update day 1

labs/notebooks/basic_tutorials/Exercises_0.10_to_0.15.ipynb

@@ -256,88 +256,6 @@
    "metadata": {},
    "source": [
     "# Exercise 0.13 \n",
-    "1) Consider the function $f(x) = (x + 2)^2 − 16 \\text{exp}(−(x − 2)^2)$. Draw a plot around the $x \\in [−8, 8]$ region."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "x = np.arange(-8,8,0.001)\n",
-    "y = list(map(lambda u: get_y(u),x))\n",
-    "plt.plot(x,y)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "2)  What is $\\frac{\\partial f}{\\partial x}$?\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "3) Use gradient descent to find a local minimum starting from $x0 = −4$ and $x0 = +4$, with $η = .01$. Plot all of the intermediate estimates that you obtain in the same plot."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "X = np.linspace(-8, 8, 1000)\n",
-    "Y = (X+2)**2 - 16*np.exp(-((X-2)**2))\n",
-    "\n",
-    "# derivative of the function f\n",
-    "def get_Y_dev(x):\n",
-    "    return (2*x+4)-16*(-2*x + 4)*np.exp(-((x-2)**2))\n",
-    "\n",
-    "def grad_desc(start_x, eps, prec):\n",
-    "    '''\n",
-    "    runs the gradient descent algorithm and returns the list of estimates\n",
-    "    example of use grad_desc(start_x=3.9, eps=0.01, prec=0.00001)\n",
-    "    '''\n",
-    "    x_new = start_x\n",
-    "    x_old = start_x + prec * 2\n",
-    "    res = [x_new]\n",
-    "    while abs(x_old-x_new) > prec:\n",
-    "        x_old = x_new\n",
-    "        x_new = x_old - eps * get_Y_dev(x_new)\n",
-    "        res.append(x_new)\n",
-    "    return np.array(res)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "res = grad_desc(4, 0.01, 0.00001)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "x = np.arange(-8,8,0.001)\n",
-    "y = list(map(lambda u: get_y(u),x))\n",
-    "plt.plot(x,y)\n",
-    "plt.plot(res, (res+2)**2 - 16*np.exp(-((res-2)**2)), '+')"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Exercise 0.14 \n",
     "Consider the linear regression problem (ordinary least squares) on the Galton dataset, with a single response\n",
     "variable\n",
     "\n",