Simple Linear Regression with Gradient Descent from Scratch

LinearRegression.ipynb

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    "def cost_function(Y, b, w, X):\n",
    "    m = len(Y)\n",
    "    sse = 0\n",
    "    for i in range(0, m):\n",
    "        y_hat = b + w * X[i]\n",
    "        y = Y[i]\n",
    "        sse += (y_hat - y) ** 2\n",
    "        \n",
    "    mse = sse / m\n",
    "    return mse"
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    "def update_weights(Y, b, w, X, learning_rate):\n",
    "    m = len(Y)\n",
    "    \n",
    "    b_deriv_sum = 0\n",
    "    w_deriv_sum = 0\n",
    "    \n",
    "    for i in range(0, m):\n",
    "        y_hat = b + w * X[i] \n",
    "        y = Y[i]\n",
    "        b_deriv_sum = (y_hat - y)\n",
    "        w_deriv_sum = (y_hat - y) * X[i]\n",
    "        \n",
    "    new_b = b - (learning_rate * 1 / m * b_deriv_sum)\n",
    "    new_w = w - (learning_rate * 1 / m * w_deriv_sum)\n",
    "    return new_b, new_w"
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   "source": [
    "def train(Y, initial_b, initial_w, X, learning_rate, num_iters):\n",
    "    print(\"Starting gradient descent at b = {0}, w = {1}, mse = {2}\".format(Y, initial_b, initial_w, X))\n",
    "    \n",
    "    \n",
    "    b = initial_b\n",
    "    w = initial_w\n",
    "    cost_history = []\n",
    "    for i in range(num_iters):\n",
    "        b, w = update_weights(Y, b, w, X, learning_rate)\n",
    "        mse = cost_function(Y, b, w, X)\n",
    "        cost_history.append(mse)\n",
    "        \n",
    "        if i%100 ==0:\n",
    "            print(\"iter={:d}   b={:.2f}   w={:.4f}   \".format(i, b, w, mse))\n",
    "            \n",
    "    print(\"after {0} iterations b = {1}, w = {2}, mse = {3}\".format(num_iters, b, w, cost_function(Y, b, w, X)))\n",
    "    return cost_history, b, w"
   ]
  }
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