survival.svm.FastSurvivalSVM

class survival.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)

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 survival.svm.FastKernelSurvivalSVM for an efficient implementation of kernel Survival Support Vector Machine.

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.

References

[R16]

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)

Attributes

coef_:	Coefficients of the features in the decision function.
optimizer_result_:	Stats returned by the optimizer. See scipy.optimize.optimize.OptimizeResult.

__init__(alpha=1, rank_ratio=1.0, fit_intercept=False, max_iter=20, verbose=False, tol=None, optimizer=None, random_state=None, timeit=False)

Methods

__init__([alpha, rank_ratio, fit_intercept, ...])
fit(X, y)	Build a survival support vector machine model from training data.
get_params([deep])	Get parameters for this estimator.
predict(X)	Rank samples according to survival times
score(X, y)
set_params(**params)	Set the parameters of this estimator.

fit(X, y)

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.

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)

Rank samples according to survival times

Lower ranks indicate shorter survival, higher ranks longer survival.

Parameters:

X : array-like of shape = [n_samples, n_features]

The input samples.

Returns:

y : array of shape = [n_samples]

Predicted ranks.

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