survival.svm.HingeLossSurvivalSVM

class survival.svm.HingeLossSurvivalSVM(solver='cvxpy', alpha=1.0, kernel='linear', gamma=None, degree=3, coef0=1, kernel_params=None, pairs='all', verbose=False, timeit=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 survival.svm.NaiveSurvivalSVM for the linear naive survival SVM based on liblinear.

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

solver : “cvxpy” | “cvxopt”, optional (default: cvxpy)

Which quadratic program solver to use.

alpha : float, positive

Weight of penalizing the hinge loss in the objective function (default: 1)

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. survival.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.

References

[R17]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
[R18]Evers, L., Messow, C.M., “Sparse kernel methods for high-dimensional survival data”, Bioinformatics 24(14), 1632-8, 2008.
[R19]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.

Attributes

X_fit_ : Training data.
coef_ : Coefficients of the features in the decision function.
__init__(solver='cvxpy', alpha=1.0, kernel='linear', gamma=None, degree=3, coef0=1, kernel_params=None, pairs='all', verbose=False, timeit=None)

Methods

__init__([solver, alpha, kernel, gamma, ...])
fit(X, y) Build a MINLIP survival model from training data.
get_params([deep]) Get parameters for this estimator.
predict(X) Predict risk score of experiencing an event.
score(X, y)
set_params(**params) Set the parameters of this estimator.
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:

self
get_params(deep=True)

Get parameters for this estimator.

Parameters:

deep: boolean, optional

If True, will return the parameters for this estimator and contained subobjects that are estimators.
Returns:

params : mapping of string to any

Parameter names mapped to their values.
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 of shape = [n_samples, n_features]

The input samples.
Returns:

y : array of shape = [n_samples]

Predicted risk.
set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as pipelines). The former have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Returns:self