chap5.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x2585c85f7f0>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import torch\n",
    "import torch.optim as optim #for later use with optimizers\n",
    "\n",
    "#magic function, plots will be visible in the notebook\n",
    "%matplotlib inline\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#statement of the problem:\n",
    "#we want to find the correlation between temperatures t_c and t_u. To be exact, we want to find the \n",
    "#transformation (possibly linear) that is needed to convert temp. units (t_u) to t_c.\n",
    "\n",
    "# temperature data\n",
    "t_c = [0.5, 14.0, 15.0, 28.0, 11.0, 8.0, 3.0, -4.0, 6.0, 13.0, 21.0]\n",
    "t_u = [35.7, 55.9, 58.2, 81.9, 56.3, 48.9, 33.9, 21.8, 48.4, 60.4, 68.4]\n",
    "t_c = torch.tensor(t_c)\n",
    "t_u = torch.tensor(t_u)\n",
    "\n",
    "plt.scatter(t_c, t_u)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(1763.8846)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# proceeding with the linear type of model (essentially defining linear regression from scratch)\n",
    "\n",
    "#approach: we want to create a linear function that converts t_u to values t_p. t_p are meant\n",
    "#to be the values as close to t_c as possible. w - weights, b - bias (y = w*x + b).\n",
    "\n",
    "def model(t_u, w, b):\n",
    "    return w * t_u + b\n",
    "\n",
    "# we are applying the L2 kind of loss (MSE). More robust for outliers, penalizes very wrong results more that L1 metric.\n",
    "\n",
    "def loss(t_p, t_c):\n",
    "    loss = (t_p - t_c)**2\n",
    "    return loss.mean()\n",
    "\n",
    "#test\n",
    "# test_c = torch.tensor([2], dtype = float)\n",
    "# test_p = torch.tensor([1], dtype = float)\n",
    "\n",
    "# print(loss(test_c, test_p))\n",
    "\n",
    "# w and b initializing\n",
    "w = torch.ones(())\n",
    "b = torch.zeros(())\n",
    "\n",
    "# calculating t_p for earlier defined t_u\n",
    "\n",
    "t_p = model(t_u, w, b)\n",
    "loss(t_p, t_c)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shapes of the tensors: x - torch.Size([]), y - torch.Size([3, 1, 1, 1, 1]))\n",
      "Shapes of the tensors: z - torch.Size([1, 3]), a - torch.Size([2, 1, 1]))\n",
      "Shapes of the tensors: y*a - torch.Size([3, 1, 2, 1, 1])\n",
      "Shapes of the tensors: a*z - torch.Size([2, 1, 3])\n",
      "Shapes of the tensors: y*a*z - torch.Size([3, 1, 2, 1, 3])\n"
     ]
    }
   ],
   "source": [
    "# BROADCASTING\n",
    "# pytorch functionality that allow us to perform operations of tensors that are not necessarily of the same size/shape.\n",
    "\n",
    "x = torch.ones(())\n",
    "y = torch.ones(3,1,1,1,1)\n",
    "z = torch.ones(1,3)\n",
    "a = torch.ones(2,1,1)\n",
    "\n",
    "print(f\"Shapes of the tensors: x - {x.shape}, y - {y.shape})\")\n",
    "print(f\"Shapes of the tensors: z - {z.shape}, a - {a.shape})\")\n",
    "print(f\"Shapes of the tensors: y*a - {(y*a).shape}\")\n",
    "print(f\"Shapes of the tensors: a*z - {(a*z).shape}\")\n",
    "print(f\"Shapes of the tensors: y*a*z - {(y*a*z).shape}\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([35.7000, 55.9000, 58.2000, 81.9000, 56.3000, 48.9000, 33.9000, 21.8000,\n",
      "        48.4000, 60.4000, 68.4000])\n",
      "tensor(51.8000)\n",
      "tensor([1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000,\n",
      "        1.0000, 1.0000])\n",
      "tensor(1.0000)\n"
     ]
    }
   ],
   "source": [
    "# rate of change calculating\n",
    "\n",
    "delta = 0.1\n",
    "loss_rate_of_change_w = (model(t_u, w + delta, b) - model(t_u, w - delta, b))/(2*delta)\n",
    "print(loss_rate_of_change_w)\n",
    "print(loss_rate_of_change_w.mean())\n",
    "\n",
    "#same calculating for the b parameter\n",
    "loss_rate_of_change_b = (model(t_u, w, b + delta) - model(t_u, w, b - delta))/(2*delta)\n",
    "print(loss_rate_of_change_b)\n",
    "print(loss_rate_of_change_b.mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([4517.2969,   82.6000])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#derivatives for the gradient descent\n",
    "\n",
    "#first, derivative of the loss function (which is a quadratic function, MSE)\n",
    "#remembering that t_p is the the variable here\n",
    "def dloss(t_p, t_c):\n",
    "    dloss = 2*(t_p - t_c)\n",
    "    return dloss / t_p.size(0) #division necessary to address the mean calculation from the model\n",
    "\n",
    "#second, derivative of the model function (linear)\n",
    "\n",
    "#two variables here, w and b, so two functions\n",
    "def dmodel_dw(t_u, w, b):\n",
    "    return t_u\n",
    "\n",
    "def dmodel_db(t_u, w, b):\n",
    "    return 1.0\n",
    "\n",
    "#calculating the whole gradient in the one function (the loss function derivative in regard to w and b parameters)\n",
    "def grad(t_u, t_c, t_p, w, b):\n",
    "    dloss_dtp = dloss(t_p, t_c)\n",
    "    \n",
    "    #chain rule\n",
    "    dloss_dw = dloss_dtp * dmodel_dw(t_u, w ,b)\n",
    "    dloss_db = dloss_dtp * dmodel_db(t_u, w ,b)\n",
    "    \n",
    "    return torch.stack([dloss_dw.sum(), dloss_db.sum()])\n",
    "    \n",
    "grad(t_u, t_c, t_p, w, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 1, Loss value: 1763.8846435546875\n",
      "Params values: w = -44.17296600341797, b = -0.8259999752044678\n",
      "Gradient value: tensor([4517.2969,   82.6000])\n",
      "Epoch: 2, Loss value: 5802485.5\n",
      "Params values: w = 2568.4013671875, b = 45.16371154785156\n",
      "Gradient value: tensor([-261257.4219,   -4598.9712])\n",
      "Epoch: 3, Loss value: 19408035840.0\n",
      "Params values: w = -148527.734375, b = -2616.393310546875\n",
      "Gradient value: tensor([15109614.0000,   266155.7188])\n",
      "Epoch: 13, Loss value: inf\n",
      "Params values: w = -6.218085327793313e+22, b = -1.0953026620805014e+21\n",
      "Gradient value: tensor([6.3256e+24, 1.1142e+23])\n",
      "Epoch: 14, Loss value: inf\n",
      "Params values: w = 3.5961806514938787e+24, b = 6.334596602673127e+22\n",
      "Gradient value: tensor([-3.6584e+26, -6.4441e+24])\n",
      "Epoch: 15, Loss value: inf\n",
      "Params values: w = -2.0798228017110418e+26, b = -3.6635645899825066e+24\n",
      "Gradient value: tensor([2.1158e+28, 3.7269e+26])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "tensor([-2.0798e+26, -3.6636e+24])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#creating the whole training loop (iterating the gradient calculation and applying it to the model parameters)\n",
    "\n",
    "def training_loop(n_epochs, learning_rate, model_params, t_u, t_c, do_print = True):\n",
    "    \n",
    "    for i in range(1, n_epochs+1):\n",
    "        w, b = model_params\n",
    "        t_p = model(t_u, w, b) #first, model value\n",
    "        model_loss = loss(t_p, t_c) #second, loss value, to print it and look if it is going down\n",
    "        grad_value = grad(t_u, t_c, t_p, w, b) #third, gradient calculation\n",
    "        \n",
    "        model_params = model_params - learning_rate * grad_value #fourth, update the parameters\n",
    "        \n",
    "        if i in [1,2,3,n_epochs, n_epochs-1, n_epochs-2] and do_print == True:\n",
    "\n",
    "            print(f\"Epoch: {i}, Loss value: {model_loss}\")\n",
    "            print(f\"Params values: w = {model_params[0]}, b = {model_params[1]}\")\n",
    "            print(f\"Gradient value: {grad_value}\")\n",
    "        \n",
    "    \n",
    "    return model_params\n",
    "\n",
    "initial_params = torch.tensor([1.0, 0.0])\n",
    "        \n",
    "training_loop(15, 1e-2, initial_params, t_u, t_c)        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 1, Loss value: 1763.8846435546875\n",
      "Params values: w = 0.9548270106315613, b = -0.0008259999449364841\n",
      "Gradient value: tensor([4517.2969,   82.6000])\n",
      "Epoch: 2, Loss value: 1565.7613525390625\n",
      "Params values: w = 0.9123117923736572, b = -0.0016051840502768755\n",
      "Gradient value: tensor([4251.5215,   77.9184])\n",
      "Epoch: 3, Loss value: 1390.2655029296875\n",
      "Params values: w = 0.8722979426383972, b = -0.002340306993573904\n",
      "Gradient value: tensor([4001.3838,   73.5123])\n",
      "Epoch: 98, Loss value: 29.117908477783203\n",
      "Params values: w = 0.23425845801830292, b = -0.016456322744488716\n",
      "Gradient value: tensor([12.5503,  3.2493])\n",
      "Epoch: 99, Loss value: 29.11627960205078\n",
      "Params values: w = 0.23414036631584167, b = -0.016488686203956604\n",
      "Gradient value: tensor([11.8088,  3.2363])\n",
      "Epoch: 100, Loss value: 29.114818572998047\n",
      "Params values: w = 0.23402926325798035, b = -0.016520926728844643\n",
      "Gradient value: tensor([11.1109,  3.2240])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "tensor([ 0.2340, -0.0165])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#the values are diverging instead of converging - possibly the result of too big learning rate. updating to 1e-5\n",
    "training_loop(100, 1e-5, initial_params, t_u, t_c)       "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([35.7000, 55.9000, 58.2000, 81.9000, 56.3000, 48.9000, 33.9000, 21.8000,\n",
      "        48.4000, 60.4000, 68.4000])\n",
      "tensor([3.5700, 5.5900, 5.8200, 8.1900, 5.6300, 4.8900, 3.3900, 2.1800, 4.8400,\n",
      "        6.0400, 6.8400])\n"
     ]
    }
   ],
   "source": [
    "#loss function stops converging. looking at the gradient it seems that the parameters of the model are of a different scale;\n",
    "#the one learning rate cannot effectively converge both parameters. better solution - normalize the inputs.\n",
    "\n",
    "print(t_u)\n",
    "t_un = t_u * 1e-1 #defining normalized version\n",
    "print(t_un)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 1, Loss value: 80.36434173583984\n",
      "Params values: w = 1.7761403322219849, b = 0.10639999061822891\n",
      "Gradient value: tensor([-77.6140, -10.6400])\n",
      "Epoch: 2, Loss value: 37.57491683959961\n",
      "Params values: w = 2.084763288497925, b = 0.13026385009288788\n",
      "Gradient value: tensor([-30.8623,  -2.3864])\n",
      "Epoch: 3, Loss value: 30.871076583862305\n",
      "Params values: w = 2.2093942165374756, b = 0.12167707830667496\n",
      "Gradient value: tensor([-12.4631,   0.8587])\n",
      "Epoch: 4998, Loss value: 2.9276468753814697\n",
      "Params values: w = 5.367081642150879, b = -17.301177978515625\n",
      "Gradient value: tensor([-0.0001,  0.0006])\n",
      "Epoch: 4999, Loss value: 2.927647352218628\n",
      "Params values: w = 5.367082595825195, b = -17.301183700561523\n",
      "Gradient value: tensor([-0.0001,  0.0006])\n",
      "Epoch: 5000, Loss value: 2.927647590637207\n",
      "Params values: w = 5.367083549499512, b = -17.301189422607422\n",
      "Gradient value: tensor([-0.0001,  0.0006])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "tensor([  5.3671, -17.3012])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#running same loop again with normalized t_u, going back to learning rate of 1e-2 (seems better), more epochs.\n",
    "training_loop(5000, 1e-2, initial_params, t_un, t_c) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([ 1.8593, 12.7008, 13.9352, 26.6552, 12.9155,  8.9439,  0.8932, -5.6009,\n",
      "         8.6755, 15.1160, 19.4097])\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 3000x1500 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#good enough approximation, the data isn't perfectly linear, error won't converge to 0.\n",
    "#take the parameters and make the final model\n",
    "\n",
    "final_params = training_loop(5000, 1e-2, initial_params, t_un, t_c, do_print = False) \n",
    "t_p = model(t_un, *final_params)\n",
    "\n",
    "#visualizing!\n",
    "\n",
    "fig = plt.figure(dpi = 300, figsize = (10,5))\n",
    "plt.xlabel(\"Fahrenheit\")\n",
    "plt.ylabel(\"Celsius\")\n",
    "plt.plot(t_un, t_p)\n",
    "plt.plot(t_un, t_c, 'o')\n",
    "plt.grid(linewidth = 0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([4517.2969,   82.6000])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#rewriting to use the autograd functionality\n",
    "params = torch.tensor([1., 0.], requires_grad = True)\n",
    "\n",
    "\n",
    "#performin the backward pass. this tracks the derivative part of previous code.\n",
    "loss_wg = loss(model(t_u, *params), t_c)\n",
    "loss_wg.backward()\n",
    "\n",
    "params.grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 1, Loss value: 80.36434173583984\n",
      "Params values: w = 1.7761403322219849, b = 0.10639999061822891\n",
      "Epoch: 2, Loss value: 37.57491683959961\n",
      "Params values: w = 2.084763288497925, b = 0.13026385009288788\n",
      "Epoch: 3, Loss value: 30.871076583862305\n",
      "Params values: w = 2.2093942165374756, b = 0.12167707830667496\n",
      "Epoch: 4998, Loss value: 2.9276466369628906\n",
      "Params values: w = 5.367082595825195, b = -17.30118179321289\n",
      "Epoch: 4999, Loss value: 2.927647590637207\n",
      "Params values: w = 5.367083549499512, b = -17.30118751525879\n",
      "Epoch: 5000, Loss value: 2.9276468753814697\n",
      "Params values: w = 5.367084503173828, b = -17.301193237304688\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "tensor([  5.3671, -17.3012], requires_grad=True)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#updating the iteration loop function to include the backward pass\n",
    "def training_loop_wg(n_epochs, learning_rate, params, t_u, t_c, do_print = True):\n",
    "    \n",
    "    for i in range(1, n_epochs+1):\n",
    "        t_p = model(t_u, *params) #first, model value\n",
    "        model_loss = loss(t_p, t_c) #second, loss value, to print it and look if it is going down\n",
    "        model_loss.backward()\n",
    "#         grad_value = grad(t_u, t_c, t_p, w, b) #we are no longer using the manual grad calculation \n",
    "                                                #(the backward loss pass is doing the job for us)\n",
    "        \n",
    "        with torch.no_grad():\n",
    "            params -= learning_rate * params.grad\n",
    "            \n",
    "        params.grad.zero_()\n",
    "        \n",
    "        if i in [1,2,3,n_epochs, n_epochs-1, n_epochs-2] and do_print == True:\n",
    "\n",
    "            print(f\"Epoch: {i}, Loss value: {model_loss}\")\n",
    "            print(f\"Params values: w = {params[0]}, b = {params[1]}\")\n",
    "#             print(f\"Gradient value: {grad_value}\")\n",
    "        \n",
    "    \n",
    "    return params\n",
    "\n",
    "params = torch.tensor([1., 0.], requires_grad = True)\n",
    "training_loop_wg(5000, 1e-2, params, t_un, t_c, do_print = True)\n",
    "params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 1, Loss value: 80.36434173583984\n",
      "Params values: w = 1.7761403322219849, b = 0.10639999061822891\n",
      "Epoch: 2, Loss value: 37.57491683959961\n",
      "Params values: w = 2.084763288497925, b = 0.13026385009288788\n",
      "Epoch: 3, Loss value: 30.871076583862305\n",
      "Params values: w = 2.2093942165374756, b = 0.12167707830667496\n",
      "Epoch: 4998, Loss value: 2.9276466369628906\n",
      "Params values: w = 5.367082595825195, b = -17.30118179321289\n",
      "Epoch: 4999, Loss value: 2.927647590637207\n",
      "Params values: w = 5.367083549499512, b = -17.30118751525879\n",
      "Epoch: 5000, Loss value: 2.9276468753814697\n",
      "Params values: w = 5.367084503173828, b = -17.301193237304688\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "tensor([  5.3671, -17.3012], requires_grad=True)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#adding the optimizer\n",
    "def training_loop_wo(n_epochs, learning_rate, params, t_u, t_c, do_print = True):\n",
    "    \n",
    "    #first, setting up the optimizer and passing the params inside\n",
    "    #for starters, the regular SGD optimizer\n",
    "    \n",
    "    import torch.optim as optim\n",
    "    optimizer = optim.SGD([params], lr = learning_rate) #passing the params and learning rate\n",
    "    \n",
    "    for i in range(1, n_epochs+1):\n",
    "        t_p = model(t_u, *params) #first, model value\n",
    "        model_loss = loss(t_p, t_c) #second, loss value, to print it and look if it is going down\n",
    "        model_loss.backward()\n",
    "#         grad_value = grad(t_u, t_c, t_p, w, b) #we are no longer using the manual grad calculation \n",
    "                                                #(the backward loss pass is doing the job for us)\n",
    "        \n",
    "#         with torch.no_grad():\n",
    "#             params -= learning_rate * params.grad #this part of the code also becomes obsolete since we now have our\n",
    "                                                    #optimizer ready to do the job\n",
    "        \n",
    "        optimizer.step() #this one updates the params values\n",
    "        optimizer.zero_grad()\n",
    "#         params.grad.zero_() #also redundant, we are using the above line for that\n",
    "        \n",
    "        if i in [1,2,3,n_epochs, n_epochs-1, n_epochs-2] and do_print == True:\n",
    "\n",
    "            print(f\"Epoch: {i}, Loss value: {model_loss}\")\n",
    "            print(f\"Params values: w = {params[0]}, b = {params[1]}\")\n",
    "#             print(f\"Gradient value: {grad_value}\")\n",
    "        \n",
    "    \n",
    "    return params\n",
    "\n",
    "params = torch.tensor([1., 0.], requires_grad = True)\n",
    "training_loop_wo(5000, 1e-2, params, t_un, t_c, do_print = True)\n",
    "params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 1, Loss value: 1763.8846435546875\n",
      "Params values: w = 0.8999999761581421, b = -0.09999999403953552\n",
      "Epoch: 2, Loss value: 1334.34912109375\n",
      "Params values: w = 0.8006196618080139, b = -0.19941246509552002\n",
      "Epoch: 3, Loss value: 967.8158569335938\n",
      "Params values: w = 0.7024322152137756, b = -0.29770106077194214\n",
      "Epoch: 1998, Loss value: 2.9276466369628906\n",
      "Params values: w = 0.5367231369018555, b = -17.30201530456543\n",
      "Epoch: 1999, Loss value: 2.927645206451416\n",
      "Params values: w = 0.5367234945297241, b = -17.302038192749023\n",
      "Epoch: 2000, Loss value: 2.9276459217071533\n",
      "Params values: w = 0.5367238521575928, b = -17.302061080932617\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "tensor([  0.5367, -17.3021], requires_grad=True)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#experimenting with ADAM optimizer\n",
    "def training_loop_w_Adam(n_epochs, learning_rate, params, t_u, t_c, do_print = True):\n",
    "    \n",
    "    #first, setting up the optimizer and passing the params inside\n",
    "    #for starters, the regular SGD optimizer\n",
    "    \n",
    "    import torch.optim as optim\n",
    "    optimizer = optim.Adam([params], lr = learning_rate) #passing the params and learning rate\n",
    "    \n",
    "    for i in range(1, n_epochs+1):\n",
    "        t_p = model(t_u, *params) #first, model value\n",
    "        model_loss = loss(t_p, t_c) #second, loss value, to print it and look if it is going down\n",
    "        model_loss.backward()\n",
    "#         grad_value = grad(t_u, t_c, t_p, w, b) #we are no longer using the manual grad calculation \n",
    "                                                #(the backward loss pass is doing the job for us)\n",
    "        \n",
    "#         with torch.no_grad():\n",
    "#             params -= learning_rate * params.grad #this part of the code also becomes obsolete since we now have our\n",
    "                                                    #optimizer ready to do the job\n",
    "        \n",
    "        optimizer.step() #this one updates the params values\n",
    "        optimizer.zero_grad()\n",
    "#         params.grad.zero_() #also redundant, we are using the above line for that\n",
    "        \n",
    "        if i in [1,2,3,n_epochs, n_epochs-1, n_epochs-2] and do_print == True:\n",
    "\n",
    "            print(f\"Epoch: {i}, Loss value: {model_loss}\")\n",
    "            print(f\"Params values: w = {params[0]}, b = {params[1]}\")\n",
    "#             print(f\"Gradient value: {grad_value}\")\n",
    "        \n",
    "    \n",
    "    return params\n",
    "\n",
    "#also changing the inputs\n",
    "#since ADAM is less scale sensitive, we are using old t_u (unnormalized input), we can also go back to\n",
    "#higher learning rate (it is adaptive) and do less epochs\n",
    "params = torch.tensor([1., 0.], requires_grad = True)\n",
    "training_loop_w_Adam(2000, 1e-1, params, t_u, t_c, do_print = True)\n",
    "params\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([6, 4, 3, 8, 9, 5, 1, 2, 0]) tensor([ 7, 10])\n"
     ]
    }
   ],
   "source": [
    "#splitting the dataset for training/validation purposes\n",
    "t_c = [0.5, 14.0, 15.0, 28.0, 11.0, 8.0, 3.0, -4.0, 6.0, 13.0, 21.0]\n",
    "t_u = [35.7, 55.9, 58.2, 81.9, 56.3, 48.9, 33.9, 21.8, 48.4, 60.4, 68.4]\n",
    "t_c = torch.tensor(t_c)\n",
    "t_u = torch.tensor(t_u)\n",
    "t_un = t_u * 1e-1\n",
    "\n",
    "n_samples = t_u.shape[0]\n",
    "n_samples\n",
    "\n",
    "#number of validation values\n",
    "n_val = int(0.2 * n_samples)\n",
    "\n",
    "shuffled_indices = torch.randperm(n_samples)\n",
    "shuffled_indices\n",
    "\n",
    "train_indices = shuffled_indices[n_val:]\n",
    "val_indices = shuffled_indices[:n_val]\n",
    "print(train_indices, val_indices)\n",
    "\n",
    "#applying the indices\n",
    "t_u_train = t_u[train_indices]\n",
    "t_c_train = t_c[train_indices]\n",
    "\n",
    "t_u_val = t_u[val_indices]\n",
    "t_c_val = t_c[val_indices]\n",
    "\n",
    "#remember about normalizing\n",
    "t_un_train = t_u_train * 1e-1\n",
    "t_un_val = t_u_val * 1e-1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 1, TRAIN Loss value: 71.70108032226562\n",
      "Epoch: 1, VAL Loss value: 119.3489990234375\n",
      "Params values: w = 1.7633227109909058, b = 0.11231110244989395\n",
      "Epoch: 2, TRAIN Loss value: 30.705928802490234\n",
      "Epoch: 2, VAL Loss value: 70.60588073730469\n",
      "Params values: w = 2.0533745288848877, b = 0.14102274179458618\n",
      "Epoch: 3, TRAIN Loss value: 24.842201232910156\n",
      "Epoch: 3, VAL Loss value: 60.34419631958008\n",
      "Params values: w = 2.1650784015655518, b = 0.1382470726966858\n",
      "Epoch: 2998, TRAIN Loss value: 2.857738971710205\n",
      "Epoch: 2998, VAL Loss value: 3.8990111351013184\n",
      "Params values: w = 5.429691314697266, b = -17.956857681274414\n",
      "Epoch: 2999, TRAIN Loss value: 2.8576955795288086\n",
      "Epoch: 2999, VAL Loss value: 3.899620532989502\n",
      "Params values: w = 5.429807662963867, b = -17.957515716552734\n",
      "Epoch: 3000, TRAIN Loss value: 2.8576502799987793\n",
      "Epoch: 3000, VAL Loss value: 3.9002249240875244\n",
      "Params values: w = 5.429924011230469, b = -17.958173751831055\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "tensor([  5.4299, -17.9582], requires_grad=True)"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#applying the changes to the function\n",
    "def training_loop_with_val(n_epochs, optimizer, params, t_u_train, t_c_train, t_u_val, t_c_val, do_print = True):\n",
    "    \n",
    "    for epoch in range(1, n_epochs+1):\n",
    "        t_p_train = model(t_u_train, *params)\n",
    "        t_p_val = model(t_u_val, *params)\n",
    "        \n",
    "        model_loss_train = loss(t_p_train, t_c_train)\n",
    "        model_loss_val = loss(t_p_val, t_c_val)\n",
    "        \n",
    "        #backprop only for the train part of the data\n",
    "        model_loss_train.backward()\n",
    "        \n",
    "        #update and zero the gradient\n",
    "        optimizer.step()\n",
    "        optimizer.zero_grad()\n",
    "        \n",
    "        if epoch in [1,2,3,n_epochs, n_epochs-1, n_epochs-2] and do_print == True:\n",
    "\n",
    "            print(f\"Epoch: {epoch}, TRAIN Loss value: {model_loss_train}\")\n",
    "            \n",
    "            print(f\"Epoch: {epoch}, VAL Loss value: {model_loss_val}\")\n",
    "            print(\"Params values: w = {}, b = {}\".format(*params))\n",
    "        \n",
    "    \n",
    "    return params\n",
    "\n",
    "learning_rate = 1e-2\n",
    "params = torch.tensor([1., 0.], requires_grad = True)\n",
    "optimizer = optim.SGD([params] , lr = learning_rate)\n",
    "training_loop_with_val(3000, optimizer, params, t_un_train, t_c_train, t_un_val, t_c_val, do_print = True)\n",
    "params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 1, TRAIN Loss value: 71.70108032226562\n",
      "Epoch: 1, VAL Loss value: 119.3489990234375\n",
      "Params values: w = 1.7633227109909058, b = 0.11231110244989395\n",
      "Epoch: 2, TRAIN Loss value: 30.705928802490234\n",
      "Epoch: 2, VAL Loss value: 70.60588073730469\n",
      "Params values: w = 2.0533745288848877, b = 0.14102274179458618\n",
      "Epoch: 3, TRAIN Loss value: 24.842201232910156\n",
      "Epoch: 3, VAL Loss value: 60.34419631958008\n",
      "Params values: w = 2.1650784015655518, b = 0.1382470726966858\n",
      "Epoch: 2998, TRAIN Loss value: 2.857738971710205\n",
      "Epoch: 2998, VAL Loss value: 3.8990111351013184\n",
      "Params values: w = 5.429691314697266, b = -17.956857681274414\n",
      "Epoch: 2999, TRAIN Loss value: 2.8576955795288086\n",
      "Epoch: 2999, VAL Loss value: 3.899620532989502\n",
      "Params values: w = 5.429807662963867, b = -17.957515716552734\n",
      "Epoch: 3000, TRAIN Loss value: 2.8576502799987793\n",
      "Epoch: 3000, VAL Loss value: 3.9002249240875244\n",
      "Params values: w = 5.429924011230469, b = -17.958173751831055\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "tensor([  5.4299, -17.9582], requires_grad=True)"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#additional update using the no_grad() method for the validation calculation. this is to prevent\n",
    "#torch from generating additional computational graph for the validation side of things\n",
    "def training_loop_with_valnograd(n_epochs, optimizer, params, t_u_train, t_c_train, t_u_val, t_c_val, do_print = True):\n",
    "    \n",
    "    for epoch in range(1, n_epochs+1):\n",
    "        t_p_train = model(t_u_train, *params)\n",
    "        model_loss_train = loss(t_p_train, t_c_train)\n",
    "        \n",
    "        with torch.no_grad(): #especially for the validation purposes\n",
    "            t_p_val = model(t_u_val, *params)\n",
    "            model_loss_val = loss(t_p_val, t_c_val)\n",
    "            assert model_loss_val.requires_grad == False #check if grad was actually disabled\n",
    "        \n",
    "        #backprop only for the train part of the data\n",
    "        model_loss_train.backward()\n",
    "        \n",
    "        #update and zero the gradient\n",
    "        optimizer.step()\n",
    "        optimizer.zero_grad()\n",
    "        \n",
    "        if epoch in [1,2,3,n_epochs, n_epochs-1, n_epochs-2] and do_print == True:\n",
    "\n",
    "            print(f\"Epoch: {epoch}, TRAIN Loss value: {model_loss_train}\")\n",
    "            \n",
    "            print(f\"Epoch: {epoch}, VAL Loss value: {model_loss_val}\")\n",
    "            print(\"Params values: w = {}, b = {}\".format(*params))\n",
    "        \n",
    "    \n",
    "    return params\n",
    "\n",
    "learning_rate = 1e-2\n",
    "params = torch.tensor([1., 0.], requires_grad = True)\n",
    "optimizer = optim.SGD([params] , lr = learning_rate)\n",
    "training_loop_with_valnograd(3000, optimizer, params, t_un_train, t_c_train, t_un_val, t_c_val, do_print = True)\n",
    "params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 1, TRAIN Loss value: 694.421142578125\n",
      "Epoch: 1, VAL Loss value: 591.9736328125\n",
      "Params values: w1 = 0.8999999761581421, w2 = 0.8999999761581421, b = -0.10000000149011612\n",
      "Epoch: 2, TRAIN Loss value: 499.45404052734375\n",
      "Epoch: 2, VAL Loss value: 420.316650390625\n",
      "Params values: w1 = 0.8007773160934448, w2 = 0.8007590770721436, b = -0.19926267862319946\n",
      "Epoch: 3, TRAIN Loss value: 337.9852600097656\n",
      "Epoch: 3, VAL Loss value: 280.1041564941406\n",
      "Params values: w1 = 0.7030926942825317, w2 = 0.7030152082443237, b = -0.2970770001411438\n",
      "Epoch: 4998, TRAIN Loss value: 2.2410688400268555\n",
      "Epoch: 4998, VAL Loss value: 2.065742015838623\n",
      "Params values: w1 = 0.31767138838768005, w2 = 1.9291660785675049, b = -8.934626579284668\n",
      "Epoch: 4999, TRAIN Loss value: 2.241068124771118\n",
      "Epoch: 4999, VAL Loss value: 2.065680980682373\n",
      "Params values: w1 = 0.3176663815975189, w2 = 1.9292261600494385, b = -8.934792518615723\n",
      "Epoch: 5000, TRAIN Loss value: 2.24106764793396\n",
      "Epoch: 5000, VAL Loss value: 2.0656137466430664\n",
      "Params values: w1 = 0.3176611363887787, w2 = 1.9292858839035034, b = -8.934958457946777\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "tensor([ 0.3177,  1.9293, -8.9350], requires_grad=True)"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "###### EXERCISES #######\n",
    "#redefining the model with using a second-degree polynomial instead of the linear function\n",
    "def training_loop_2nd(n_epochs, optimizer, params, t_u_train, t_c_train, t_u_val, t_c_val, do_print = True):\n",
    "\n",
    "    for epoch in range(1, n_epochs+1):\n",
    "        t_p_train = model_poly(t_u_train, *params)\n",
    "        model_loss_train = loss_poly(t_p_train, t_c_train)\n",
    "        \n",
    "        with torch.no_grad(): #especially for the validation purposes\n",
    "            t_p_val = model_poly(t_u_val, *params)\n",
    "            model_loss_val = loss_poly(t_p_val, t_c_val)\n",
    "            assert model_loss_val.requires_grad == False #check if grad was actually disabled\n",
    "        \n",
    "        #backprop only for the train part of the data\n",
    "        model_loss_train.backward()\n",
    "        \n",
    "        #update and zero the gradient\n",
    "        optimizer.step()\n",
    "        optimizer.zero_grad()\n",
    "        \n",
    "        if epoch in [1,2,3,n_epochs, n_epochs-1, n_epochs-2] and do_print == True:\n",
    "\n",
    "            print(f\"Epoch: {epoch}, TRAIN Loss value: {model_loss_train}\")\n",
    "            \n",
    "            print(f\"Epoch: {epoch}, VAL Loss value: {model_loss_val}\")\n",
    "            print(\"Params values: w1 = {}, w2 = {}, b = {}\".format(*params))\n",
    "        \n",
    "    \n",
    "    return params\n",
    "\n",
    "def model_poly(t, w2, w1, b):\n",
    "    return w2 * t ** 2 + w1 * t + b\n",
    "\n",
    "def loss_poly(t_p, t_c):\n",
    "    loss = (t_p - t_c)**2\n",
    "    return loss.mean()\n",
    "\n",
    "learning_rate = 1e-1\n",
    "params_2nd = torch.tensor([1., 1., 0.], requires_grad = True)\n",
    "optimizer = optim.Adam([params_2nd] , lr = learning_rate)\n",
    "training_loop_2nd(5000, optimizer, params_2nd, t_un_train, t_c_train, t_un_val, t_c_val, do_print = True)\n",
    "params_2nd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 1, TRAIN Loss value: 675.7943115234375\n",
      "Params values: w1 = 0.8999999761581421, w2 = 0.9000000357627869, b = -0.09999998658895493\n",
      "Epoch: 2, TRAIN Loss value: 485.0655212402344\n",
      "Params values: w1 = 0.8007911443710327, w2 = 0.8007677793502808, b = -0.19926884770393372\n",
      "Epoch: 3, TRAIN Loss value: 327.47955322265625\n",
      "Params values: w1 = 0.7031512260437012, w2 = 0.7030516266822815, b = -0.2971033453941345\n",
      "Epoch: 4998, TRAIN Loss value: 2.0907211303710938\n",
      "Params values: w1 = 0.28304538130760193, w2 = 2.4760162830352783, b = -10.64955997467041\n",
      "Epoch: 4999, TRAIN Loss value: 2.090721607208252\n",
      "Params values: w1 = 0.2830454707145691, w2 = 2.4760165214538574, b = -10.64955997467041\n",
      "Epoch: 5000, TRAIN Loss value: 2.0907208919525146\n",
      "Params values: w1 = 0.28304535150527954, w2 = 2.4760165214538574, b = -10.649560928344727\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 3000x1500 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Q: what parts of the training loop, and so on, need to change to accommodate\n",
    "#this redefinition?\n",
    "#A: the model definition, the loss function, number of parameters\n",
    "\n",
    "#Q: what parts are agnostic to swapping out the model?\n",
    "#A: the choice of the optimizer\n",
    "\n",
    "#Q: is the resulting loss higher or lower after training?\n",
    "#A: it's smaller due to the changed optimizer.\n",
    "\n",
    "#Q: is the actual result better or worse?\n",
    "#A: some plotting first:\n",
    "\n",
    "#taking whole model for a spin first\n",
    "def training_loop_final2nd(n_epochs, learning_rate, params, t_u, t_c, do_print = True):\n",
    "    \n",
    "    for epoch in range(1, n_epochs+1):\n",
    "        t_p = model_poly(t_u, *params)\n",
    "        model_loss_train = loss_poly(t_p, t_c)\n",
    "        \n",
    "        #backprop only for the train part of the data\n",
    "        model_loss_train.backward()\n",
    "        \n",
    "        #update and zero the gradient\n",
    "        optimizer.step()\n",
    "        optimizer.zero_grad()\n",
    "        \n",
    "        if epoch in [1,2,3,n_epochs, n_epochs-1, n_epochs-2] and do_print == True:\n",
    "\n",
    "            print(f\"Epoch: {epoch}, TRAIN Loss value: {model_loss_train}\")\n",
    "            print(\"Params values: w1 = {}, w2 = {}, b = {}\".format(*params))\n",
    "        \n",
    "    \n",
    "    return params\n",
    "\n",
    "learning_rate = 1e-1\n",
    "params_2nd = torch.tensor([1., 1., 0.], requires_grad = True)\n",
    "optimizer = optim.Adam([params_2nd] , lr = learning_rate)\n",
    "final_params_2nd = training_loop_final2nd(5000, optimizer, params_2nd, t_un, t_c, do_print = True)\n",
    "params_2nd\n",
    "tp_2nd = model_poly(t_un, *final_params_2nd)\n",
    "\n",
    "# final_params_2nd = training_loop_2nd(5000, optimizer, params_2nd, t_un_train, t_c_train, t_un_val, t_c_val, do_print = False)\n",
    "# final_params_2nd = training_loop_2nd(5000, optimizer, params_2nd, t_un_train, t_c_train, t_un_val, t_c_val, do_print = False)\n",
    "# tp_2nd = model_poly(t_un, *final_params_2nd)\n",
    "\n",
    "# print(t_un)\n",
    "\n",
    "\n",
    "def f(t):\n",
    "    return 0.28 * t ** 2 + 2.47 * t - 10\n",
    "\n",
    "fig = plt.figure(dpi = 300, figsize = (10,5))\n",
    "plt.plot(t_un, f(t_un))\n",
    "plt.plot(t_un, t_c, 'o')\n",
    "plt.grid(linewidth = 0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}