.. _example_linear_model_plot_theilsen.py: ==================== Theil-Sen Regression ==================== Computes a Theil-Sen Regression on a synthetic dataset. See :ref:`theil_sen_regression` for more information on the regressor. Compared to the OLS (ordinary least squares) estimator, the Theil-Sen estimator is robust against outliers. It has a breakdown point of about 29.3% in case of a simple linear regression which means that it can tolerate arbitrary corrupted data (outliers) of up to 29.3% in the two-dimensional case. The estimation of the model is done by calculating the slopes and intercepts of a subpopulation of all possible combinations of p subsample points. If an intercept is fitted, p must be greater than or equal to n_features + 1. The final slope and intercept is then defined as the spatial median of these slopes and intercepts. In certain cases Theil-Sen performs better than :ref:`RANSAC ` which is also a robust method. This is illustrated in the second example below where outliers with respect to the x-axis perturb RANSAC. Tuning the ``residual_threshold`` parameter of RANSAC remedies this but in general a priori knowledge about the data and the nature of the outliers is needed. Due to the computational complexity of Theil-Sen it is recommended to use it only for small problems in terms of number of samples and features. For larger problems the ``max_subpopulation`` parameter restricts the magnitude of all possible combinations of p subsample points to a randomly chosen subset and therefore also limits the runtime. Therefore, Theil-Sen is applicable to larger problems with the drawback of losing some of its mathematical properties since it then works on a random subset. .. rst-class:: horizontal * .. image:: images/plot_theilsen_001.png :scale: 47 * .. image:: images/plot_theilsen_002.png :scale: 47 **Python source code:** :download:`plot_theilsen.py ` .. literalinclude:: plot_theilsen.py :lines: 36- **Total running time of the example:** 1.63 seconds ( 0 minutes 1.63 seconds)