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
. Ifrank_ratio = 1
, only ranking is performed, ifrank_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 ifrank_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
See also
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.
Returns: Return type: self
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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. Returns: y – Predicted ranks. Return type: ndarray, shape = (n_samples,)
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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.
Returns: cindex – Estimated concordance index.
Return type: float