05_1_gradientdescent_manually.ipynb

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   "source": [
    "import numpy as np\n",
    "import icecream as ic"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "Compute every step manually"
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    "Linear regression\n",
    "f = w * x"
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     "text": [
      "[1. 2. 3. 4.]\n",
      "[2. 4. 6. 8.]\n"
     ]
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   "source": [
    "# here : f = 2 * x\n",
    "X = np.array([1, 2, 3, 4], dtype=np.float32)\n",
    "Y = np.array([2, 4, 6, 8], dtype=np.float32)\n",
    "print(X)\n",
    "print(Y)"
   ]
  },
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   "source": [
    "w = 0.0"
   ]
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   "source": [
    "# model output\n",
    "def forward(x):\n",
    "    return w * x"
   ]
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   "id": "14b6f056",
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   "source": [
    "# loss = MSE\n",
    "def loss(y, y_pred):\n",
    "    return ((y_pred - y) ** 2).mean()"
   ]
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   "source": [
    "# J = MSE = 1/N * (w*x - y)**2\n",
    "# dJ/dw = 1/N * 2x(w*x - y)\n",
    "def gradient(x, y, y_pred):\n",
    "    return np.mean(2 * x * (y_pred - y))"
   ]
  },
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   "execution_count": 9,
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   "outputs": [
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     "name": "stdout",
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     "text": [
      "Prediction before training: f(5) = 0.000\n"
     ]
    }
   ],
   "source": [
    "print(f\"Prediction before training: f(5) = {forward(5):.3f}\")"
   ]
  },
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   "cell_type": "code",
   "execution_count": 10,
   "id": "033762a6",
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   "outputs": [],
   "source": [
    "# Training\n",
    "learning_rate = 0.01\n",
    "n_iters = 20"
   ]
  },
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   "cell_type": "code",
   "execution_count": 11,
   "id": "61b1867a",
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     "text": [
      "epoch 1: w = 0.300, loss = 30.00000000\n",
      "epoch 3: w = 0.772, loss = 15.66018677\n",
      "epoch 5: w = 1.113, loss = 8.17471600\n",
      "epoch 7: w = 1.359, loss = 4.26725292\n",
      "epoch 9: w = 1.537, loss = 2.22753215\n",
      "epoch 11: w = 1.665, loss = 1.16278565\n",
      "epoch 13: w = 1.758, loss = 0.60698175\n",
      "epoch 15: w = 1.825, loss = 0.31684822\n",
      "epoch 17: w = 1.874, loss = 0.16539653\n",
      "epoch 19: w = 1.909, loss = 0.08633806\n"
     ]
    }
   ],
   "source": [
    "for epoch in range(n_iters):\n",
    "    # predict = forward pass\n",
    "    y_pred = forward(X)\n",
    "\n",
    "    # loss\n",
    "    l = loss(Y, y_pred)\n",
    "\n",
    "    # calculate gradients\n",
    "    dw = gradient(X, Y, y_pred)\n",
    "\n",
    "    # update weights\n",
    "    w -= learning_rate * dw\n",
    "\n",
    "    if epoch % 2 == 0:\n",
    "        print(f\"epoch {epoch+1}: w = {w:.3f}, loss = {l:.8f}\")"
   ]
  },
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     "name": "stdout",
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     "text": [
      "Prediction after training: f(5) = 9.612\n"
     ]
    }
   ],
   "source": [
    "print(f\"Prediction after training: f(5) = {forward(5):.3f}\")"
   ]
  }
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