skpp module

class skpp.ProjectionPursuitClassifier(r=10, fit_type='polyfit', degree=3, opt_level='high', example_weights='uniform', pairwise_loss_matrix=None, eps_stage=0.0001, eps_backfit=0.01, stage_maxiter=100, backfit_maxiter=10, random_state=None, show_plots=False, plot_epoch=50)

Bases: sklearn.base.BaseEstimator, sklearn.base.ClassifierMixin

Perform classification with projection pursuit.

Parameters

pairwise_loss_matrix (array-like of dimension (n_classes, n_classes), default=None) – The adjacency matrix L has entries L[c,k]=l_ck specifying the weight of the penalty of predicting the answer is class k when it is actually class c. If unspecified, all penalties are considered to have the same importance.

See also

ProjectionPursuitRegressor

for definitions of other parameters

fit(X, Y)

Train the model.

Parameters

• X (array-like of shape (n_samples, n_features)) – The training input samples.

• Y (array-like, shape (n_samples,) or (n_samples, n_outputs)) – The target values.

Returns

self – A trained model.

Return type

ProjectionPursuitClassifier:

predict(X)

Use the fitted estimator to make predictions on new data.

Parameters

X (array-like of shape (n_samples, n_features)) – The input samples.

Returns

Y – The result of passing X through the evaluation function, taking the argmax of the output, and mapping it back to a class.

Return type

array of shape (n_samples)

class skpp.ProjectionPursuitRegressor(r=10, fit_type='polyfit', degree=3, opt_level='high', example_weights='uniform', out_dim_weights='inverse-variance', eps_stage=0.0001, eps_backfit=0.01, stage_maxiter=100, backfit_maxiter=10, random_state=None, show_plots=False, plot_epoch=50)

Bases: sklearn.base.BaseEstimator, sklearn.base.TransformerMixin, sklearn.base.RegressorMixin, sklearn.base.MultiOutputMixin

This class implements the PPR algorithm as detailed in math.pdf.

Parameters

• r (int, default=10) – The number of terms in the underlying additive model. The input will be put through r projections, r functions of those projections, and then multiplication by r output vectors to determine output.

• fit_type ({'polyfit', 'spline'}, default='polyfit') – The kind of function to fit at each stage.

• degree (int, default=3:) – The degree of polynomials or spline-sections used as the univariate approximator between projection and weighted residual targets.

• opt_level ({'high', 'medium', 'low'}, default='high') – ‘low’ opt_level will disable backfitting. ‘medium’ backfits previous 2D functional fits only (not projections). ‘high’ backfits everything.

• example_weights (string or array-like of dimension (n_samples,), default='uniform') – The relative importances given to training examples when calculating loss and solving for parameters.

• out_dim_weights (string or array-like, default='inverse-variance') – The relative importances given to output dimensions when calculating the weighted residual (output of the univariate functions f_j). If all dimensions are of the same importance, but outputs are of different scales, then using the inverse variance is a good choice. Possible values: ‘inverse-variance’: Divide outputs by their variances, ‘uniform’: Use a vector of ones as the weights, array: Provide a custom vector of weights of dimension (n_outputs,)

• eps_stage (float, default=0.0001) – The mean squared difference between the predictions of the PPR at subsequent iterations of a “stage” (fitting an f, beta pair) must reach below this epsilon in order for the stage to be considered converged.

• eps_backfit (float, default=0.01) – The mean squared difference between the predictions of the PPR at subsequent iterations of a “backfit” must reach below this epsilon in order for backfitting to be considered converged.

• stage_maxiter (int, default=100) – If a stage does not converge within this many iterations, end the loop and move on. This is useful for divergent cases.

• backfit_maxiter (int, default=10) – If a backfit does not converge withint this many iterations, end the loop and move on. Smaller values may be preferred here since backfit iterations are expensive.

• random_state (int, numpy.RandomState, default=None) – An optional object with which to seed randomness.

• show_plots (boolean, default=False) – Whether to produce plots of projections versus residual variance throughout the training process.

• plot_epoch (int, default=50:) – If plots are displayed, show them every plot_epoch iterations of the stage-fitting process.

fit(X, Y)

Train the model.

Parameters

• X (array-like of shape (n_samples, n_features)) – The training input samples.

• Y (array-like, shape (n_samples,) or (n_samples, n_outputs)) – The target values.

Returns

self – A trained model.

Return type

ProjectionPursuitRegressor

predict(X)

Use the fitted estimator to make predictions on new data.

Parameters

X (array-like of shape (n_samples, n_features)) – The input samples.

Returns

Y – The result of passing X through the evaluation function.

Return type

array of shape (n_samples) or (n_samples, n_outputs)

transform(X)

Find the projections of X through all alpha vectors in the PPR.

\(A\) is a p x r matrix with projection vectors in each column, and \(X\) is an n x p matrix with examples in each row, so the inner product of the two stores projections.

Parameters

X (array-like of shape (n_samples, n_features)) – The input samples.

Returns

Projections – where r is the hyperparameter given to the constructor, the number of terms in the additive model, and the jth column is the projection of \(X\) through \(\alpha_j\).

Return type

an array of shape (n_samples, r)