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<meta property="og:description" content="This example demonstrates the class_likelihood_ratios function, which computes the positive and negative likelihood ratios ( LR+, LR-) to assess the predictive power of a binary classifier. As we w..." />
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<meta name="description" content="This example demonstrates the class_likelihood_ratios function, which computes the positive and negative likelihood ratios ( LR+, LR-) to assess the predictive power of a binary classifier. As we w..." />
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<li class="toctree-l1 has-children"><a class="reference internal" href="../release_highlights/index.html">Release Highlights</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../release_highlights/plot_release_highlights_1_6_0.html">Release Highlights for scikit-learn 1.6</a></li>
<li class="toctree-l2"><a class="reference internal" href="../release_highlights/plot_release_highlights_1_5_0.html">Release Highlights for scikit-learn 1.5</a></li>
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<li class="toctree-l1 has-children"><a class="reference internal" href="../bicluster/index.html">Biclustering</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../bicluster/plot_spectral_biclustering.html">A demo of the Spectral Biclustering algorithm</a></li>
<li class="toctree-l2"><a class="reference internal" href="../bicluster/plot_spectral_coclustering.html">A demo of the Spectral Co-Clustering algorithm</a></li>
<li class="toctree-l2"><a class="reference internal" href="../bicluster/plot_bicluster_newsgroups.html">Biclustering documents with the Spectral Co-clustering algorithm</a></li>
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<li class="toctree-l1 has-children"><a class="reference internal" href="../calibration/index.html">Calibration</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../calibration/plot_compare_calibration.html">Comparison of Calibration of Classifiers</a></li>
<li class="toctree-l2"><a class="reference internal" href="../calibration/plot_calibration_curve.html">Probability Calibration curves</a></li>
<li class="toctree-l2"><a class="reference internal" href="../calibration/plot_calibration_multiclass.html">Probability Calibration for 3-class classification</a></li>
<li class="toctree-l2"><a class="reference internal" href="../calibration/plot_calibration.html">Probability calibration of classifiers</a></li>
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<li class="toctree-l1 has-children"><a class="reference internal" href="../classification/index.html">Classification</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../classification/plot_classifier_comparison.html">Classifier comparison</a></li>
<li class="toctree-l2"><a class="reference internal" href="../classification/plot_lda_qda.html">Linear and Quadratic Discriminant Analysis with covariance ellipsoid</a></li>
<li class="toctree-l2"><a class="reference internal" href="../classification/plot_lda.html">Normal, Ledoit-Wolf and OAS Linear Discriminant Analysis for classification</a></li>
<li class="toctree-l2"><a class="reference internal" href="../classification/plot_classification_probability.html">Plot classification probability</a></li>
<li class="toctree-l2"><a class="reference internal" href="../classification/plot_digits_classification.html">Recognizing hand-written digits</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../cluster/index.html">Clustering</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_kmeans_digits.html">A demo of K-Means clustering on the handwritten digits data</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_coin_ward_segmentation.html">A demo of structured Ward hierarchical clustering on an image of coins</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_mean_shift.html">A demo of the mean-shift clustering algorithm</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_adjusted_for_chance_measures.html">Adjustment for chance in clustering performance evaluation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_agglomerative_clustering.html">Agglomerative clustering with and without structure</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_agglomerative_clustering_metrics.html">Agglomerative clustering with different metrics</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_kmeans_plusplus.html">An example of K-Means++ initialization</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_bisect_kmeans.html">Bisecting K-Means and Regular K-Means Performance Comparison</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_birch_vs_minibatchkmeans.html">Compare BIRCH and MiniBatchKMeans</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_cluster_comparison.html">Comparing different clustering algorithms on toy datasets</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_linkage_comparison.html">Comparing different hierarchical linkage methods on toy datasets</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_mini_batch_kmeans.html">Comparison of the K-Means and MiniBatchKMeans clustering algorithms</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_dbscan.html">Demo of DBSCAN clustering algorithm</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_hdbscan.html">Demo of HDBSCAN clustering algorithm</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_optics.html">Demo of OPTICS clustering algorithm</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_affinity_propagation.html">Demo of affinity propagation clustering algorithm</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_kmeans_assumptions.html">Demonstration of k-means assumptions</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_kmeans_stability_low_dim_dense.html">Empirical evaluation of the impact of k-means initialization</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_digits_agglomeration.html">Feature agglomeration</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_feature_agglomeration_vs_univariate_selection.html">Feature agglomeration vs. univariate selection</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_ward_structured_vs_unstructured.html">Hierarchical clustering: structured vs unstructured ward</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_inductive_clustering.html">Inductive Clustering</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_dict_face_patches.html">Online learning of a dictionary of parts of faces</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_agglomerative_dendrogram.html">Plot Hierarchical Clustering Dendrogram</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_coin_segmentation.html">Segmenting the picture of greek coins in regions</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_kmeans_silhouette_analysis.html">Selecting the number of clusters with silhouette analysis on KMeans clustering</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_segmentation_toy.html">Spectral clustering for image segmentation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_digits_linkage.html">Various Agglomerative Clustering on a 2D embedding of digits</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_face_compress.html">Vector Quantization Example</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../covariance/index.html">Covariance estimation</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../covariance/plot_lw_vs_oas.html">Ledoit-Wolf vs OAS estimation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../covariance/plot_mahalanobis_distances.html">Robust covariance estimation and Mahalanobis distances relevance</a></li>
<li class="toctree-l2"><a class="reference internal" href="../covariance/plot_robust_vs_empirical_covariance.html">Robust vs Empirical covariance estimate</a></li>
<li class="toctree-l2"><a class="reference internal" href="../covariance/plot_covariance_estimation.html">Shrinkage covariance estimation: LedoitWolf vs OAS and max-likelihood</a></li>
<li class="toctree-l2"><a class="reference internal" href="../covariance/plot_sparse_cov.html">Sparse inverse covariance estimation</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../cross_decomposition/index.html">Cross decomposition</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../cross_decomposition/plot_compare_cross_decomposition.html">Compare cross decomposition methods</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cross_decomposition/plot_pcr_vs_pls.html">Principal Component Regression vs Partial Least Squares Regression</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../datasets/index.html">Dataset examples</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../datasets/plot_random_multilabel_dataset.html">Plot randomly generated multilabel dataset</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../tree/index.html">Decision Trees</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../tree/plot_tree_regression.html">Decision Tree Regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../tree/plot_iris_dtc.html">Plot the decision surface of decision trees trained on the iris dataset</a></li>
<li class="toctree-l2"><a class="reference internal" href="../tree/plot_cost_complexity_pruning.html">Post pruning decision trees with cost complexity pruning</a></li>
<li class="toctree-l2"><a class="reference internal" href="../tree/plot_unveil_tree_structure.html">Understanding the decision tree structure</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../decomposition/index.html">Decomposition</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../decomposition/plot_ica_blind_source_separation.html">Blind source separation using FastICA</a></li>
<li class="toctree-l2"><a class="reference internal" href="../decomposition/plot_pca_vs_lda.html">Comparison of LDA and PCA 2D projection of Iris dataset</a></li>
<li class="toctree-l2"><a class="reference internal" href="../decomposition/plot_faces_decomposition.html">Faces dataset decompositions</a></li>
<li class="toctree-l2"><a class="reference internal" href="../decomposition/plot_varimax_fa.html">Factor Analysis (with rotation) to visualize patterns</a></li>
<li class="toctree-l2"><a class="reference internal" href="../decomposition/plot_ica_vs_pca.html">FastICA on 2D point clouds</a></li>
<li class="toctree-l2"><a class="reference internal" href="../decomposition/plot_image_denoising.html">Image denoising using dictionary learning</a></li>
<li class="toctree-l2"><a class="reference internal" href="../decomposition/plot_incremental_pca.html">Incremental PCA</a></li>
<li class="toctree-l2"><a class="reference internal" href="../decomposition/plot_kernel_pca.html">Kernel PCA</a></li>
<li class="toctree-l2"><a class="reference internal" href="../decomposition/plot_pca_vs_fa_model_selection.html">Model selection with Probabilistic PCA and Factor Analysis (FA)</a></li>
<li class="toctree-l2"><a class="reference internal" href="../decomposition/plot_pca_iris.html">Principal Component Analysis (PCA) on Iris Dataset</a></li>
<li class="toctree-l2"><a class="reference internal" href="../decomposition/plot_sparse_coding.html">Sparse coding with a precomputed dictionary</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../developing_estimators/index.html">Developing Estimators</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../developing_estimators/sklearn_is_fitted.html"><code class="docutils literal notranslate"><span class="pre">__sklearn_is_fitted__</span></code> as Developer API</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../ensemble/index.html">Ensemble methods</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_gradient_boosting_categorical.html">Categorical Feature Support in Gradient Boosting</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_stack_predictors.html">Combine predictors using stacking</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_forest_hist_grad_boosting_comparison.html">Comparing Random Forests and Histogram Gradient Boosting models</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_random_forest_regression_multioutput.html">Comparing random forests and the multi-output meta estimator</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_adaboost_regression.html">Decision Tree Regression with AdaBoost</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_gradient_boosting_early_stopping.html">Early stopping in Gradient Boosting</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_forest_importances.html">Feature importances with a forest of trees</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_feature_transformation.html">Feature transformations with ensembles of trees</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_hgbt_regression.html">Features in Histogram Gradient Boosting Trees</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_gradient_boosting_oob.html">Gradient Boosting Out-of-Bag estimates</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_gradient_boosting_regression.html">Gradient Boosting regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_gradient_boosting_regularization.html">Gradient Boosting regularization</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_random_forest_embedding.html">Hashing feature transformation using Totally Random Trees</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_isolation_forest.html">IsolationForest example</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_monotonic_constraints.html">Monotonic Constraints</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_adaboost_multiclass.html">Multi-class AdaBoosted Decision Trees</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_ensemble_oob.html">OOB Errors for Random Forests</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_voting_probas.html">Plot class probabilities calculated by the VotingClassifier</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_voting_regressor.html">Plot individual and voting regression predictions</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_voting_decision_regions.html">Plot the decision boundaries of a VotingClassifier</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_forest_iris.html">Plot the decision surfaces of ensembles of trees on the iris dataset</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_gradient_boosting_quantile.html">Prediction Intervals for Gradient Boosting Regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_bias_variance.html">Single estimator versus bagging: bias-variance decomposition</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_adaboost_twoclass.html">Two-class AdaBoost</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../applications/index.html">Examples based on real world datasets</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_tomography_l1_reconstruction.html">Compressive sensing: tomography reconstruction with L1 prior (Lasso)</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_face_recognition.html">Faces recognition example using eigenfaces and SVMs</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_digits_denoising.html">Image denoising using kernel PCA</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_time_series_lagged_features.html">Lagged features for time series forecasting</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_model_complexity_influence.html">Model Complexity Influence</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_out_of_core_classification.html">Out-of-core classification of text documents</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_outlier_detection_wine.html">Outlier detection on a real data set</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_prediction_latency.html">Prediction Latency</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_species_distribution_modeling.html">Species distribution modeling</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_cyclical_feature_engineering.html">Time-related feature engineering</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_topics_extraction_with_nmf_lda.html">Topic extraction with Non-negative Matrix Factorization and Latent Dirichlet Allocation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_stock_market.html">Visualizing the stock market structure</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/wikipedia_principal_eigenvector.html">Wikipedia principal eigenvector</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../feature_selection/index.html">Feature Selection</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../feature_selection/plot_f_test_vs_mi.html">Comparison of F-test and mutual information</a></li>
<li class="toctree-l2"><a class="reference internal" href="../feature_selection/plot_select_from_model_diabetes.html">Model-based and sequential feature selection</a></li>
<li class="toctree-l2"><a class="reference internal" href="../feature_selection/plot_feature_selection_pipeline.html">Pipeline ANOVA SVM</a></li>
<li class="toctree-l2"><a class="reference internal" href="../feature_selection/plot_rfe_digits.html">Recursive feature elimination</a></li>
<li class="toctree-l2"><a class="reference internal" href="../feature_selection/plot_rfe_with_cross_validation.html">Recursive feature elimination with cross-validation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../feature_selection/plot_feature_selection.html">Univariate Feature Selection</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../frozen/index.html">Frozen Estimators</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../frozen/plot_frozen_examples.html">Examples of Using <code class="docutils literal notranslate"><span class="pre">FrozenEstimator</span></code></a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../mixture/index.html">Gaussian Mixture Models</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../mixture/plot_concentration_prior.html">Concentration Prior Type Analysis of Variation Bayesian Gaussian Mixture</a></li>
<li class="toctree-l2"><a class="reference internal" href="../mixture/plot_gmm_pdf.html">Density Estimation for a Gaussian mixture</a></li>
<li class="toctree-l2"><a class="reference internal" href="../mixture/plot_gmm_init.html">GMM Initialization Methods</a></li>
<li class="toctree-l2"><a class="reference internal" href="../mixture/plot_gmm_covariances.html">GMM covariances</a></li>
<li class="toctree-l2"><a class="reference internal" href="../mixture/plot_gmm.html">Gaussian Mixture Model Ellipsoids</a></li>
<li class="toctree-l2"><a class="reference internal" href="../mixture/plot_gmm_selection.html">Gaussian Mixture Model Selection</a></li>
<li class="toctree-l2"><a class="reference internal" href="../mixture/plot_gmm_sin.html">Gaussian Mixture Model Sine Curve</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../gaussian_process/index.html">Gaussian Process for Machine Learning</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../gaussian_process/plot_gpr_noisy.html">Ability of Gaussian process regression (GPR) to estimate data noise-level</a></li>
<li class="toctree-l2"><a class="reference internal" href="../gaussian_process/plot_compare_gpr_krr.html">Comparison of kernel ridge and Gaussian process regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../gaussian_process/plot_gpr_co2.html">Forecasting of CO2 level on Mona Loa dataset using Gaussian process regression (GPR)</a></li>
<li class="toctree-l2"><a class="reference internal" href="../gaussian_process/plot_gpr_noisy_targets.html">Gaussian Processes regression: basic introductory example</a></li>
<li class="toctree-l2"><a class="reference internal" href="../gaussian_process/plot_gpc_iris.html">Gaussian process classification (GPC) on iris dataset</a></li>
<li class="toctree-l2"><a class="reference internal" href="../gaussian_process/plot_gpr_on_structured_data.html">Gaussian processes on discrete data structures</a></li>
<li class="toctree-l2"><a class="reference internal" href="../gaussian_process/plot_gpc_xor.html">Illustration of Gaussian process classification (GPC) on the XOR dataset</a></li>
<li class="toctree-l2"><a class="reference internal" href="../gaussian_process/plot_gpr_prior_posterior.html">Illustration of prior and posterior Gaussian process for different kernels</a></li>
<li class="toctree-l2"><a class="reference internal" href="../gaussian_process/plot_gpc_isoprobability.html">Iso-probability lines for Gaussian Processes classification (GPC)</a></li>
<li class="toctree-l2"><a class="reference internal" href="../gaussian_process/plot_gpc.html">Probabilistic predictions with Gaussian process classification (GPC)</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../linear_model/index.html">Generalized Linear Models</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_ard.html">Comparing Linear Bayesian Regressors</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_sgd_comparison.html">Comparing various online solvers</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_bayesian_ridge_curvefit.html">Curve Fitting with Bayesian Ridge Regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_logistic_multinomial.html">Decision Boundaries of Multinomial and One-vs-Rest Logistic Regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_sgd_early_stopping.html">Early stopping of Stochastic Gradient Descent</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_elastic_net_precomputed_gram_matrix_with_weighted_samples.html">Fitting an Elastic Net with a precomputed Gram Matrix and Weighted Samples</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_huber_vs_ridge.html">HuberRegressor vs Ridge on dataset with strong outliers</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_multi_task_lasso_support.html">Joint feature selection with multi-task Lasso</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_logistic_l1_l2_sparsity.html">L1 Penalty and Sparsity in Logistic Regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_lasso_and_elasticnet.html">L1-based models for Sparse Signals</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_lasso_lars_ic.html">Lasso model selection via information criteria</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_lasso_model_selection.html">Lasso model selection: AIC-BIC / cross-validation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_lasso_dense_vs_sparse_data.html">Lasso on dense and sparse data</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_lasso_lasso_lars_elasticnet_path.html">Lasso, Lasso-LARS, and Elastic Net paths</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_logistic.html">Logistic function</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_sparse_logistic_regression_mnist.html">MNIST classification using multinomial logistic + L1</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_sparse_logistic_regression_20newsgroups.html">Multiclass sparse logistic regression on 20newgroups</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_nnls.html">Non-negative least squares</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_sgdocsvm_vs_ocsvm.html">One-Class SVM versus One-Class SVM using Stochastic Gradient Descent</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_ols.html">Ordinary Least Squares Example</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_ols_ridge_variance.html">Ordinary Least Squares and Ridge Regression Variance</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_omp.html">Orthogonal Matching Pursuit</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_ridge_path.html">Plot Ridge coefficients as a function of the regularization</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_sgd_iris.html">Plot multi-class SGD on the iris dataset</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_poisson_regression_non_normal_loss.html">Poisson regression and non-normal loss</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_polynomial_interpolation.html">Polynomial and Spline interpolation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_quantile_regression.html">Quantile regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_logistic_path.html">Regularization path of L1- Logistic Regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_ridge_coeffs.html">Ridge coefficients as a function of the L2 Regularization</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_robust_fit.html">Robust linear estimator fitting</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_ransac.html">Robust linear model estimation using RANSAC</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_sgd_separating_hyperplane.html">SGD: Maximum margin separating hyperplane</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_sgd_penalties.html">SGD: Penalties</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_sgd_weighted_samples.html">SGD: Weighted samples</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_sgd_loss_functions.html">SGD: convex loss functions</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_theilsen.html">Theil-Sen Regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_tweedie_regression_insurance_claims.html">Tweedie regression on insurance claims</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../inspection/index.html">Inspection</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../inspection/plot_linear_model_coefficient_interpretation.html">Common pitfalls in the interpretation of coefficients of linear models</a></li>
<li class="toctree-l2"><a class="reference internal" href="../inspection/plot_causal_interpretation.html">Failure of Machine Learning to infer causal effects</a></li>
<li class="toctree-l2"><a class="reference internal" href="../inspection/plot_partial_dependence.html">Partial Dependence and Individual Conditional Expectation Plots</a></li>
<li class="toctree-l2"><a class="reference internal" href="../inspection/plot_permutation_importance.html">Permutation Importance vs Random Forest Feature Importance (MDI)</a></li>
<li class="toctree-l2"><a class="reference internal" href="../inspection/plot_permutation_importance_multicollinear.html">Permutation Importance with Multicollinear or Correlated Features</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../kernel_approximation/index.html">Kernel Approximation</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../kernel_approximation/plot_scalable_poly_kernels.html">Scalable learning with polynomial kernel approximation</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../manifold/index.html">Manifold learning</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../manifold/plot_compare_methods.html">Comparison of Manifold Learning methods</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manifold/plot_manifold_sphere.html">Manifold Learning methods on a severed sphere</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manifold/plot_lle_digits.html">Manifold learning on handwritten digits: Locally Linear Embedding, Isomap…</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manifold/plot_mds.html">Multi-dimensional scaling</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manifold/plot_swissroll.html">Swiss Roll And Swiss-Hole Reduction</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manifold/plot_t_sne_perplexity.html">t-SNE: The effect of various perplexity values on the shape</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../miscellaneous/index.html">Miscellaneous</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_partial_dependence_visualization_api.html">Advanced Plotting With Partial Dependence</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_anomaly_comparison.html">Comparing anomaly detection algorithms for outlier detection on toy datasets</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_kernel_ridge_regression.html">Comparison of kernel ridge regression and SVR</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_pipeline_display.html">Displaying Pipelines</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_estimator_representation.html">Displaying estimators and complex pipelines</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_outlier_detection_bench.html">Evaluation of outlier detection estimators</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_kernel_approximation.html">Explicit feature map approximation for RBF kernels</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_multioutput_face_completion.html">Face completion with a multi-output estimators</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_set_output.html">Introducing the <code class="docutils literal notranslate"><span class="pre">set_output</span></code> API</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_isotonic_regression.html">Isotonic Regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_metadata_routing.html">Metadata Routing</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_multilabel.html">Multilabel classification</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_roc_curve_visualization_api.html">ROC Curve with Visualization API</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_johnson_lindenstrauss_bound.html">The Johnson-Lindenstrauss bound for embedding with random projections</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_display_object_visualization.html">Visualizations with Display Objects</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../impute/index.html">Missing Value Imputation</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../impute/plot_missing_values.html">Imputing missing values before building an estimator</a></li>
<li class="toctree-l2"><a class="reference internal" href="../impute/plot_iterative_imputer_variants_comparison.html">Imputing missing values with variants of IterativeImputer</a></li>
</ul>
</details></li>
<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Model Selection</a><details open="open"><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul class="current">
<li class="toctree-l2"><a class="reference internal" href="plot_grid_search_refit_callable.html">Balance model complexity and cross-validated score</a></li>
<li class="toctree-l2 current active"><a class="current reference internal" href="#">Class Likelihood Ratios to measure classification performance</a></li>
<li class="toctree-l2"><a class="reference internal" href="plot_randomized_search.html">Comparing randomized search and grid search for hyperparameter estimation</a></li>
<li class="toctree-l2"><a class="reference internal" href="plot_successive_halving_heatmap.html">Comparison between grid search and successive halving</a></li>
<li class="toctree-l2"><a class="reference internal" href="plot_confusion_matrix.html">Confusion matrix</a></li>
<li class="toctree-l2"><a class="reference internal" href="plot_grid_search_digits.html">Custom refit strategy of a grid search with cross-validation</a></li>
<li class="toctree-l2"><a class="reference internal" href="plot_multi_metric_evaluation.html">Demonstration of multi-metric evaluation on cross_val_score and GridSearchCV</a></li>
<li class="toctree-l2"><a class="reference internal" href="plot_det.html">Detection error tradeoff (DET) curve</a></li>
<li class="toctree-l2"><a class="reference internal" href="plot_train_error_vs_test_error.html">Effect of model regularization on training and test error</a></li>
<li class="toctree-l2"><a class="reference internal" href="plot_roc.html">Multiclass Receiver Operating Characteristic (ROC)</a></li>
<li class="toctree-l2"><a class="reference internal" href="plot_nested_cross_validation_iris.html">Nested versus non-nested cross-validation</a></li>
<li class="toctree-l2"><a class="reference internal" href="plot_cv_predict.html">Plotting Cross-Validated Predictions</a></li>
<li class="toctree-l2"><a class="reference internal" href="plot_learning_curve.html">Plotting Learning Curves and Checking Models’ Scalability</a></li>
<li class="toctree-l2"><a class="reference internal" href="plot_tuned_decision_threshold.html">Post-hoc tuning the cut-off point of decision function</a></li>
<li class="toctree-l2"><a class="reference internal" href="plot_cost_sensitive_learning.html">Post-tuning the decision threshold for cost-sensitive learning</a></li>
<li class="toctree-l2"><a class="reference internal" href="plot_precision_recall.html">Precision-Recall</a></li>
<li class="toctree-l2"><a class="reference internal" href="plot_roc_crossval.html">Receiver Operating Characteristic (ROC) with cross validation</a></li>
<li class="toctree-l2"><a class="reference internal" href="plot_grid_search_text_feature_extraction.html">Sample pipeline for text feature extraction and evaluation</a></li>
<li class="toctree-l2"><a class="reference internal" href="plot_grid_search_stats.html">Statistical comparison of models using grid search</a></li>
<li class="toctree-l2"><a class="reference internal" href="plot_successive_halving_iterations.html">Successive Halving Iterations</a></li>
<li class="toctree-l2"><a class="reference internal" href="plot_permutation_tests_for_classification.html">Test with permutations the significance of a classification score</a></li>
<li class="toctree-l2"><a class="reference internal" href="plot_underfitting_overfitting.html">Underfitting vs. Overfitting</a></li>
<li class="toctree-l2"><a class="reference internal" href="plot_cv_indices.html">Visualizing cross-validation behavior in scikit-learn</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../multiclass/index.html">Multiclass methods</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../multiclass/plot_multiclass_overview.html">Overview of multiclass training meta-estimators</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../multioutput/index.html">Multioutput methods</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../multioutput/plot_classifier_chain_yeast.html">Multilabel classification using a classifier chain</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../neighbors/index.html">Nearest Neighbors</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../neighbors/approximate_nearest_neighbors.html">Approximate nearest neighbors in TSNE</a></li>
<li class="toctree-l2"><a class="reference internal" href="../neighbors/plot_caching_nearest_neighbors.html">Caching nearest neighbors</a></li>
<li class="toctree-l2"><a class="reference internal" href="../neighbors/plot_nca_classification.html">Comparing Nearest Neighbors with and without Neighborhood Components Analysis</a></li>
<li class="toctree-l2"><a class="reference internal" href="../neighbors/plot_nca_dim_reduction.html">Dimensionality Reduction with Neighborhood Components Analysis</a></li>
<li class="toctree-l2"><a class="reference internal" href="../neighbors/plot_species_kde.html">Kernel Density Estimate of Species Distributions</a></li>
<li class="toctree-l2"><a class="reference internal" href="../neighbors/plot_digits_kde_sampling.html">Kernel Density Estimation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../neighbors/plot_nearest_centroid.html">Nearest Centroid Classification</a></li>
<li class="toctree-l2"><a class="reference internal" href="../neighbors/plot_classification.html">Nearest Neighbors Classification</a></li>
<li class="toctree-l2"><a class="reference internal" href="../neighbors/plot_regression.html">Nearest Neighbors regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../neighbors/plot_nca_illustration.html">Neighborhood Components Analysis Illustration</a></li>
<li class="toctree-l2"><a class="reference internal" href="../neighbors/plot_lof_novelty_detection.html">Novelty detection with Local Outlier Factor (LOF)</a></li>
<li class="toctree-l2"><a class="reference internal" href="../neighbors/plot_lof_outlier_detection.html">Outlier detection with Local Outlier Factor (LOF)</a></li>
<li class="toctree-l2"><a class="reference internal" href="../neighbors/plot_kde_1d.html">Simple 1D Kernel Density Estimation</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../neural_networks/index.html">Neural Networks</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../neural_networks/plot_mlp_training_curves.html">Compare Stochastic learning strategies for MLPClassifier</a></li>
<li class="toctree-l2"><a class="reference internal" href="../neural_networks/plot_rbm_logistic_classification.html">Restricted Boltzmann Machine features for digit classification</a></li>
<li class="toctree-l2"><a class="reference internal" href="../neural_networks/plot_mlp_alpha.html">Varying regularization in Multi-layer Perceptron</a></li>
<li class="toctree-l2"><a class="reference internal" href="../neural_networks/plot_mnist_filters.html">Visualization of MLP weights on MNIST</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../compose/index.html">Pipelines and composite estimators</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../compose/plot_column_transformer.html">Column Transformer with Heterogeneous Data Sources</a></li>
<li class="toctree-l2"><a class="reference internal" href="../compose/plot_column_transformer_mixed_types.html">Column Transformer with Mixed Types</a></li>
<li class="toctree-l2"><a class="reference internal" href="../compose/plot_feature_union.html">Concatenating multiple feature extraction methods</a></li>
<li class="toctree-l2"><a class="reference internal" href="../compose/plot_transformed_target.html">Effect of transforming the targets in regression model</a></li>
<li class="toctree-l2"><a class="reference internal" href="../compose/plot_digits_pipe.html">Pipelining: chaining a PCA and a logistic regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../compose/plot_compare_reduction.html">Selecting dimensionality reduction with Pipeline and GridSearchCV</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../preprocessing/index.html">Preprocessing</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../preprocessing/plot_all_scaling.html">Compare the effect of different scalers on data with outliers</a></li>
<li class="toctree-l2"><a class="reference internal" href="../preprocessing/plot_target_encoder.html">Comparing Target Encoder with Other Encoders</a></li>
<li class="toctree-l2"><a class="reference internal" href="../preprocessing/plot_discretization_strategies.html">Demonstrating the different strategies of KBinsDiscretizer</a></li>
<li class="toctree-l2"><a class="reference internal" href="../preprocessing/plot_discretization_classification.html">Feature discretization</a></li>
<li class="toctree-l2"><a class="reference internal" href="../preprocessing/plot_scaling_importance.html">Importance of Feature Scaling</a></li>
<li class="toctree-l2"><a class="reference internal" href="../preprocessing/plot_map_data_to_normal.html">Map data to a normal distribution</a></li>
<li class="toctree-l2"><a class="reference internal" href="../preprocessing/plot_target_encoder_cross_val.html">Target Encoder’s Internal Cross fitting</a></li>
<li class="toctree-l2"><a class="reference internal" href="../preprocessing/plot_discretization.html">Using KBinsDiscretizer to discretize continuous features</a></li>
</ul>
</details></li>
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<li class="toctree-l2"><a class="reference internal" href="../semi_supervised/plot_label_propagation_digits.html">Label Propagation digits: Demonstrating performance</a></li>
<li class="toctree-l2"><a class="reference internal" href="../semi_supervised/plot_label_propagation_structure.html">Label Propagation learning a complex structure</a></li>
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<li class="toctree-l1 has-children"><a class="reference internal" href="../text/index.html">Working with text documents</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../text/plot_document_classification_20newsgroups.html">Classification of text documents using sparse features</a></li>
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<section class="sphx-glr-example-title" id="class-likelihood-ratios-to-measure-classification-performance">
<span id="sphx-glr-auto-examples-model-selection-plot-likelihood-ratios-py"></span><h1>Class Likelihood Ratios to measure classification performance<a class="headerlink" href="#class-likelihood-ratios-to-measure-classification-performance" title="Link to this heading">#</a></h1>
<p>This example demonstrates the <a class="reference internal" href="../../modules/generated/sklearn.metrics.class_likelihood_ratios.html#sklearn.metrics.class_likelihood_ratios" title="sklearn.metrics.class_likelihood_ratios"><code class="xref py py-func docutils literal notranslate"><span class="pre">class_likelihood_ratios</span></code></a>
function, which computes the positive and negative likelihood ratios (<code class="docutils literal notranslate"><span class="pre">LR+</span></code>,