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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img width=\"800px\" src=\"../fidle/img/00-Fidle-header-01.svg\"></img>\n",
    "\n",
    "# <!-- TITLE --> [GRAD1] - Linear regression with gradient descent\n",
    "<!-- DESC --> Low level implementation of a solution by gradient descent. Basic and stochastic approach.\n",
    "<!-- AUTHOR : Jean-Luc Parouty (CNRS/SIMaP) -->\n",
    "\n",
    "\n",
    "## Objectives :\n",
    " - To illustrate the iterative approach of a gradient descent\n",
    "\n",
    "## What we're going to do :\n",
    "\n",
    "Equation : $ Y = X.\\Theta + N$  \n",
    "Where N is a noise vector\n",
    "and $\\Theta = (a,b)$ a vector as y = a.x + b\n",
    "\n",
    "We will calculate a loss function and its gradient.  \n",
    "We will descend this gradient in order to find a minimum value of our loss function.\n",
    "\n",
    "$\n",
    "\\triangledown_\\theta MSE(\\Theta)=\\begin{bmatrix}\n",
    "\\frac{\\partial}{\\partial \\theta_0}MSE(\\Theta)\\\\\n",
    "\\frac{\\partial}{\\partial \\theta_1}MSE(\\Theta)\\\\\n",
    "\\vdots\\\\\n",
    "\\frac{\\partial}{\\partial \\theta_n}MSE(\\Theta)\n",
    "\\end{bmatrix}=\\frac2m X^T\\cdot(X\\cdot\\Theta-Y)\n",
    "$  \n",
    "\n",
    "and :  \n",
    "\n",
    "$\\Theta \\leftarrow \\Theta - \\eta \\cdot \\triangledown_\\theta MSE(\\Theta)$\n",
    "\n",
    "where $\\eta$ is the learning rate\n",
    "\n",
    "## Step 1 - Import and init\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import sys\n",
    "\n",
    "sys.path.append('..')\n",
    "import fidle.pwk as pwk\n",
    "\n",
    "from modules.RegressionCooker import RegressionCooker \n",
    "\n",
    "# ---- Init Fidle stuffs\n",
    "#\n",
    "datasets_dir = pwk.init('GRAD1')\n",
    "\n",
    "# ---- Instanciate a Regression Cooker\n",
    "#\n",
    "cooker = RegressionCooker(pwk)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 2 - Get a dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "X,Y = cooker.get_dataset(1000000)\n",
    "\n",
    "cooker.plot_dataset(X,Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 3 : Data normalization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_norm     = ( X - X.mean() ) / X.std()\n",
    "Y_norm     = ( Y - Y.mean() ) / Y.std()\n",
    "\n",
    "cooker.vector_infos('X origine',X)\n",
    "cooker.vector_infos('X normalized',X_norm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 4 - Basic descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta = cooker.basic_descent(X_norm, Y_norm, epochs=200, eta=0.01)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 5 - Minibatch descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta = cooker.minibatch_descent(X_norm, Y_norm, epochs=10, batchs=20, batch_size=10, eta=0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "pwk.end()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "<img width=\"80px\" src=\"../fidle/img/00-Fidle-logo-01.svg\"></img>"
   ]
  }
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