survival.svm.NaiveSurvivalSVM

class survival.svm.NaiveSurvivalSVM(penalty='l2', loss='squared_hinge', dual=False, tol=0.0001, alpha=1.0, verbose=0, random_state=None, max_iter=1000)

Naive version of linear Survival Support Vector Machine.

Uses regular linear support vector classifier (liblinear). 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(n_samples^2) space.

See survival.svm.HingeLossSurvivalSVM for the kernel naive survival SVM.

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

Parameters:

alpha : float, positive (default=1.0)

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

loss : string, ‘hinge’ or ‘squared_hinge’ (default=’squared_hinge’)

Specifies the loss function. ‘hinge’ is the standard SVM loss (used e.g. by the SVC class) while ‘squared_hinge’ is the square of the hinge loss.

penalty : string, ‘l1’ or ‘l2’ (default=’l2’)

Specifies the norm used in the penalization. The ‘l2’ penalty is the standard used in SVC. The ‘l1’ leads to coef_ vectors that are sparse.

dual : bool, (default=True)

Select the algorithm to either solve the dual or primal optimization problem. Prefer dual=False when n_samples > n_features.

tol : float, optional (default=1e-4)

Tolerance for stopping criteria.

verbose : int (default=0)

Enable verbose output. Note that this setting takes advantage of a per-process runtime setting in liblinear that, if enabled, may not work properly in a multithreaded context.

random_state : int seed, RandomState instance, or None (default=None)

The seed of the pseudo random number generator to use when shuffling the data.

max_iter : int (default=1000)

The maximum number of iterations to be run.

References

[R21]

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

[R22]

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

__init__(penalty='l2', loss='squared_hinge', dual=False, tol=0.0001, alpha=1.0, verbose=0, random_state=None, max_iter=1000)

Methods

__init__([penalty, loss, dual, tol, alpha, ...])
decision_function(X)	Predict confidence scores for samples.
densify()	Convert coefficient matrix to dense array format.
fit(X, y)	Build a survival support vector machine model from training data.
fit_transform(X[, y])	Fit to data, then transform it.
get_params([deep])	Get parameters for this estimator.
predict(X)	Rank samples according to survival times
score(X, y[, sample_weight])	Returns the mean accuracy on the given test data and labels.
set_params(**params)	Set the parameters of this estimator.
sparsify()	Convert coefficient matrix to sparse format.
transform(*args, **kwargs)	DEPRECATED: Support to use estimators as feature selectors will be removed in version 0.19.

decision_function(X)

Predict confidence scores for samples.

The confidence score for a sample is the signed distance of that sample to the hyperplane.

Parameters:

X : {array-like, sparse matrix}, shape = (n_samples, n_features)

Samples.

Returns:

array, shape=(n_samples,) if n_classes == 2 else (n_samples, n_classes)

Confidence scores per (sample, class) combination. In the binary case, confidence score for self.classes_[1] where >0 means this class would be predicted.

densify()

Convert coefficient matrix to dense array format.

Converts the coef_ member (back) to a numpy.ndarray. This is the default format of coef_ and is required for fitting, so calling this method is only required on models that have previously been sparsified; otherwise, it is a no-op.

Returns:self: 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

fit_transform(X, y=None, **fit_params)

Fit to data, then transform it.

Fits transformer to X and y with optional parameters fit_params and returns a transformed version of X.

Parameters:

X : numpy array of shape [n_samples, n_features]

Training set.

y : numpy array of shape [n_samples]

Target values.

Returns:

X_new : numpy array of shape [n_samples, n_features_new]

Transformed array.

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.

score(X, y, sample_weight=None)

Returns the mean accuracy on the given test data and labels.

In multi-label classification, this is the subset accuracy which is a harsh metric since you require for each sample that each label set be correctly predicted.

Parameters:

X : array-like, shape = (n_samples, n_features)

Test samples.

y : array-like, shape = (n_samples) or (n_samples, n_outputs)

True labels for X.

sample_weight : array-like, shape = [n_samples], optional

Sample weights.

Returns:

score : float

Mean accuracy of self.predict(X) wrt. y.

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

sparsify()

Convert coefficient matrix to sparse format.

Converts the coef_ member to a scipy.sparse matrix, which for L1-regularized models can be much more memory- and storage-efficient than the usual numpy.ndarray representation.

The intercept_ member is not converted.

Returns:self: estimator

Notes

For non-sparse models, i.e. when there are not many zeros in coef_, this may actually increase memory usage, so use this method with care. A rule of thumb is that the number of zero elements, which can be computed with (coef_ == 0).sum(), must be more than 50% for this to provide significant benefits.

After calling this method, further fitting with the partial_fit method (if any) will not work until you call densify.

transform(*args, **kwargs)

DEPRECATED: Support to use estimators as feature selectors will be removed in version 0.19. Use SelectFromModel instead.

Reduce X to its most important features.

Uses coef_ or feature_importances_ to determine the most important features. For models with a coef_ for each class, the absolute sum over the classes is used.

Parameters:

X : array or scipy sparse matrix of shape [n_samples, n_features]

The input samples.

threshold

: string, float or None, optional (default=None)

The threshold value to use for feature selection. Features whose importance is greater or equal are kept while the others are discarded. If “median” (resp. “mean”), then the threshold value is the median (resp. the mean) of the feature importances. A scaling factor (e.g., “1.25*mean”) may also be used. If None and if available, the object attribute threshold is used. Otherwise, “mean” is used by default.

Returns:

X_r : array of shape [n_samples, n_selected_features]

The input samples with only the selected features.