Use the Akaike information criterion (AIC), the Bayes Information criterion (BIC) and cross-validation to select an optimal value of the regularization parameter alpha of the Lasso estimator. Results obtained with LassoLarsIC are based on AIC/BIC criteria. Information-criterion based model selection is very fast, but it relies on a proper estimation of degrees of freedom, are derived for large samples (asymptotic results) and assume the model is correct, i.e. that the data are actually generat

Estimates Lasso and Elastic-Net regression models on a manually generated sparse signal corrupted with an additive noise. Estimated coefficients are compared with the ground-truth. print(__doc__) import numpy as np import matplotlib.pyplot as plt from sklearn.metrics import r2_score generate some sparse data to play with np.random.seed(42) n_samples, n_features = 50, 200 X = np.random.randn(n_samples, n_features) coef = 3 * np.random.randn(n_features) inds = np.arange(n_features) np.random

Lasso and elastic net (L1 and L2 penalisation) implemented using a coordinate descent. The coefficients can be forced to be positive. Out: Computing regularization path using the lasso... Computing regularization path using the positive lasso... Computing regularization path using the elastic net... Computing regularization path using the positive elastic net... print(__doc__) # Author: Alexandre Gramfort <alexandre.gramfort@inria.fr> # License: BSD 3 clause from itertools

Example of LabelPropagation learning a complex internal structure to demonstrate ?manifold learning?. The outer circle should be labeled ?red? and the inner circle ?blue?. Because both label groups lie inside their own distinct shape, we can see that the labels propagate correctly around the circle. print(__doc__) # Authors: Clay Woolam <clay@woolam.org> # Andreas Mueller <amueller@ais.uni-bonn.de> # License: BSD import numpy as np import matplotlib.pyplot as plt from sk

Demonstrates an active learning technique to learn handwritten digits using label propagation. We start by training a label propagation model with only 10 labeled points, then we select the top five most uncertain points to label. Next, we train with 15 labeled points (original 10 + 5 new ones). We repeat this process four times to have a model trained with 30 labeled examples. A plot will appear showing the top 5 most uncertain digits for each iteration of training. These may or may not conta

This example demonstrates the power of semisupervised learning by training a Label Spreading model to classify handwritten digits with sets of very few labels. The handwritten digit dataset has 1797 total points. The model will be trained using all points, but only 30 will be labeled. Results in the form of a confusion matrix and a series of metrics over each class will be very good. At the end, the top 10 most uncertain predictions will be shown. print(__doc__) # Authors: Clay Woolam <cla

Comparison of the sparsity (percentage of zero coefficients) of solutions when L1 and L2 penalty are used for different values of C. We can see that large values of C give more freedom to the model. Conversely, smaller values of C constrain the model more. In the L1 penalty case, this leads to sparser solutions. We classify 8x8 images of digits into two classes: 0-4 against 5-9. The visualization shows coefficients of the models for varying C. Out: C=100.00 Sparsity with L1 penalty: 6.25

class sklearn.kernel_ridge.KernelRidge(alpha=1, kernel='linear', gamma=None, degree=3, coef0=1, kernel_params=None) [source] Kernel ridge regression. Kernel ridge regression (KRR) combines ridge regression (linear least squares with l2-norm regularization) with the kernel trick. It thus learns a linear function in the space induced by the respective kernel and the data. For non-linear kernels, this corresponds to a non-linear function in the original space. The form of the model learned by

class sklearn.kernel_approximation.SkewedChi2Sampler(skewedness=1.0, n_components=100, random_state=None) [source] Approximates feature map of the ?skewed chi-squared? kernel by Monte Carlo approximation of its Fourier transform. Read more in the User Guide. Parameters: skewedness : float ?skewedness? parameter of the kernel. Needs to be cross-validated. n_components : int number of Monte Carlo samples per original feature. Equals the dimensionality of the computed feature space. rando

class sklearn.kernel_approximation.RBFSampler(gamma=1.0, n_components=100, random_state=None) [source] Approximates feature map of an RBF kernel by Monte Carlo approximation of its Fourier transform. It implements a variant of Random Kitchen Sinks.[1] Read more in the User Guide. Parameters: gamma : float Parameter of RBF kernel: exp(-gamma * x^2) n_components : int Number of Monte Carlo samples per original feature. Equals the dimensionality of the computed feature space. random_state