sksurv.ensemble.
ComponentwiseGradientBoostingSurvivalAnalysis
Gradient boosting with component-wise least squares as base learner.
See the User Guide and 1 for further description.
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 inverse-probability 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 trade-off between learning_rate and n_estimators.
n_estimators (int, default: 100) – The number of boosting stages to perform. Gradient boosting is fairly robust to over-fitting 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.
array, shape = (n_features + 1,)
loss_
The concrete LossFunction object.
LossFunction
estimators_
The collection of fitted sub-estimators.
list of base learners
train_score_
The i-th score train_score_[i] is the deviance (= loss) of the model at iteration i on the in-bag sample. If subsample == 1 this is the deviance on the training data.
train_score_[i]
i
subsample == 1
array, shape = (n_estimators,)
oob_improvement_
The improvement in loss (= deviance) on the out-of-bag samples relative to the previous iteration. oob_improvement_[0] is the improvement in loss of the first stage over the init estimator.
oob_improvement_[0]
init
References
Hothorn, T., Bühlmann, P., Dudoit, S., Molinaro, A., van der Laan, M. J., “Survival ensembles”, Biostatistics, 7(3), 355-73, 2006
__init__
Initialize self. See help(type(self)) for accurate signature.
Methods
__init__([loss, learning_rate, …])
Initialize self.
fit(X, y[, sample_weight])
fit
Fit estimator.
predict(X)
predict
Predict risk scores.
predict_cumulative_hazard_function(X)
predict_cumulative_hazard_function
Predict cumulative hazard function.
predict_survival_function(X)
predict_survival_function
Predict survival function.
score(X, y)
score
Returns the concordance index of the prediction.
Attributes
coef_
Return the aggregated coefficients.
feature_importances_
coef_ – Coefficients of features. The first element denotes the intercept.
ndarray, shape = (n_features + 1,)
X (array-like, 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 (array-like, shape = (n_samples,), optional) – Weights given to each sample. If omitted, all samples have weight 1.
self
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.
X (array-like, shape = (n_samples, n_features)) – Data matrix.
risk_score – Predicted risk scores.
array, shape = (n_samples,)
Only available if fit() has been called with loss = “coxph”.
fit()
The cumulative hazard function for an individual with feature vector \(x\) is defined as
where \(f(\cdot)\) is the additive ensemble of base learners, and \(H_0(t)\) is the baseline hazard function, estimated by Breslow’s estimator.
cum_hazard – Predicted cumulative hazard functions.
ndarray of sksurv.functions.StepFunction, shape = (n_samples,)
sksurv.functions.StepFunction
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()
The survival function for an individual with feature vector \(x\) is defined as
where \(f(\cdot)\) is the additive ensemble of base learners, and \(S_0(t)\) is the baseline survival function, estimated by Breslow’s estimator.
survival – Predicted survival functions.
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()
X (array-like, shape = (n_samples, n_features)) – Test samples.
cindex – Estimated concordance index.
float