sksurv.svm.HingeLossSurvivalSVM

class sksurv.svm.HingeLossSurvivalSVM(solver='cvxpy', alpha=1.0, kernel='linear', gamma=None, degree=3, coef0=1, kernel_params=None, pairs='all', verbose=False, timeit=None, max_iter=None)

Naive implementation of kernel survival support vector machine.

A new set of samples is created by building the difference between any two feature vectors in the original data, thus this version requires \(O(\text{n_samples}^4)\) space and \(O(\text{n_samples}^6 \cdot \text{n_features})\).

See sksurv.svm.NaiveSurvivalSVM for the linear naive survival SVM based on liblinear.

\[ \begin{align}\begin{aligned}\begin{split}\min_{\mathbf{w}}\quad \frac{1}{2} \lVert \mathbf{w} \rVert_2^2 + \gamma \sum_{i = 1}^n \xi_i \\ \text{subject to}\quad \mathbf{w}^\top \phi(\mathbf{x})_i - \mathbf{w}^\top \phi(\mathbf{x})_j \geq 1 - \xi_{ij},\quad \forall (i, j) \in \mathcal{P}, \\ \xi_i \geq 0,\quad \forall (i, j) \in \mathcal{P}.\end{split}\\\mathcal{P} = \{ (i, j) \mid y_i > y_j \land \delta_j = 1 \}_{i,j=1,\dots,n}.\end{aligned}\end{align} \]

See [1], [2], [3] for further description.

Parameters:
  • solver ("cvxpy" | "cvxopt" | "osqp", optional, default: cvxpy) – Which quadratic program solver to use.
  • alpha (float, positive, default: 1) – Weight of penalizing the hinge loss in the objective function.
  • kernel ("linear" | "poly" | "rbf" | "sigmoid" | "cosine" | "precomputed") – Kernel. Default: “linear”
  • gamma (float, optional) – Kernel coefficient for rbf and poly kernels. Default: 1/n_features. Ignored by other kernels.
  • degree (int, default: 3) – Degree for poly kernels. Ignored by other kernels.
  • coef0 (float, optional) – Independent term in poly and sigmoid kernels. Ignored by other kernels.
  • kernel_params (mapping of string to any, optional) – Parameters (keyword arguments) and values for kernel passed as call
  • pairs ("all" | "nearest" | "next", optional, default: "all") –

    Which constraints to use in the optimization problem.

    • all: Use all comparable pairs. Scales quadratic in number of samples.
    • nearest: Only considers comparable pairs \((i, j)\) where \(j\) is the uncensored sample with highest survival time smaller than \(y_i\). Scales linear in number of samples (cf. sksurv.svm.MinlipSurvivalSVM).
    • next: Only compare against direct nearest neighbor according to observed time, disregarding its censoring status. Scales linear in number of samples.
  • verbose (bool, default: False) – Enable verbose output of solver.
  • timeit (False or int) – If non-zero value is provided the time it takes for optimization is measured. The given number of repetitions are performed. Results can be accessed from the timings_ attribute.
  • max_iter (int, optional) – Maximum number of iterations to perform. By default use solver’s default value.
X_fit_

Training data.

Type:ndarray
coef_

Coefficients of the features in the decision function.

Type:ndarray, shape = (n_samples,)

References

[1]Van Belle, V., Pelckmans, K., Suykens, J. A., & Van Huffel, S. Support Vector Machines for Survival Analysis. In Proc. of the 3rd Int. Conf. on Computational Intelligence in Medicine and Healthcare (CIMED). 1-8. 2007
[2]Evers, L., Messow, C.M., “Sparse kernel methods for high-dimensional survival data”, Bioinformatics 24(14), 1632-8, 2008.
[3]Van Belle, V., Pelckmans, K., Suykens, J.A., Van Huffel, S., “Survival SVM: a practical scalable algorithm”, In: Proc. of 16th European Symposium on Artificial Neural Networks, 89-94, 2008.
__init__(solver='cvxpy', alpha=1.0, kernel='linear', gamma=None, degree=3, coef0=1, kernel_params=None, pairs='all', verbose=False, timeit=None, max_iter=None)

Initialize self. See help(type(self)) for accurate signature.

Methods

__init__([solver, alpha, kernel, gamma, …]) Initialize self.
fit(X, y) Build a MINLIP survival model from training data.
predict(X) Predict risk score of experiencing an event.
score(X, y) Returns the concordance index of the prediction.
fit(X, y)

Build a MINLIP survival model from training data.

Parameters:
  • 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.
Returns:

Return type:

self

predict(X)

Predict risk score of experiencing an event.

Higher scores indicate shorter survival (high risk), lower scores longer survival (low risk).

Parameters:X (array-like, shape = (n_samples, n_features)) – The input samples.
Returns:y – Predicted risk.
Return type:ndarray, shape = (n_samples,)
score(X, y)

Returns the concordance index of the prediction.

Parameters:
  • X (array-like, 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