LinRegressionPyTorch.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 157,
   "id": "48ea94a2-352b-4deb-8449-a4226d6a97a0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.3.0.post100\n",
      "0.15.2a0\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import numpy as np\n",
    "import torchvision\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib_inline.backend_inline\n",
    "matplotlib_inline.backend_inline.set_matplotlib_formats('svg')\n",
    "print(torch.__version__)\n",
    "print(torchvision.__version__)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ac838fd2-bd31-4c96-9aad-c85bb5dd4300",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = torch.tensor(2.0, requires_grad=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "6d95cdc2-617a-489c-8a55-ae10c51124c6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor(63., grad_fn=<AddBackward0>)\n"
     ]
    }
   ],
   "source": [
    "y = 2*x**4 + x**3 + 3*x**2 + 5*x + 1\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "e4c10cf2-fdc1-4392-ba9d-ff7db07c58c2",
   "metadata": {},
   "outputs": [],
   "source": [
    "y.backward()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "407c0d33-b050-442b-b979-db38be2b2661",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor(93.)\n"
     ]
    }
   ],
   "source": [
    "print(x.grad)  #slope of the polynomial at the point 2,63"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "6b014ff6-3700-4fa9-9a16-5b6511b9d0e5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[1., 2., 3.],\n",
      "        [3., 2., 1.]], requires_grad=True)\n"
     ]
    }
   ],
   "source": [
    "x = torch.tensor([[1.,2,3],[3,2,1]], requires_grad=True)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "50cafa60-d08e-46a4-8fc2-02f91c69a188",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[ 5.,  8., 11.],\n",
      "        [11.,  8.,  5.]], grad_fn=<AddBackward0>)\n"
     ]
    }
   ],
   "source": [
    "y = 3*x + 2\n",
    "print(y) #first tensor layer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "8def948c-08bc-4c75-b514-6f59feea9a91",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[ 50., 128., 242.],\n",
      "        [242., 128.,  50.]], grad_fn=<MulBackward0>)\n"
     ]
    }
   ],
   "source": [
    "z = 2*y**2\n",
    "print(z)    #second layer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "4a3af955-994c-44bd-a989-69c48f6f3fef",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor(140., grad_fn=<MeanBackward0>)\n"
     ]
    }
   ],
   "source": [
    "out = z.mean()\n",
    "print(out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "6669b572-f802-4586-a9b7-8a6c88028511",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[10., 16., 22.],\n",
      "        [22., 16., 10.]])\n"
     ]
    }
   ],
   "source": [
    "out.backward()\n",
    "print(x.grad)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "92f33de8-9f0e-4c36-b667-6b6c8ca6e11b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "cf872260-cd9e-419f-a7d2-3529a2725802",
   "metadata": {},
   "outputs": [],
   "source": [
    "#over all goal minimize the error between model and data using loss function mean-squared-error\n",
    "X = torch.linspace(1,50,50).reshape(-1,1)  #create tensor but without gradient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "94f042c1-dfc7-40c5-a652-f34238f91d16",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor(0.)\n"
     ]
    }
   ],
   "source": [
    "torch.manual_seed(71) # to obtain reproducible results\n",
    "e = torch.randint(-8,9,(50,1),dtype=torch.float)\n",
    "print(e.sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "794bca04-3dd1-4c37-951e-35598fc2a948",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([50, 1])\n"
     ]
    }
   ],
   "source": [
    "y = 2*X + 1 + e\n",
    "print(y.shape)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "20dd10da-7278-46e1-b7ce-83365b3fc3d2",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X.numpy(), y.numpy())\n",
    "plt.ylabel('y')\n",
    "plt.xlabel('x');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b624a22f-eb9f-49d0-a098-43c23cd33d85",
   "metadata": {},
   "outputs": [],
   "source": [
    "#X doesn't have gradient so can't get backwards y fxn, use nn.Linear() to predict relationship instead "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "id": "14e3f0e7-36f4-4b8b-a5a4-c98d03763c28",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameter containing:\n",
      "tensor([[-0.4078]], requires_grad=True)\n",
      "Parameter containing:\n",
      "tensor([0.0331], requires_grad=True)\n"
     ]
    }
   ],
   "source": [
    "torch.manual_seed(123)\n",
    "model = nn.Linear(in_features=1, out_features=1)\n",
    "print(model.weight)\n",
    "print(model.bias)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "id": "4b14a2ec-5a58-4064-b6f6-7289bdee2371",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Model(nn.Module):\n",
    "    def __init__(self, in_features, out_features):\n",
    "        super().__init__()\n",
    "        self.linear = nn.Linear(in_features, out_features) #doesn't refer to linear regression, its nn related\n",
    "    def forward(self, x):   #method defines how the data flows through the model\n",
    "        y_pred = self.linear(x)\n",
    "        return y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "id": "0bfae620-b9f1-4225-a33c-8236da8feef9",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Model(nn.Module):\n",
    "    def __init__(self, in_features, out_features):\n",
    "        super().__init__()\n",
    "        self.linear = nn.Linear(in_features, out_features)  # Define the linear layer\n",
    "\n",
    "    def forward(self, x):\n",
    "        y_pred = self.linear(x)  # Define the forward pass\n",
    "        return y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "id": "76cea8d8-89de-48fb-84c7-9f7c841e84c1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model(\n",
      "  (linear): Linear(in_features=1, out_features=1, bias=True)\n",
      ")\n",
      "Weight: -0.4077761173248291\n",
      "Bias:   0.033124566078186035\n"
     ]
    }
   ],
   "source": [
    "torch.manual_seed(123)\n",
    "model = Model(1, 1)  #1 input feature, 1 output feature \n",
    "print(model)\n",
    "print('Weight:', model.linear.weight.item())\n",
    "print('Bias:  ', model.linear.bias.item())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "id": "ccb7cf4e-f023-48d1-b21c-d2d64716b4c8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "linear.weight \t -0.4077761173248291\n",
      "linear.bias \t 0.033124566078186035\n"
     ]
    }
   ],
   "source": [
    "for name, param in model.named_parameters():\n",
    "    print(name, '\\t', param.item())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "id": "040cf796-1b0e-4b81-8338-ff4224cdce96",
   "metadata": {},
   "outputs": [],
   "source": [
    "#pass tensor into the model "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "id": "572cb058-e6b7-4e1a-aa26-e2076880a4ba",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([-0.7824], grad_fn=<ViewBackward0>)\n"
     ]
    }
   ],
   "source": [
    "x = torch.tensor([2.0])\n",
    "print(model.forward(x))   # equivalent to print(model(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "id": "65db67c5-be04-4874-820c-958080a69155",
   "metadata": {},
   "outputs": [],
   "source": [
    "#plot initial model "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "id": "0f07101e-0e75-4b48-9af6-f9b400ae44f6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1. 50.]\n"
     ]
    }
   ],
   "source": [
    "x1 = np.array([X.min(),X.max()])\n",
    "print(x1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "id": "3d91f56e-401e-466a-a292-6bb058c16e34",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial weight: -0.40777612, Initial bias: 0.03312457\n",
      "\n",
      "[ -0.37465155 -20.35568   ]\n"
     ]
    }
   ],
   "source": [
    "w1,b1 = model.linear.weight.item(), model.linear.bias.item()\n",
    "print(f'Initial weight: {w1:.8f}, Initial bias: {b1:.8f}')\n",
    "print()\n",
    "\n",
    "y1 = x1*w1 + b1\n",
    "print(y1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "id": "b4fcd174-60e7-405d-8073-2f0630a01079",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X.numpy(), y.numpy())\n",
    "plt.plot(x1,y1,'r')\n",
    "plt.title('Initial Model')\n",
    "plt.ylabel('y')\n",
    "plt.xlabel('x');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "id": "8f38117f-9e5a-4187-b477-6ecc7c1957b6",
   "metadata": {},
   "outputs": [],
   "source": [
    "criterion = nn.MSELoss()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "id": "e53f93f7-e2a3-478f-adb2-f0178a687e50",
   "metadata": {},
   "outputs": [],
   "source": [
    "optimizer = torch.optim.SGD(model.parameters(), lr = 0.001) # stochastic gradient descent with\n",
    "#applied learning rate (lr) of 0.001"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "id": "9675a64e-fd87-4409-81df-ebec0269ebe1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch:  1  loss: 5057.90136719  weight: -0.40777612  bias: 0.03312457\n",
      "epoch:  2  loss: 2621.83251953  weight: 3.75072598  bias: 0.15785491\n",
      "epoch:  3  loss: 1364.17724609  weight: 0.76271904  bias: 0.07025218\n",
      "epoch:  4  loss: 714.89428711  weight: 2.90958762  bias: 0.13521300\n",
      "epoch:  5  loss: 379.69201660  weight: 1.36696982  bias: 0.09055360\n",
      "epoch:  6  loss: 206.63841248  weight: 2.47530437  bias: 0.12465703\n",
      "epoch:  7  loss: 117.29640961  weight: 1.67888927  bias: 0.10216720\n",
      "epoch:  8  loss: 71.17169189  weight: 2.25106597  bias: 0.12033951\n",
      "epoch:  9  loss: 47.35845566  weight: 1.83988845  bias: 0.10929446\n",
      "epoch: 10  loss: 35.06388855  weight: 2.13526607  bias: 0.11924156\n",
      "epoch: 11  loss: 28.71597481  weight: 1.92297292  bias: 0.11410451\n",
      "epoch: 12  loss: 25.43810081  weight: 2.07544899  bias: 0.11980468\n",
      "epoch: 13  loss: 23.74520493  weight: 1.96583307  bias: 0.11771718\n",
      "epoch: 14  loss: 22.87056160  weight: 2.04453421  bias: 0.12122425\n",
      "epoch: 15  loss: 22.41835022  weight: 1.98792660  bias: 0.12071056\n",
      "epoch: 16  loss: 22.18423843  weight: 2.02854037  bias: 0.12308488\n",
      "epoch: 17  loss: 22.06271935  weight: 1.99929917  bias: 0.12338315\n",
      "epoch: 18  loss: 21.99932671  weight: 2.02025008  bias: 0.12517212\n",
      "epoch: 19  loss: 21.96594238  weight: 2.00513673  bias: 0.12588902\n",
      "epoch: 20  loss: 21.94804764  weight: 2.01593661  bias: 0.12737526\n",
      "epoch: 21  loss: 21.93815422  weight: 2.00811744  bias: 0.12830774\n",
      "epoch: 22  loss: 21.93239784  weight: 2.01367593  bias: 0.12963714\n",
      "epoch: 23  loss: 21.92876625  weight: 2.00962281  bias: 0.13068038\n",
      "epoch: 24  loss: 21.92624283  weight: 2.01247573  bias: 0.13192825\n",
      "epoch: 25  loss: 21.92428207  weight: 2.01036668  bias: 0.13302813\n",
      "epoch: 26  loss: 21.92262268  weight: 2.01182270  bias: 0.13423339\n",
      "epoch: 27  loss: 21.92111778  weight: 2.01071739  bias: 0.13536197\n",
      "epoch: 28  loss: 21.91968536  weight: 2.01145220  bias: 0.13654466\n",
      "epoch: 29  loss: 21.91829681  weight: 2.01086497  bias: 0.13768750\n",
      "epoch: 30  loss: 21.91693306  weight: 2.01122785  bias: 0.13885802\n",
      "epoch: 31  loss: 21.91557884  weight: 2.01090789  bias: 0.14000769\n",
      "epoch: 32  loss: 21.91422844  weight: 2.01107860  bias: 0.14117138\n",
      "epoch: 33  loss: 21.91289139  weight: 2.01089692  bias: 0.14232403\n",
      "epoch: 34  loss: 21.91154861  weight: 2.01096821  bias: 0.14348364\n",
      "epoch: 35  loss: 21.91020966  weight: 2.01085806  bias: 0.14463729\n",
      "epoch: 36  loss: 21.90887451  weight: 2.01087832  bias: 0.14579424\n",
      "epoch: 37  loss: 21.90753937  weight: 2.01080465  bias: 0.14694786\n",
      "epoch: 38  loss: 21.90620804  weight: 2.01079869  bias: 0.14810292\n",
      "epoch: 39  loss: 21.90487099  weight: 2.01074409  bias: 0.14925599\n",
      "epoch: 40  loss: 21.90353966  weight: 2.01072454  bias: 0.15040953\n",
      "epoch: 41  loss: 21.90221596  weight: 2.01067972  bias: 0.15156177\n",
      "epoch: 42  loss: 21.90088844  weight: 2.01065278  bias: 0.15271397\n",
      "epoch: 43  loss: 21.89955902  weight: 2.01061344  bias: 0.15386525\n",
      "epoch: 44  loss: 21.89823723  weight: 2.01058316  bias: 0.15501623\n",
      "epoch: 45  loss: 21.89691353  weight: 2.01054597  bias: 0.15616645\n",
      "epoch: 46  loss: 21.89558792  weight: 2.01051402  bias: 0.15731627\n",
      "epoch: 47  loss: 21.89426804  weight: 2.01047826  bias: 0.15846542\n",
      "epoch: 48  loss: 21.89294434  weight: 2.01044536  bias: 0.15961410\n",
      "epoch: 49  loss: 21.89162827  weight: 2.01041031  bias: 0.16076216\n",
      "epoch: 50  loss: 21.89031029  weight: 2.01037693  bias: 0.16190971\n"
     ]
    }
   ],
   "source": [
    "epochs = 50 #num passes through the dataset\n",
    "losses = []  #create data frame to store loss values\n",
    "\n",
    "for i in range(epochs):  #iterate through epochs\n",
    "    i+=1\n",
    "    y_pred = model.forward(X)   #prediction set\n",
    "    loss = criterion(y_pred, y)  #loss calculation\n",
    "    losses.append(loss.item()) #keep track of losses\n",
    "    print(f'epoch: {i:2}  loss: {loss.item():10.8f}  weight: {model.linear.weight.item():10.8f}  \\\n",
    "bias: {model.linear.bias.item():10.8f}') \n",
    "    optimizer.zero_grad()   #reset the gradient through each epoch\n",
    "    loss.backward()    #backpropagation \n",
    "    optimizer.step()   #model hyperparameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "id": "5d7e543d-4bfa-4d1c-99fb-bead0653782e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(range(epochs), losses)\n",
    "plt.ylabel('Loss')\n",
    "plt.xlabel('epoch');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "id": "ccefdf43-1b56-4e3e-8000-91bb9f9df5bf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Current weight: 2.01034236, Current bias: 0.16305667\n",
      "\n",
      "[ 1. 50.]\n",
      "[  2.173399 100.680176]\n"
     ]
    }
   ],
   "source": [
    "w1,b1 = model.linear.weight.item(), model.linear.bias.item()\n",
    "print(f'Current weight: {w1:.8f}, Current bias: {b1:.8f}')\n",
    "print()\n",
    "\n",
    "y1 = x1*w1 + b1\n",
    "print(x1)\n",
    "print(y1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "id": "4e0992c7-38a2-44b5-96ec-117a6362d12b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X.numpy(), y.numpy())\n",
    "plt.plot(x1,y1,'r')\n",
    "plt.title('Current Model')\n",
    "plt.ylabel('y')\n",
    "plt.xlabel('x');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "6712e69d-ed09-4d12-8897-39d6e0ef97ab",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
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       "   <cc:Work>\n",
       "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
       "    <dc:date>2024-06-23T18:41:51.515544</dc:date>\n",
       "    <dc:format>image/svg+xml</dc:format>\n",
       "    <dc:creator>\n",
       "     <cc:Agent>\n",
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       "     </cc:Agent>\n",
       "    </dc:creator>\n",
       "   </cc:Work>\n",
       "  </rdf:RDF>\n",
       " </metadata>\n",
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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
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     "metadata": {},
     "output_type": "display_data"
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   ],
   "source": [
    "#another dataset\n",
    "N = 50\n",
    "x = torch.randn(N,1)\n",
    "noise=0.9  #0.1-5 with 5 being low noise \n",
    "y = x + torch.randn(N,1)/noise  #with a \"noise\" level\n",
    "\n",
    "# and plot\n",
    "plt.plot(x,y,'s')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "4386a37e-c41b-4e95-b581-e18da5438f07",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.3.0.post100\n",
      "0.15.2a0\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import numpy as np\n",
    "import torchvision\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib_inline.backend_inline\n",
    "matplotlib_inline.backend_inline.set_matplotlib_formats('svg')\n",
    "print(torch.__version__)\n",
    "print(torchvision.__version__)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "fc2bbf65-f46a-4fe4-b84f-c308c97f5404",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Sequential(\n",
       "  (0): Linear(in_features=1, out_features=1, bias=True)\n",
       "  (1): ReLU()\n",
       "  (2): Linear(in_features=1, out_features=1, bias=True)\n",
       ")"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#linear regression model \n",
    "ANNregression = nn.Sequential(\n",
    "    nn.Linear(1,1),  # input layer\n",
    "    nn.ReLU(),       # activation function\n",
    "    nn.Linear(1,1)   # output layer\n",
    "    )\n",
    "ANNregression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "82d9d164-5dd0-48db-973d-9afbf158ea81",
   "metadata": {},
   "outputs": [],
   "source": [
    "# learning rate\n",
    "learningRate = .05\n",
    "\n",
    "# loss function:MSE for continuous data with a numerical prediction\n",
    "lossfun = nn.MSELoss()\n",
    "\n",
    "# optimizer, stochastic gradient descent \n",
    "optimizer = torch.optim.SGD(ANNregression.parameters(),lr=learningRate)\n",
    "\n",
    "#then perform the forward pass, compute the loss, backpropagate the gradients, \n",
    "#and update the model parameters using the optimizer in each epoch."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "18dd07f0-478e-45fd-9b2b-ddc8f5d3cb3c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# train the model\n",
    "numepochs = 500\n",
    "losses = torch.zeros(numepochs)\n",
    "\n",
    "## Train the model!\n",
    "for epochi in range(numepochs):\n",
    "\n",
    "  # forward pass\n",
    "  yHat = ANNregression(x)\n",
    "\n",
    "  # compute loss\n",
    "  loss = lossfun(yHat,y)\n",
    "  losses[epochi] = loss\n",
    "\n",
    "  # backprop\n",
    "  optimizer.zero_grad()\n",
    "  loss.backward()\n",
    "  optimizer.step()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "aa5bcd2b-c6eb-40a1-9882-171a60ba5ff9",
   "metadata": {},
   "outputs": [
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    "# manually compute losses\n",
    "# final forward pass\n",
    "predictions = ANNregression(x)\n",
    "\n",
    "# final loss (MSE)\n",
    "testloss = (predictions-y).pow(2).mean()\n",
    "\n",
    "plt.plot(losses.detach(),'o',markerfacecolor='w',linewidth=.1)\n",
    "plt.plot(numepochs,testloss.detach(),'ro')\n",
    "plt.xlabel('Epoch')\n",
    "plt.ylabel('Loss')\n",
    "plt.title('Final loss = %g' %testloss.item())\n",
    "plt.show()"
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  {
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   "execution_count": null,
   "id": "7e24bcbb-43c6-491e-a674-9c4bb81b7ffb",
   "metadata": {},
   "outputs": [],
   "source": [
    "testloss.item()"
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  {
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   "execution_count": null,
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   "metadata": {},
   "outputs": [],
   "source": [
    "# plot the data\n",
    "plt.plot(x,y,'bo',label='Real data')\n",
    "plt.plot(x,predictions.detach(),'rs',label='Predictions')\n",
    "plt.title(f'prediction-data r={np.corrcoef(y.T,predictions.detach().T)[0,1]:.2f}')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
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  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "dcd27179-23e1-4b14-b6c8-2a5f26f0b169",
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   "outputs": [],
   "source": [
    "#training function that outputs final predictions and losses \n",
    "def linmodel(x,y): \n",
    "    ANNregression = nn.Sequential(\n",
    "    nn.Linear(1,1),  # input layer\n",
    "    nn.ReLU(),       # activation function\n",
    "    nn.Linear(1,1)   # output layer\n",
    "    )\n",
    "    # learning rate\n",
    "    learningRate = .05\n",
    "    numepochs = 500\n",
    "    # loss function:MSE for continuous data with a numerical prediction\n",
    "    lossfun = nn.MSELoss()\n",
    "    \n",
    "    # optimizer, stochastic gradient descent \n",
    "    optimizer = torch.optim.SGD(ANNregression.parameters(),lr=learningRate)\n",
    "    losses = torch.zeros(numepochs)\n",
    "    \n",
    "    for epochs in range(numepochs):\n",
    "\n",
    "          # forward pass\n",
    "          yHat = ANNregression(x)\n",
    "        \n",
    "          # compute loss\n",
    "          loss = lossfun(yHat,y)\n",
    "          losses[epochs] = loss;\n",
    "        \n",
    "          # backprop\n",
    "          optimizer.zero_grad()\n",
    "          loss.backward()\n",
    "          optimizer.step()\n",
    "    ypred = ANNregression(x)\n",
    "\n",
    "# final loss (MSE)\n",
    "    testloss = (ypred-y).pow(2).mean();\n",
    "    \n",
    "    plt.plot(losses.detach(),'o',markerfacecolor='w',linewidth=.1)  #detach creates copy without gradient \n",
    "    plt.plot(numepochs,testloss.detach(),'ro')\n",
    "    plt.xlabel('Epoch')\n",
    "    plt.ylabel('Loss')\n",
    "    plt.title('Final loss = %g' %testloss.item())\n",
    "    plt.show()\n",
    "    \n",
    "    return ypred,lossfun"
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   "execution_count": 29,
   "id": "e17ac381-3c05-4773-b166-de3e309f05bb",
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   "source": [
    "#function to generate model data\n",
    "def modeldata(npoints,noise):\n",
    "    x=torch.randn(npoints,1);\n",
    "    y=x + torch.randn(npoints,1)/noise;\n",
    "    plt.plot(x,y,'s')\n",
    "    plt.show()\n",
    "    return x,y;"
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   "cell_type": "code",
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      "text/plain": [
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   ],
   "source": [
    "npoints,noise= modeldata(50,1)"
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  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "03f25568-8e51-4204-bd1a-0f17e36ca035",
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      "text/plain": [
       "<Figure size 1200x400 with 2 Axes>"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ypred,lossfun= linmodel(x,y)\n",
    "yhat = ypred.detach()\n",
    "fig,ax = plt.subplots(1,2,figsize=(12,4))\n",
    "\n",
    "ax[0].plot(losses.detach(),'o',markerfacecolor='w',linewidth=.1)\n",
    "ax[0].set_xlabel('Epoch')\n",
    "ax[0].set_title('Loss')\n",
    "\n",
    "ax[1].plot(x,y,'bo',label='Real data')\n",
    "ax[1].plot(x,yhat,'rs',label='Predictions')\n",
    "ax[1].set_xlabel('x')\n",
    "ax[1].set_ylabel('y')\n",
    "#Computes corr coeff between y and yhat, t transposes y and yhat  \n",
    "#bc np.corrcoef expects rows as variables and columns as observations\n",
    "ax[1].set_title(f'prediction-data corr = {np.corrcoef(y.T,yhat.T)[0,1]:.2f}')\n",
    "ax[1].legend()\n",
    "\n",
    "plt.show()"
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
   "id": "20bc1a32-5826-42b6-be50-3b11e82ab748",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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