{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# Example 3:Ridge Regression\n",
    "This example try to show how to use our PLQ Composite Decomposition tool to perform Ridge Regression."
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "# 1. Data Generation"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "source": [
    "from plqcom import PLQLoss, plq_to_rehloss, affine_transformation\n",
    "import numpy as np\n",
    "from rehline import ReHLine\n",
    "\n",
    "n_samples, n_features = 1000, 5\n",
    "rng = np.random.RandomState(0)\n",
    "X = rng.randn(n_samples, n_features)\n",
    "beta = rng.randn(n_features)\n",
    "y = np.dot(X, beta) + rng.normal(scale=0.1, size=n_samples)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    },
    "ExecuteTime": {
     "end_time": "2025-01-03T09:26:29.875018Z",
     "start_time": "2025-01-03T09:26:29.357142Z"
    }
   },
   "outputs": [],
   "execution_count": 1
  },
  {
   "cell_type": "markdown",
   "source": [
    "# 2.Create and Decompose the PLQ Loss"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "source": [
    "plqloss = PLQLoss(quad_coef={'a': np.array([1.]), 'b': np.array([0.]), 'c': np.array([0.])},\n",
    "                  cutpoints=np.array([]))"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    },
    "ExecuteTime": {
     "end_time": "2025-01-03T09:26:31.934888Z",
     "start_time": "2025-01-03T09:26:31.931230Z"
    }
   },
   "outputs": [],
   "execution_count": 2
  },
  {
   "cell_type": "code",
   "source": [
    "rehloss = plq_to_rehloss(plqloss)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    },
    "ExecuteTime": {
     "end_time": "2025-01-03T09:26:32.245900Z",
     "start_time": "2025-01-03T09:26:32.242660Z"
    }
   },
   "outputs": [],
   "execution_count": 3
  },
  {
   "cell_type": "code",
   "source": [
    "rehloss.rehu_cut, rehloss.rehu_coef, rehloss.rehu_intercept"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    },
    "ExecuteTime": {
     "end_time": "2025-01-03T09:26:33.249899Z",
     "start_time": "2025-01-03T09:26:33.244088Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[inf],\n",
       "        [inf]]),\n",
       " array([[-1.41421356],\n",
       "        [ 1.41421356]]),\n",
       " array([[-0.],\n",
       "        [ 0.]]))"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 4
  },
  {
   "cell_type": "markdown",
   "source": [
    "# 3. Broadcast to all samples"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "source": [
    "rehloss = affine_transformation(rehloss, n=X.shape[0], c=1, p=-1, q=y)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    },
    "ExecuteTime": {
     "end_time": "2025-01-03T09:26:38.134329Z",
     "start_time": "2025-01-03T09:26:38.131467Z"
    }
   },
   "outputs": [],
   "execution_count": 5
  },
  {
   "cell_type": "markdown",
   "source": [
    "# 4. Use the ReHLine to solve the problem"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "source": [
    "clf = ReHLine()\n",
    "C = 1\n",
    "clf.Tau, clf.S, clf.T, clf.C = rehloss.rehu_cut, rehloss.rehu_coef, rehloss.rehu_intercept, C\n",
    "clf.fit(X=X)\n",
    "print('sol privided by rehline: %s' % clf.coef_)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    },
    "ExecuteTime": {
     "end_time": "2025-01-03T09:27:10.594222Z",
     "start_time": "2025-01-03T09:27:10.579926Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sol privided by rehline: [ 0.31029299 -0.73855141 -1.53883908 -0.56076169 -1.6047202 ]\n"
     ]
    }
   ],
   "execution_count": 6
  },
  {
   "cell_type": "markdown",
   "source": [
    "Compare with the solution provided by sklearn"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "clf1 = Ridge(alpha=0.5)\n",
    "clf1.fit(X, y)\n",
    "print('sol privided by sklearn: %s' % clf1.coef_)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    },
    "ExecuteTime": {
     "end_time": "2025-01-03T09:27:16.507328Z",
     "start_time": "2025-01-03T09:27:16.078233Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sol privided by sklearn: [ 0.31017419 -0.73849146 -1.53893293 -0.56084128 -1.60476756]\n"
     ]
    }
   ],
   "execution_count": 7
  }
 ],
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