# sksurv.svm.FastSurvivalSVM¶

class sksurv.svm.FastSurvivalSVM(alpha=1, rank_ratio=1.0, fit_intercept=False, max_iter=20, verbose=False, tol=None, optimizer=None, random_state=None, timeit=False)[source]

Efficient Training of linear Survival Support Vector Machine

Training data consists of n triplets $$(\mathbf{x}_i, y_i, \delta_i)$$, where $$\mathbf{x}_i$$ is a d-dimensional feature vector, $$y_i > 0$$ the survival time or time of censoring, and $$\delta_i \in \{0,1\}$$ the binary event indicator. Using the training data, the objective is to minimize the following function:

\begin{align}\begin{aligned} \arg \min_{\mathbf{w}, b} \frac{1}{2} \mathbf{w}^\top \mathbf{w} + \frac{\alpha}{2} \left[ r \sum_{i,j \in \mathcal{P}} \max(0, 1 - (\mathbf{w}^\top \mathbf{x}_i - \mathbf{w}^\top \mathbf{x}_j))^2 + (1 - r) \sum_{i=0}^n \left( \zeta_{\mathbf{w}, b} (y_i, x_i, \delta_i) \right)^2 \right]\\\begin{split}\zeta_{\mathbf{w},b} (y_i, \mathbf{x}_i, \delta_i) = \begin{cases} \max(0, y_i - \mathbf{w}^\top \mathbf{x}_i - b) \quad \text{if \delta_i = 0,} \\ y_i - \mathbf{w}^\top \mathbf{x}_i - b \quad \text{if \delta_i = 1,} \\ \end{cases}\end{split}\\\mathcal{P} = \{ (i, j) \mid y_i > y_j \land \delta_j = 1 \}_{i,j=1,\dots,n}\end{aligned}\end{align}

The hyper-parameter $$\alpha > 0$$ determines the amount of regularization to apply: a smaller value increases the amount of regularization and a higher value reduces the amount of regularization. The hyper-parameter $$r \in [0; 1]$$ determines the trade-off between the ranking objective and the regresson objective. If $$r = 1$$ it reduces to the ranking objective, and if $$r = 0$$ to the regression objective. If the regression objective is used, survival/censoring times are log-transform and thus cannot be zero or negative.

See [1] for further description.

Parameters: alpha (float, positive, default: 1) – Weight of penalizing the squared hinge loss in the objective function rank_ratio (float, optional, default: 1.0) – Mixing parameter between regression and ranking objective with 0 <= rank_ratio <= 1. If rank_ratio = 1, only ranking is performed, if rank_ratio = 0, only regression is performed. A non-zero value is only allowed if optimizer is one of ‘avltree’, ‘rbtree’, or ‘direct-count’. fit_intercept (boolean, optional, default: False) – Whether to calculate an intercept for the regression model. If set to False, no intercept will be calculated. Has no effect if rank_ratio = 1, i.e., only ranking is performed. max_iter (int, optional, default: 20) – Maximum number of iterations to perform in Newton optimization verbose (bool, optional, default: False) – Whether to print messages during optimization tol (float, optional) – Tolerance for termination. For detailed control, use solver-specific options. optimizer ("avltree" | "direct-count" | "PRSVM" | "rbtree" | "simple", optional, default: avltree) – Which optimizer to use. random_state (int or numpy.random.RandomState instance, optional) – Random number generator (used to resolve ties in survival times). 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 optimizer_result_ attribute.
coef_

Coefficients of the features in the decision function.

Type: ndarray, shape = (n_features,)
optimizer_result_

Stats returned by the optimizer. See scipy.optimize.optimize.OptimizeResult.

Type: scipy.optimize.optimize.OptimizeResult

FastKernelSurvivalSVM
Fast implementation for arbitrary kernel functions.

References

 [1] Pölsterl, S., Navab, N., and Katouzian, A., “Fast Training of Support Vector Machines for Survival Analysis”, Machine Learning and Knowledge Discovery in Databases: European Conference, ECML PKDD 2015, Porto, Portugal, Lecture Notes in Computer Science, vol. 9285, pp. 243-259 (2015)
__init__(alpha=1, rank_ratio=1.0, fit_intercept=False, max_iter=20, verbose=False, tol=None, optimizer=None, random_state=None, timeit=False)[source]

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

Methods

 __init__([alpha, rank_ratio, fit_intercept, …]) Initialize self. fit(X, y) Build a survival support vector machine model from training data. predict(X) Rank samples according to survival times score(X, y) Returns the concordance index of the prediction.
fit(X, y)[source]

Build a survival support vector machine 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. self
predict(X)[source]

Rank samples according to survival times

Lower ranks indicate shorter survival, higher ranks longer survival.

Parameters: X (array-like, shape = (n_samples, n_features)) – The input samples. y – Predicted ranks. ndarray, shape = (n_samples,)
score(X, y)[source]

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. cindex – Estimated concordance index. float