib.pyplot as plt >>> from sksurv.datasets import load_whas500 >>> from sksurv.ensemble import ComponentwiseGradientBoostingSurvivalAnalysis
Load the data.
>>> X, y = load_whas500() >>> X = X.astype(float)
Fit the model.
>>> estimator = ComponentwiseGradientBoostingSurvivalAnalysis(loss="coxph").fit(X, y)
Estimate the cumulative hazard function for the first 10 samples.
>>> chf_funcs = estimator.predict_cumulative_hazard_function(X.iloc[:10])
Plot the estimated cumulative hazard functions.
>>> for fn in chf_funcs: ... plt.step(fn.x, fn(fn.x), where="post") ... >>> plt.ylim(0, 1) >>> plt.show()

predict_survival_function
(X)[source]¶ Predict survival function.
Only available if
fit()
has been called with loss = “coxph”.The survival function for an individual with feature vector \(x\) is defined as
\[S(t \mid x) = S_0(t)^{\exp(f(x)} ,\]where \(f(\cdot)\) is the additive ensemble of base learners, and \(S_0(t)\) is the baseline survival function, estimated by Breslow’s estimator.
 Parameters
X (arraylike, shape = (n_samples, n_features)) – Data matrix.
 Returns
survival – Predicted survival functions.
 Return type
ndarray of
sksurv.functions.StepFunction
, shape = (n_samples,)
Examples
>>> import matplotlib.pyplot as plt >>> from sksurv.datasets import load_whas500 >>> from sksurv.ensemble import ComponentwiseGradientBoostingSurvivalAnalysis
Load the data.
>>> X, y = load_whas500() >>> X = X.astype(float)
Fit the model.
>>> estimator = ComponentwiseGradientBoostingSurvivalAnalysis(loss="coxph").fit(X, y)
Estimate the survival function for the first 10 samples.
>>> surv_funcs = estimator.predict_survival_function(X.iloc[:10])
Plot the estimated survival functions.
>>> for fn in surv_funcs: ... plt.step(fn.x, fn(fn.x), where="post") ... >>> plt.ylim(0, 1) >>> plt.show()

score
(X, y)[source]¶ Returns the concordance index of the prediction.
 Parameters
X (arraylike, shape = (n_samples, n_features)) – Test samples.
y (structured array, shape = (n_samples,)) – A structured array containing the binary event indicator as first field, and time of event or time of censoring as second field.
 Returns
cindex – Estimated concordance index.
 Return type
float