{
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# Custom QR\n",
        "\n",
        "The Custom QR solves the following optimization problem:\n",
        "\n",
        "$$\n",
        "\\min_{\\mathbf{\\beta} \\in \\mathbb{R}^d}\n",
        "C\\sum_{i=1}^n \\rho_{\\kappa}(y_i-\\mathbf{x}_i^\\top\\mathbf{\\beta})\n",
        "+\\frac{1}{2}\\|\\mathbf{\\beta}\\|_2^2,\n",
        "$$\n",
        "\n",
        "$$\n",
        "\\text{subject to} \\quad A\\mathbf{\\beta}+b \\ge 0,\n",
        "$$\n",
        "\n",
        "where:\n",
        "\n",
        "* $\\mathbf{x}_i \\in \\mathbb{R}^d$ is a feature vector\n",
        "* $y_i \\in \\mathbb{R}$ is a continuous response variable\n",
        "* $\\rho_{\\kappa}(u)=u\\big(\\kappa-\\mathbf{1}(u<0)\\big)$ is the quantile (check) loss\n",
        "* $A \\in \\mathbb{R}^{K \\times d}$ and $b \\in \\mathbb{R}^{K}$ define custom linear constraints\n",
        "\n",
        "The custom constraints allow arbitrary prior knowledge (e.g. sign, ordering, budget, or linear relation constraints) to be incorporated into quantile regression.\n",
        "\n",
        "> **Note.** Since the check loss is a plq function and the constraints are linear ($A\\beta+b\\ge0$), we can optimize it using `rehline.plq_Ridge_Regressor`."
      ],
      "metadata": {
        "id": "VMY5iF-Wgfm9"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "350gRKl8oZO8"
      },
      "outputs": [],
      "source": [
        "## install rehline\n",
        "%pip install rehline -q"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "MbOVhGJWC1bM"
      },
      "outputs": [],
      "source": [
        "## simulate data\n",
        "from sklearn.datasets import make_regression\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "import numpy as np\n",
        "\n",
        "scaler = StandardScaler()\n",
        "\n",
        "n, d = 10000, 5\n",
        "X, y = make_regression(n_samples=n, n_features=d, noise=1.0, random_state=42)\n",
        "X = scaler.fit_transform(X)\n",
        "y = y / y.std()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "FGHO9F1QZK5M"
      },
      "outputs": [],
      "source": [
        "# Example: beta_0 + beta_1 >= 3\n",
        "A = np.zeros((1, d))\n",
        "A[0, 0] = 1\n",
        "A[0, 1] = 1\n",
        "b = np.array([-3.0])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jAQHQ9HRcbzd"
      },
      "source": [
        "## QR as baseline"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 80
        },
        "id": "F4kiv_VqJF6t",
        "outputId": "1af75ee7-5a23-4909-8541-6ac79ad14768"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "plq_Ridge_Regressor(fit_intercept=False, max_iter=10000)"
            ],
            "text/html": [
              "<style>#sk-container-id-1 {\n",
              "  /* Definition of color scheme common for light and dark mode */\n",
              "  --sklearn-color-text: #000;\n",
              "  --sklearn-color-text-muted: #666;\n",
              "  --sklearn-color-line: gray;\n",
              "  /* Definition of color scheme for unfitted estimators */\n",
              "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
              "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
              "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
              "  --sklearn-color-unfitted-level-3: chocolate;\n",
              "  /* Definition of color scheme for fitted estimators */\n",
              "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
              "  --sklearn-color-fitted-level-1: #d4ebff;\n",
              "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
              "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
              "\n",
              "  /* Specific color for light theme */\n",
              "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
              "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
              "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
              "  --sklearn-color-icon: #696969;\n",
              "\n",
              "  @media (prefers-color-scheme: dark) {\n",
              "    /* Redefinition of color scheme for dark theme */\n",
              "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
              "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
              "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
              "    --sklearn-color-icon: #878787;\n",
              "  }\n",
              "}\n",
              "\n",
              "#sk-container-id-1 {\n",
              "  color: var(--sklearn-color-text);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 pre {\n",
              "  padding: 0;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 input.sk-hidden--visually {\n",
              "  border: 0;\n",
              "  clip: rect(1px 1px 1px 1px);\n",
              "  clip: rect(1px, 1px, 1px, 1px);\n",
              "  height: 1px;\n",
              "  margin: -1px;\n",
              "  overflow: hidden;\n",
              "  padding: 0;\n",
              "  position: absolute;\n",
              "  width: 1px;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-dashed-wrapped {\n",
              "  border: 1px dashed var(--sklearn-color-line);\n",
              "  margin: 0 0.4em 0.5em 0.4em;\n",
              "  box-sizing: border-box;\n",
              "  padding-bottom: 0.4em;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-container {\n",
              "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
              "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
              "     so we also need the `!important` here to be able to override the\n",
              "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
              "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
              "  display: inline-block !important;\n",
              "  position: relative;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-text-repr-fallback {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              "div.sk-parallel-item,\n",
              "div.sk-serial,\n",
              "div.sk-item {\n",
              "  /* draw centered vertical line to link estimators */\n",
              "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
              "  background-size: 2px 100%;\n",
              "  background-repeat: no-repeat;\n",
              "  background-position: center center;\n",
              "}\n",
              "\n",
              "/* Parallel-specific style estimator block */\n",
              "\n",
              "#sk-container-id-1 div.sk-parallel-item::after {\n",
              "  content: \"\";\n",
              "  width: 100%;\n",
              "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
              "  flex-grow: 1;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-parallel {\n",
              "  display: flex;\n",
              "  align-items: stretch;\n",
              "  justify-content: center;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  position: relative;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-parallel-item {\n",
              "  display: flex;\n",
              "  flex-direction: column;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-parallel-item:first-child::after {\n",
              "  align-self: flex-end;\n",
              "  width: 50%;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-parallel-item:last-child::after {\n",
              "  align-self: flex-start;\n",
              "  width: 50%;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-parallel-item:only-child::after {\n",
              "  width: 0;\n",
              "}\n",
              "\n",
              "/* Serial-specific style estimator block */\n",
              "\n",
              "#sk-container-id-1 div.sk-serial {\n",
              "  display: flex;\n",
              "  flex-direction: column;\n",
              "  align-items: center;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  padding-right: 1em;\n",
              "  padding-left: 1em;\n",
              "}\n",
              "\n",
              "\n",
              "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
              "clickable and can be expanded/collapsed.\n",
              "- Pipeline and ColumnTransformer use this feature and define the default style\n",
              "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
              "*/\n",
              "\n",
              "/* Pipeline and ColumnTransformer style (default) */\n",
              "\n",
              "#sk-container-id-1 div.sk-toggleable {\n",
              "  /* Default theme specific background. It is overwritten whether we have a\n",
              "  specific estimator or a Pipeline/ColumnTransformer */\n",
              "  background-color: var(--sklearn-color-background);\n",
              "}\n",
              "\n",
              "/* Toggleable label */\n",
              "#sk-container-id-1 label.sk-toggleable__label {\n",
              "  cursor: pointer;\n",
              "  display: flex;\n",
              "  width: 100%;\n",
              "  margin-bottom: 0;\n",
              "  padding: 0.5em;\n",
              "  box-sizing: border-box;\n",
              "  text-align: center;\n",
              "  align-items: start;\n",
              "  justify-content: space-between;\n",
              "  gap: 0.5em;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 label.sk-toggleable__label .caption {\n",
              "  font-size: 0.6rem;\n",
              "  font-weight: lighter;\n",
              "  color: var(--sklearn-color-text-muted);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 label.sk-toggleable__label-arrow:before {\n",
              "  /* Arrow on the left of the label */\n",
              "  content: \"▸\";\n",
              "  float: left;\n",
              "  margin-right: 0.25em;\n",
              "  color: var(--sklearn-color-icon);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {\n",
              "  color: var(--sklearn-color-text);\n",
              "}\n",
              "\n",
              "/* Toggleable content - dropdown */\n",
              "\n",
              "#sk-container-id-1 div.sk-toggleable__content {\n",
              "  max-height: 0;\n",
              "  max-width: 0;\n",
              "  overflow: hidden;\n",
              "  text-align: left;\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-toggleable__content.fitted {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-toggleable__content pre {\n",
              "  margin: 0.2em;\n",
              "  border-radius: 0.25em;\n",
              "  color: var(--sklearn-color-text);\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-toggleable__content.fitted pre {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
              "  /* Expand drop-down */\n",
              "  max-height: 200px;\n",
              "  max-width: 100%;\n",
              "  overflow: auto;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
              "  content: \"▾\";\n",
              "}\n",
              "\n",
              "/* Pipeline/ColumnTransformer-specific style */\n",
              "\n",
              "#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Estimator-specific style */\n",
              "\n",
              "/* Colorize estimator box */\n",
              "#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-label label.sk-toggleable__label,\n",
              "#sk-container-id-1 div.sk-label label {\n",
              "  /* The background is the default theme color */\n",
              "  color: var(--sklearn-color-text-on-default-background);\n",
              "}\n",
              "\n",
              "/* On hover, darken the color of the background */\n",
              "#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "/* Label box, darken color on hover, fitted */\n",
              "#sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Estimator label */\n",
              "\n",
              "#sk-container-id-1 div.sk-label label {\n",
              "  font-family: monospace;\n",
              "  font-weight: bold;\n",
              "  display: inline-block;\n",
              "  line-height: 1.2em;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-label-container {\n",
              "  text-align: center;\n",
              "}\n",
              "\n",
              "/* Estimator-specific */\n",
              "#sk-container-id-1 div.sk-estimator {\n",
              "  font-family: monospace;\n",
              "  border: 1px dotted var(--sklearn-color-border-box);\n",
              "  border-radius: 0.25em;\n",
              "  box-sizing: border-box;\n",
              "  margin-bottom: 0.5em;\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-estimator.fitted {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "/* on hover */\n",
              "#sk-container-id-1 div.sk-estimator:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-estimator.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
              "\n",
              "/* Common style for \"i\" and \"?\" */\n",
              "\n",
              ".sk-estimator-doc-link,\n",
              "a:link.sk-estimator-doc-link,\n",
              "a:visited.sk-estimator-doc-link {\n",
              "  float: right;\n",
              "  font-size: smaller;\n",
              "  line-height: 1em;\n",
              "  font-family: monospace;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  border-radius: 1em;\n",
              "  height: 1em;\n",
              "  width: 1em;\n",
              "  text-decoration: none !important;\n",
              "  margin-left: 0.5em;\n",
              "  text-align: center;\n",
              "  /* unfitted */\n",
              "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-unfitted-level-1);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link.fitted,\n",
              "a:link.sk-estimator-doc-link.fitted,\n",
              "a:visited.sk-estimator-doc-link.fitted {\n",
              "  /* fitted */\n",
              "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-fitted-level-1);\n",
              "}\n",
              "\n",
              "/* On hover */\n",
              "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
              ".sk-estimator-doc-link:hover,\n",
              "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
              ".sk-estimator-doc-link:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
              ".sk-estimator-doc-link.fitted:hover,\n",
              "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
              ".sk-estimator-doc-link.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "/* Span, style for the box shown on hovering the info icon */\n",
              ".sk-estimator-doc-link span {\n",
              "  display: none;\n",
              "  z-index: 9999;\n",
              "  position: relative;\n",
              "  font-weight: normal;\n",
              "  right: .2ex;\n",
              "  padding: .5ex;\n",
              "  margin: .5ex;\n",
              "  width: min-content;\n",
              "  min-width: 20ex;\n",
              "  max-width: 50ex;\n",
              "  color: var(--sklearn-color-text);\n",
              "  box-shadow: 2pt 2pt 4pt #999;\n",
              "  /* unfitted */\n",
              "  background: var(--sklearn-color-unfitted-level-0);\n",
              "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link.fitted span {\n",
              "  /* fitted */\n",
              "  background: var(--sklearn-color-fitted-level-0);\n",
              "  border: var(--sklearn-color-fitted-level-3);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link:hover span {\n",
              "  display: block;\n",
              "}\n",
              "\n",
              "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
              "\n",
              "#sk-container-id-1 a.estimator_doc_link {\n",
              "  float: right;\n",
              "  font-size: 1rem;\n",
              "  line-height: 1em;\n",
              "  font-family: monospace;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  border-radius: 1rem;\n",
              "  height: 1rem;\n",
              "  width: 1rem;\n",
              "  text-decoration: none;\n",
              "  /* unfitted */\n",
              "  color: var(--sklearn-color-unfitted-level-1);\n",
              "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 a.estimator_doc_link.fitted {\n",
              "  /* fitted */\n",
              "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-fitted-level-1);\n",
              "}\n",
              "\n",
              "/* On hover */\n",
              "#sk-container-id-1 a.estimator_doc_link:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 a.estimator_doc_link.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-3);\n",
              "}\n",
              "</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>plq_Ridge_Regressor(fit_intercept=False, max_iter=10000)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow\"><div><div>plq_Ridge_Regressor</div></div><div><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></div></label><div class=\"sk-toggleable__content fitted\"><pre>plq_Ridge_Regressor(fit_intercept=False, max_iter=10000)</pre></div> </div></div></div></div>"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ],
      "source": [
        "## we first run a QR\n",
        "from rehline import plq_Ridge_Regressor\n",
        "\n",
        "clf = plq_Ridge_Regressor(\n",
        "    loss={'name': 'QR', 'qt': 0.5},\n",
        "    C=1.0,\n",
        "    max_iter=10000,\n",
        "    fit_intercept=False\n",
        ")\n",
        "clf.fit(X=X, y=y)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NHjMQ-vnclTL"
      },
      "source": [
        "## Custom Constraint"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 114
        },
        "id": "beKf5mp-R3_5",
        "outputId": "d2b0afc2-95c6-4492-ae2b-61d6826c0ba7"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "plq_Ridge_Regressor(constraint=[{'A': array([[1., 1., 0., 0., 0.]]),\n",
              "                                 'b': array([-3.]), 'name': 'custom'}],\n",
              "                    fit_intercept=False, max_iter=10000)"
            ],
            "text/html": [
              "<style>#sk-container-id-2 {\n",
              "  /* Definition of color scheme common for light and dark mode */\n",
              "  --sklearn-color-text: #000;\n",
              "  --sklearn-color-text-muted: #666;\n",
              "  --sklearn-color-line: gray;\n",
              "  /* Definition of color scheme for unfitted estimators */\n",
              "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
              "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
              "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
              "  --sklearn-color-unfitted-level-3: chocolate;\n",
              "  /* Definition of color scheme for fitted estimators */\n",
              "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
              "  --sklearn-color-fitted-level-1: #d4ebff;\n",
              "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
              "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
              "\n",
              "  /* Specific color for light theme */\n",
              "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
              "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
              "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
              "  --sklearn-color-icon: #696969;\n",
              "\n",
              "  @media (prefers-color-scheme: dark) {\n",
              "    /* Redefinition of color scheme for dark theme */\n",
              "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
              "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
              "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
              "    --sklearn-color-icon: #878787;\n",
              "  }\n",
              "}\n",
              "\n",
              "#sk-container-id-2 {\n",
              "  color: var(--sklearn-color-text);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 pre {\n",
              "  padding: 0;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 input.sk-hidden--visually {\n",
              "  border: 0;\n",
              "  clip: rect(1px 1px 1px 1px);\n",
              "  clip: rect(1px, 1px, 1px, 1px);\n",
              "  height: 1px;\n",
              "  margin: -1px;\n",
              "  overflow: hidden;\n",
              "  padding: 0;\n",
              "  position: absolute;\n",
              "  width: 1px;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-dashed-wrapped {\n",
              "  border: 1px dashed var(--sklearn-color-line);\n",
              "  margin: 0 0.4em 0.5em 0.4em;\n",
              "  box-sizing: border-box;\n",
              "  padding-bottom: 0.4em;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-container {\n",
              "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
              "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
              "     so we also need the `!important` here to be able to override the\n",
              "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
              "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
              "  display: inline-block !important;\n",
              "  position: relative;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-text-repr-fallback {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              "div.sk-parallel-item,\n",
              "div.sk-serial,\n",
              "div.sk-item {\n",
              "  /* draw centered vertical line to link estimators */\n",
              "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
              "  background-size: 2px 100%;\n",
              "  background-repeat: no-repeat;\n",
              "  background-position: center center;\n",
              "}\n",
              "\n",
              "/* Parallel-specific style estimator block */\n",
              "\n",
              "#sk-container-id-2 div.sk-parallel-item::after {\n",
              "  content: \"\";\n",
              "  width: 100%;\n",
              "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
              "  flex-grow: 1;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-parallel {\n",
              "  display: flex;\n",
              "  align-items: stretch;\n",
              "  justify-content: center;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  position: relative;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-parallel-item {\n",
              "  display: flex;\n",
              "  flex-direction: column;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-parallel-item:first-child::after {\n",
              "  align-self: flex-end;\n",
              "  width: 50%;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-parallel-item:last-child::after {\n",
              "  align-self: flex-start;\n",
              "  width: 50%;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-parallel-item:only-child::after {\n",
              "  width: 0;\n",
              "}\n",
              "\n",
              "/* Serial-specific style estimator block */\n",
              "\n",
              "#sk-container-id-2 div.sk-serial {\n",
              "  display: flex;\n",
              "  flex-direction: column;\n",
              "  align-items: center;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  padding-right: 1em;\n",
              "  padding-left: 1em;\n",
              "}\n",
              "\n",
              "\n",
              "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
              "clickable and can be expanded/collapsed.\n",
              "- Pipeline and ColumnTransformer use this feature and define the default style\n",
              "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
              "*/\n",
              "\n",
              "/* Pipeline and ColumnTransformer style (default) */\n",
              "\n",
              "#sk-container-id-2 div.sk-toggleable {\n",
              "  /* Default theme specific background. It is overwritten whether we have a\n",
              "  specific estimator or a Pipeline/ColumnTransformer */\n",
              "  background-color: var(--sklearn-color-background);\n",
              "}\n",
              "\n",
              "/* Toggleable label */\n",
              "#sk-container-id-2 label.sk-toggleable__label {\n",
              "  cursor: pointer;\n",
              "  display: flex;\n",
              "  width: 100%;\n",
              "  margin-bottom: 0;\n",
              "  padding: 0.5em;\n",
              "  box-sizing: border-box;\n",
              "  text-align: center;\n",
              "  align-items: start;\n",
              "  justify-content: space-between;\n",
              "  gap: 0.5em;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 label.sk-toggleable__label .caption {\n",
              "  font-size: 0.6rem;\n",
              "  font-weight: lighter;\n",
              "  color: var(--sklearn-color-text-muted);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 label.sk-toggleable__label-arrow:before {\n",
              "  /* Arrow on the left of the label */\n",
              "  content: \"▸\";\n",
              "  float: left;\n",
              "  margin-right: 0.25em;\n",
              "  color: var(--sklearn-color-icon);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 label.sk-toggleable__label-arrow:hover:before {\n",
              "  color: var(--sklearn-color-text);\n",
              "}\n",
              "\n",
              "/* Toggleable content - dropdown */\n",
              "\n",
              "#sk-container-id-2 div.sk-toggleable__content {\n",
              "  max-height: 0;\n",
              "  max-width: 0;\n",
              "  overflow: hidden;\n",
              "  text-align: left;\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-toggleable__content.fitted {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-toggleable__content pre {\n",
              "  margin: 0.2em;\n",
              "  border-radius: 0.25em;\n",
              "  color: var(--sklearn-color-text);\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-toggleable__content.fitted pre {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
              "  /* Expand drop-down */\n",
              "  max-height: 200px;\n",
              "  max-width: 100%;\n",
              "  overflow: auto;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
              "  content: \"▾\";\n",
              "}\n",
              "\n",
              "/* Pipeline/ColumnTransformer-specific style */\n",
              "\n",
              "#sk-container-id-2 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Estimator-specific style */\n",
              "\n",
              "/* Colorize estimator box */\n",
              "#sk-container-id-2 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-label label.sk-toggleable__label,\n",
              "#sk-container-id-2 div.sk-label label {\n",
              "  /* The background is the default theme color */\n",
              "  color: var(--sklearn-color-text-on-default-background);\n",
              "}\n",
              "\n",
              "/* On hover, darken the color of the background */\n",
              "#sk-container-id-2 div.sk-label:hover label.sk-toggleable__label {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "/* Label box, darken color on hover, fitted */\n",
              "#sk-container-id-2 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Estimator label */\n",
              "\n",
              "#sk-container-id-2 div.sk-label label {\n",
              "  font-family: monospace;\n",
              "  font-weight: bold;\n",
              "  display: inline-block;\n",
              "  line-height: 1.2em;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-label-container {\n",
              "  text-align: center;\n",
              "}\n",
              "\n",
              "/* Estimator-specific */\n",
              "#sk-container-id-2 div.sk-estimator {\n",
              "  font-family: monospace;\n",
              "  border: 1px dotted var(--sklearn-color-border-box);\n",
              "  border-radius: 0.25em;\n",
              "  box-sizing: border-box;\n",
              "  margin-bottom: 0.5em;\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-estimator.fitted {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "/* on hover */\n",
              "#sk-container-id-2 div.sk-estimator:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-estimator.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
              "\n",
              "/* Common style for \"i\" and \"?\" */\n",
              "\n",
              ".sk-estimator-doc-link,\n",
              "a:link.sk-estimator-doc-link,\n",
              "a:visited.sk-estimator-doc-link {\n",
              "  float: right;\n",
              "  font-size: smaller;\n",
              "  line-height: 1em;\n",
              "  font-family: monospace;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  border-radius: 1em;\n",
              "  height: 1em;\n",
              "  width: 1em;\n",
              "  text-decoration: none !important;\n",
              "  margin-left: 0.5em;\n",
              "  text-align: center;\n",
              "  /* unfitted */\n",
              "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-unfitted-level-1);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link.fitted,\n",
              "a:link.sk-estimator-doc-link.fitted,\n",
              "a:visited.sk-estimator-doc-link.fitted {\n",
              "  /* fitted */\n",
              "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-fitted-level-1);\n",
              "}\n",
              "\n",
              "/* On hover */\n",
              "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
              ".sk-estimator-doc-link:hover,\n",
              "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
              ".sk-estimator-doc-link:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
              ".sk-estimator-doc-link.fitted:hover,\n",
              "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
              ".sk-estimator-doc-link.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "/* Span, style for the box shown on hovering the info icon */\n",
              ".sk-estimator-doc-link span {\n",
              "  display: none;\n",
              "  z-index: 9999;\n",
              "  position: relative;\n",
              "  font-weight: normal;\n",
              "  right: .2ex;\n",
              "  padding: .5ex;\n",
              "  margin: .5ex;\n",
              "  width: min-content;\n",
              "  min-width: 20ex;\n",
              "  max-width: 50ex;\n",
              "  color: var(--sklearn-color-text);\n",
              "  box-shadow: 2pt 2pt 4pt #999;\n",
              "  /* unfitted */\n",
              "  background: var(--sklearn-color-unfitted-level-0);\n",
              "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link.fitted span {\n",
              "  /* fitted */\n",
              "  background: var(--sklearn-color-fitted-level-0);\n",
              "  border: var(--sklearn-color-fitted-level-3);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link:hover span {\n",
              "  display: block;\n",
              "}\n",
              "\n",
              "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
              "\n",
              "#sk-container-id-2 a.estimator_doc_link {\n",
              "  float: right;\n",
              "  font-size: 1rem;\n",
              "  line-height: 1em;\n",
              "  font-family: monospace;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  border-radius: 1rem;\n",
              "  height: 1rem;\n",
              "  width: 1rem;\n",
              "  text-decoration: none;\n",
              "  /* unfitted */\n",
              "  color: var(--sklearn-color-unfitted-level-1);\n",
              "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 a.estimator_doc_link.fitted {\n",
              "  /* fitted */\n",
              "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-fitted-level-1);\n",
              "}\n",
              "\n",
              "/* On hover */\n",
              "#sk-container-id-2 a.estimator_doc_link:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 a.estimator_doc_link.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-3);\n",
              "}\n",
              "</style><div id=\"sk-container-id-2\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>plq_Ridge_Regressor(constraint=[{&#x27;A&#x27;: array([[1., 1., 0., 0., 0.]]),\n",
              "                                 &#x27;b&#x27;: array([-3.]), &#x27;name&#x27;: &#x27;custom&#x27;}],\n",
              "                    fit_intercept=False, max_iter=10000)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" checked><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow\"><div><div>plq_Ridge_Regressor</div></div><div><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></div></label><div class=\"sk-toggleable__content fitted\"><pre>plq_Ridge_Regressor(constraint=[{&#x27;A&#x27;: array([[1., 1., 0., 0., 0.]]),\n",
              "                                 &#x27;b&#x27;: array([-3.]), &#x27;name&#x27;: &#x27;custom&#x27;}],\n",
              "                    fit_intercept=False, max_iter=10000)</pre></div> </div></div></div></div>"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ],
      "source": [
        "## solve custom via `plq_Ridge_Regressor` by adding `constraint`\n",
        "from rehline import plq_Ridge_Regressor\n",
        "\n",
        "cclf = plq_Ridge_Regressor(\n",
        "    loss={'name': 'QR', 'qt': 0.5},\n",
        "    constraint=[{'name': 'custom', 'A': A, 'b': b}],\n",
        "    C=1.0,\n",
        "    max_iter=10000,\n",
        "    fit_intercept=False\n",
        ")\n",
        "cclf.fit(X=X, y=y)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zQOfvMjRR6Fn",
        "outputId": "0f4461a4-6b1e-4119-d3b7-cee46823d8f0"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "    Model  Train MSE\n",
            "       QR   0.000097\n",
            "Custom QR   1.352705\n",
            "\n",
            "coef_0 + coef_1 = 3.00000008 >= 3: True\n"
          ]
        }
      ],
      "source": [
        "import pandas as pd\n",
        "## score\n",
        "score = clf.predict(X)\n",
        "cscore = cclf.predict(X)\n",
        "\n",
        "qr_perf = np.mean((y - score)**2)\n",
        "cqr_perf = np.mean((y - cscore)**2)\n",
        "\n",
        "# Create a pandas DataFrame to store the results\n",
        "results = pd.DataFrame({\n",
        "    'Model': ['QR', 'Custom QR'],\n",
        "    'Train MSE': [qr_perf, cqr_perf]\n",
        "})\n",
        "\n",
        "# Print the results as a table\n",
        "print(results.to_string(index=False))\n",
        "#Print the results of custom constraint\n",
        "lhs = cclf.coef_[0] + cclf.coef_[1]\n",
        "print(f\"\\ncoef_0 + coef_1 = {lhs:.8f} >= 3: {lhs >= 3}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 884
        },
        "id": "zWGh56JmZ00l",
        "outputId": "a1b5a1a3-4635-4968-e6df-57ac88e9b7b6"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "import seaborn as sns\n",
        "import pandas as pd\n",
        "import warnings\n",
        "import matplotlib.pyplot as plt\n",
        "warnings.filterwarnings(\"ignore\", \"is_categorical_dtype\")\n",
        "warnings.filterwarnings(\"ignore\", \"use_inf_as_na\")\n",
        "\n",
        "n_sample = 50\n",
        "X_sample, y_sample = X[:n_sample], y[:n_sample]\n",
        "qr_sample = clf.predict(X_sample)\n",
        "cqr_sample = cclf.predict(X_sample)\n",
        "\n",
        "df = pd.DataFrame({\n",
        "    'x0': X_sample[:, 0],\n",
        "    'real_y': y_sample,\n",
        "    'QR': qr_sample,\n",
        "    'Custom_QR': cqr_sample\n",
        "})\n",
        "\n",
        "df1 = df[['x0', 'real_y', 'QR']].melt(id_vars='x0')\n",
        "sns.scatterplot(data=df1, x='x0', y='value', hue='variable').set_title(\"QR\")\n",
        "plt.show()\n",
        "df2 = df[['x0', 'real_y', 'Custom_QR']].melt(id_vars='x0')\n",
        "sns.scatterplot(data=df2, x='x0', y='value', hue='variable').set_title(\"Custom QR\")\n",
        "plt.show()"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}