User Guide

• 1. Supervised learning
  • 1.1. Linear Models
    • 1.1.1. Ordinary Least Squares
    • 1.1.2. Ridge regression and classification
    • 1.1.3. Lasso
    • 1.1.4. Multi-task Lasso
    • 1.1.5. Elastic-Net
    • 1.1.6. Multi-task Elastic-Net
    • 1.1.7. Least Angle Regression
    • 1.1.8. LARS Lasso
    • 1.1.9. Orthogonal Matching Pursuit (OMP)
    • 1.1.10. Bayesian Regression
    • 1.1.11. Logistic regression
    • 1.1.12. Generalized Linear Models
    • 1.1.13. Stochastic Gradient Descent - SGD
    • 1.1.14. Perceptron
    • 1.1.15. Passive Aggressive Algorithms
    • 1.1.16. Robustness regression: outliers and modeling errors
    • 1.1.17. Quantile Regression
    • 1.1.18. Polynomial regression: extending linear models with basis functions
  • 1.2. Linear and Quadratic Discriminant Analysis
    • 1.2.1. Dimensionality reduction using Linear Discriminant Analysis
    • 1.2.2. Mathematical formulation of the LDA and QDA classifiers
    • 1.2.3. Mathematical formulation of LDA dimensionality reduction
    • 1.2.4. Shrinkage and Covariance Estimator
    • 1.2.5. Estimation algorithms
  • 1.3. Kernel ridge regression
  • 1.4. Support Vector Machines
    • 1.4.1. Classification
    • 1.4.2. Regression
    • 1.4.3. Density estimation, novelty detection
    • 1.4.4. Complexity
    • 1.4.5. Tips on Practical Use
    • 1.4.6. Kernel functions
    • 1.4.7. Mathematical formulation
    • 1.4.8. Implementation details
  • 1.5. Stochastic Gradient Descent
    • 1.5.1. Classification
    • 1.5.2. Regression
    • 1.5.3. Online One-Class SVM
    • 1.5.4. Stochastic Gradient Descent for sparse data
    • 1.5.5. Complexity
    • 1.5.6. Stopping criterion
    • 1.5.7. Tips on Practical Use
    • 1.5.8. Mathematical formulation
    • 1.5.9. Implementation details
  • 1.6. Nearest Neighbors
    • 1.6.1. Unsupervised Nearest Neighbors
    • 1.6.2. Nearest Neighbors Classification
    • 1.6.3. Nearest Neighbors Regression
    • 1.6.4. Nearest Neighbor Algorithms
    • 1.6.5. Nearest Centroid Classifier
    • 1.6.6. Nearest Neighbors Transformer
    • 1.6.7. Neighborhood Components Analysis
  • 1.7. Gaussian Processes
    • 1.7.1. Gaussian Process Regression (GPR)
    • 1.7.2. GPR examples
    • 1.7.3. Gaussian Process Classification (GPC)
    • 1.7.4. GPC examples
    • 1.7.5. Kernels for Gaussian Processes
  • 1.8. Cross decomposition
    • 1.8.1. PLSCanonical
    • 1.8.2. PLSSVD
    • 1.8.3. PLSRegression
    • 1.8.4. Canonical Correlation Analysis
  • 1.9. Naive Bayes
    • 1.9.1. Gaussian Naive Bayes
    • 1.9.2. Multinomial Naive Bayes
    • 1.9.3. Complement Naive Bayes
    • 1.9.4. Bernoulli Naive Bayes
    • 1.9.5. Categorical Naive Bayes
    • 1.9.6. Out-of-core naive Bayes model fitting
  • 1.10. Decision Trees
    • 1.10.1. Classification
    • 1.10.2. Regression
    • 1.10.3. Multi-output problems
    • 1.10.4. Complexity
    • 1.10.5. Tips on practical use
    • 1.10.6. Tree algorithms: ID3, C4.5, C5.0 and CART
    • 1.10.7. Mathematical formulation
    • 1.10.8. Minimal Cost-Complexity Pruning
  • 1.11. Ensemble methods
    • 1.11.1. Bagging meta-estimator
    • 1.11.2. Forests of randomized trees
    • 1.11.3. AdaBoost
    • 1.11.4. Gradient Tree Boosting
    • 1.11.5. Histogram-Based Gradient Boosting
    • 1.11.6. Voting Classifier
    • 1.11.7. Voting Regressor
    • 1.11.8. Stacked generalization
  • 1.12. Multiclass and multioutput algorithms
    • 1.12.1. Multiclass classification
    • 1.12.2. Multilabel classification
    • 1.12.3. Multiclass-multioutput classification
    • 1.12.4. Multioutput regression
  • 1.13. Feature selection
    • 1.13.1. Removing features with low variance
    • 1.13.2. Univariate feature selection
    • 1.13.3. Recursive feature elimination
    • 1.13.4. Feature selection using SelectFromModel
    • 1.13.5. Sequential Feature Selection
    • 1.13.6. Feature selection as part of a pipeline
  • 1.14. Semi-supervised learning
    • 1.14.1. Self Training
    • 1.14.2. Label Propagation
  • 1.15. Isotonic regression
  • 1.16. Probability calibration
    • 1.16.1. Calibration curves
    • 1.16.2. Calibrating a classifier
    • 1.16.3. Usage
  • 1.17. Neural network models (supervised)
    • 1.17.1. Multi-layer Perceptron
    • 1.17.2. Classification
    • 1.17.3. Regression
    • 1.17.4. Regularization
    • 1.17.5. Algorithms
    • 1.17.6. Complexity
    • 1.17.7. Mathematical formulation
    • 1.17.8. Tips on Practical Use
    • 1.17.9. More control with warm_start
• 2. Unsupervised learning
  • 2.1. Gaussian mixture models
    • 2.1.1. Gaussian Mixture
    • 2.1.2. Variational Bayesian Gaussian Mixture
  • 2.2. Manifold learning
    • 2.2.1. Introduction
    • 2.2.2. Isomap
    • 2.2.3. Locally Linear Embedding
    • 2.2.4. Modified Locally Linear Embedding
    • 2.2.5. Hessian Eigenmapping
    • 2.2.6. Spectral Embedding
    • 2.2.7. Local Tangent Space Alignment
    • 2.2.8. Multi-dimensional Scaling (MDS)
    • 2.2.9. t-distributed Stochastic Neighbor Embedding (t-SNE)
    • 2.2.10. Tips on practical use
  • 2.3. Clustering
    • 2.3.1. Overview of clustering methods
    • 2.3.2. K-means
    • 2.3.3. Affinity Propagation
    • 2.3.4. Mean Shift
    • 2.3.5. Spectral clustering
    • 2.3.6. Hierarchical clustering
    • 2.3.7. DBSCAN
    • 2.3.8. OPTICS
    • 2.3.9. BIRCH
    • 2.3.10. Clustering performance evaluation
  • 2.4. Biclustering
    • 2.4.1. Spectral Co-Clustering
    • 2.4.2. Spectral Biclustering
    • 2.4.3. Biclustering evaluation
  • 2.5. Decomposing signals in components (matrix factorization problems)
    • 2.5.1. Principal component analysis (PCA)
    • 2.5.2. Kernel Principal Component Analysis (kPCA)
    • 2.5.3. Truncated singular value decomposition and latent semantic analysis
    • 2.5.4. Dictionary Learning
    • 2.5.5. Factor Analysis
    • 2.5.6. Independent component analysis (ICA)
    • 2.5.7. Non-negative matrix factorization (NMF or NNMF)
    • 2.5.8. Latent Dirichlet Allocation (LDA)
  • 2.6. Covariance estimation
    • 2.6.1. Empirical covariance
    • 2.6.2. Shrunk Covariance
    • 2.6.3. Sparse inverse covariance
    • 2.6.4. Robust Covariance Estimation
  • 2.7. Novelty and Outlier Detection
    • 2.7.1. Overview of outlier detection methods
    • 2.7.2. Novelty Detection
    • 2.7.3. Outlier Detection
    • 2.7.4. Novelty detection with Local Outlier Factor
  • 2.8. Density Estimation
    • 2.8.1. Density Estimation: Histograms
    • 2.8.2. Kernel Density Estimation
  • 2.9. Neural network models (unsupervised)
    • 2.9.1. Restricted Boltzmann machines
• 3. Model selection and evaluation
  • 3.1. Cross-validation: evaluating estimator performance
    • 3.1.1. Computing cross-validated metrics
    • 3.1.2. Cross validation iterators
    • 3.1.3. A note on shuffling
    • 3.1.4. Cross validation and model selection
    • 3.1.5. Permutation test score
  • 3.2. Tuning the hyper-parameters of an estimator
    • 3.2.1. Exhaustive Grid Search
    • 3.2.2. Randomized Parameter Optimization
    • 3.2.3. Searching for optimal parameters with successive halving
    • 3.2.4. Tips for parameter search
    • 3.2.5. Alternatives to brute force parameter search
  • 3.3. Metrics and scoring: quantifying the quality of predictions
    • 3.3.1. The scoring parameter: defining model evaluation rules
    • 3.3.2. Classification metrics
    • 3.3.3. Multilabel ranking metrics
    • 3.3.4. Regression metrics
    • 3.3.5. Clustering metrics
    • 3.3.6. Dummy estimators
  • 3.4. Validation curves: plotting scores to evaluate models
    • 3.4.1. Validation curve
    • 3.4.2. Learning curve
• 4. Inspection
  • 4.1. Partial Dependence and Individual Conditional Expectation plots
    • 4.1.1. Partial dependence plots
    • 4.1.2. Individual conditional expectation (ICE) plot
    • 4.1.3. Mathematical Definition
    • 4.1.4. Computation methods
  • 4.2. Permutation feature importance
    • 4.2.1. Outline of the permutation importance algorithm
    • 4.2.2. Relation to impurity-based importance in trees
    • 4.2.3. Misleading values on strongly correlated features
• 5. Visualizations
  • 5.1. Available Plotting Utilities
    • 5.1.1. Display Objects
• 6. Dataset transformations
  • 6.1. Pipelines and composite estimators
    • 6.1.1. Pipeline: chaining estimators
    • 6.1.2. Transforming target in regression
    • 6.1.3. FeatureUnion: composite feature spaces
    • 6.1.4. ColumnTransformer for heterogeneous data
    • 6.1.5. Visualizing Composite Estimators
  • 6.2. Feature extraction
    • 6.2.1. Loading features from dicts
    • 6.2.2. Feature hashing
    • 6.2.3. Text feature extraction
    • 6.2.4. Image feature extraction
  • 6.3. Preprocessing data
    • 6.3.1. Standardization, or mean removal and variance scaling
    • 6.3.2. Non-linear transformation
    • 6.3.3. Normalization
    • 6.3.4. Encoding categorical features
    • 6.3.5. Discretization
    • 6.3.6. Imputation of missing values
    • 6.3.7. Generating polynomial features
    • 6.3.8. Custom transformers
  • 6.4. Imputation of missing values
    • 6.4.1. Univariate vs. Multivariate Imputation
    • 6.4.2. Univariate feature imputation
    • 6.4.3. Multivariate feature imputation
    • 6.4.4. Nearest neighbors imputation
    • 6.4.5. Keeping the number of features constants
    • 6.4.6. Marking imputed values
    • 6.4.7. Estimators that handle NaN values
  • 6.5. Unsupervised dimensionality reduction
    • 6.5.1. PCA: principal component analysis
    • 6.5.2. Random projections
    • 6.5.3. Feature agglomeration
  • 6.6. Random Projection
    • 6.6.1. The Johnson-Lindenstrauss lemma
    • 6.6.2. Gaussian random projection
    • 6.6.3. Sparse random projection
    • 6.6.4. Inverse Transform
  • 6.7. Kernel Approximation
    • 6.7.1. Nystroem Method for Kernel Approximation
    • 6.7.2. Radial Basis Function Kernel
    • 6.7.3. Additive Chi Squared Kernel
    • 6.7.4. Skewed Chi Squared Kernel
    • 6.7.5. Polynomial Kernel Approximation via Tensor Sketch
    • 6.7.6. Mathematical Details
  • 6.8. Pairwise metrics, Affinities and Kernels
    • 6.8.1. Cosine similarity
    • 6.8.2. Linear kernel
    • 6.8.3. Polynomial kernel
    • 6.8.4. Sigmoid kernel
    • 6.8.5. RBF kernel
    • 6.8.6. Laplacian kernel
    • 6.8.7. Chi-squared kernel
  • 6.9. Transforming the prediction target (y)
    • 6.9.1. Label binarization
    • 6.9.2. Label encoding
• 7. Dataset loading utilities
  • 7.1. Toy datasets
    • 7.1.1. Iris plants dataset
    • 7.1.2. Diabetes dataset
    • 7.1.3. Optical recognition of handwritten digits dataset
    • 7.1.4. Linnerrud dataset
    • 7.1.5. Wine recognition dataset
    • 7.1.6. Breast cancer wisconsin (diagnostic) dataset
  • 7.2. Real world datasets
    • 7.2.1. The Olivetti faces dataset
    • 7.2.2. The 20 newsgroups text dataset
    • 7.2.3. The Labeled Faces in the Wild face recognition dataset
    • 7.2.4. Forest covertypes
    • 7.2.5. RCV1 dataset
    • 7.2.6. Kddcup 99 dataset
    • 7.2.7. California Housing dataset
  • 7.3. Generated datasets
    • 7.3.1. Generators for classification and clustering
    • 7.3.2. Generators for regression
    • 7.3.3. Generators for manifold learning
    • 7.3.4. Generators for decomposition
  • 7.4. Loading other datasets
    • 7.4.1. Sample images
    • 7.4.2. Datasets in svmlight / libsvm format
    • 7.4.3. Downloading datasets from the openml.org repository
    • 7.4.4. Loading from external datasets
• 8. Computing with scikit-learn
  • 8.1. Strategies to scale computationally: bigger data
    • 8.1.1. Scaling with instances using out-of-core learning
  • 8.2. Computational Performance
    • 8.2.1. Prediction Latency
    • 8.2.2. Prediction Throughput
    • 8.2.3. Tips and Tricks
  • 8.3. Parallelism, resource management, and configuration
    • 8.3.1. Parallelism
    • 8.3.2. Configuration switches
• 9. Model persistence
  • 9.1. Python specific serialization
    • 9.1.1. Security & maintainability limitations
    • 9.1.2. A more secure format: skops
  • 9.2. Interoperable formats
• 10. Common pitfalls and recommended practices
  • 10.1. Inconsistent preprocessing
  • 10.2. Data leakage
    • 10.2.1. Data leakage during pre-processing
    • 10.2.2. How to avoid data leakage
  • 10.3. Controlling randomness
    • 10.3.1. Using None or RandomState instances, and repeated calls to fit and split
    • 10.3.2. Common pitfalls and subtleties
    • 10.3.3. General recommendations
• 11. Dispatching
  • 11.1. Array API support (experimental)
    • 11.1.1. Example usage
    • 11.1.2. Estimators with support for Array API-compatible inputs