{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Ridge Composite Quantile Regression\n", "\n", "[![Slides](https://img.shields.io/badge/🦌-ReHLine-blueviolet)](https://rehline-python.readthedocs.io/en/latest/)\n", "\n", "The regularized composite quantile regression solves the following optimization problem:\n", "\n", "\n", "\n", "\n", "$$\n", "min_{\\beta \\in \\mathbb{R}^{d}, \\alpha \\in \\mathbb{R}^{K}} \\ C \\sum_{k=1}^K \\sum_{i=1}^n \\rho_\\kappa ( y_i - x^\\intercal_i \\beta - \\alpha_k) + \\frac{1}{2} (\\| \\beta \\|^2 + \\| \\alpha \\|^2),\n", "$$\n", "\n", "\n", "where $\\alpha_k$ is the intercept associated with k-th quantile, $\\rho_\\kappa(u) = u\\cdot(\\kappa - \\mathbf{1}(u < 0))$ is the check loss,\n", "$x_i \\in \\mathbb{R}^d$ is a feature vector, $y_i \\in \\mathbb{R}$ is the response variable." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "## simulate data\n", "from sklearn.datasets import make_regression\n", "from sklearn.preprocessing import StandardScaler\n", "\n", "scaler = StandardScaler()\n", "\n", "n, d = 1000, 1\n", "X, y, coef = make_regression(n_samples=n, n_features=d, noise=50.0, coef=True)\n", "X = scaler.fit_transform(X)\n", "y = y / y.std()" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "## fit model\n", "from rehline import CQR_Ridge\n", "\n", "cqr = CQR_Ridge(quantiles=[0.05, 0.5, 0.95])\n", "cqr.fit(X, y)\n", "y_pred = cqr.predict(X) # 3 columns, each represents the prediction for a quantile" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "## plot QR results\n", "import matplotlib.pyplot as plt\n", "import pandas as pd\n", "import seaborn as sns\n", "\n", "df = pd.DataFrame({\"X\": X.squeeze(), \"real_y\": y, \"q05\": y_pred[:, 0], \"q50\": y_pred[:, 1], \"q95\": y_pred[:, 2]})\n", "\n", "## scatter plot of the data\n", "sns.scatterplot(df, x=\"X\", y=\"real_y\", color=\"blue\")\n", "\n", "## plot the quantile regression lines\n", "sns.lineplot(df, x=\"X\", y=\"q05\", color=\"red\", label=\"Quantile: 0.05\")\n", "sns.lineplot(df, x=\"X\", y=\"q50\", color=\"orange\", label=\"Quantile: 0.50\")\n", "sns.lineplot(df, x=\"X\", y=\"q95\", color=\"purple\", label=\"Quantile: 0.95\")\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "cqr", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.13.1" } }, "nbformat": 4, "nbformat_minor": 2 }