Skip to content

Instantly share code, notes, and snippets.

@psambit9791
Created December 17, 2019 13:31
Show Gist options
  • Star 0 You must be signed in to star a gist
  • Fork 1 You must be signed in to fork a gist
  • Save psambit9791/c803e601ed93c6782122ed84757f79b9 to your computer and use it in GitHub Desktop.
Save psambit9791/c803e601ed93c6782122ed84757f79b9 to your computer and use it in GitHub Desktop.
Visualisation of 1D & 2D Error Manifolds for a Single Training Data Point
Display the source blob
Display the rendered blob
Raw
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Importing Libraries and Setting up variables"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from mpl_toolkits.mplot3d import Axes3D"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this example, we aim to show what the error manifold looks like.\n",
"The error manifold can be considered the shape the error value makes with espect to the weights\n",
"\n",
"For this example, we use only one data against which we are plotting values.\n",
"We have a list of weights (slopes and intercepts) each of which we apply on the simple equation of a straight line:\n",
"\n",
"\\begin{align*}\n",
"y = mx+c\n",
"\\end{align*}\n",
"\n",
"The 'm' values are selected from the <b>slopes</b> array and 'c' values are selected from the <b>intercepts</b> array."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##### Weight Space"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"slopes = [-4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6]\n",
"intercepts = [-4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##### Feature Space"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"X = 1\n",
"Y = 4"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### 1 dimensional error manifold"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"List of errors for different m values: [ 9 4 1 0 1 4 9 16 25 36 49]\n",
"Minima is at index: -1\n"
]
}
],
"source": [
"error_list = []\n",
"\n",
"for m in slopes:\n",
" error_list.append((Y - (m*X+5))**2)\n",
"error_list = np.array(error_list)\n",
"print(\"List of errors for different m values: \", error_list)\n",
"\n",
"index = np.where(error_list==0)[0][0]\n",
"index = slopes[index]\n",
"print(\"Minima is at index: \", index)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We use only the 'slopes' array here while keeping the intercept at a constant of 5.\n",
"If you observe the graph underneath, you will see that the error value reduces to 0 when the weight value is 2.\n",
"This can also be computed by taking the minima as:\n",
"\n",
"\\begin{align*}\n",
" \\frac{de}{dw} = 0\n",
"\\end{align*}"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 504x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"\n",
"fig = plt.figure(figsize=(7, 5))\n",
"plt.plot(slopes, error_list)\n",
"plt.scatter(index, 0, marker='x', color='black', s=120)\n",
"plt.title(\"Error Manifold 1D\", fontsize=18)\n",
"plt.xlabel('Weights (w)', fontsize=12)\n",
"plt.ylabel('Squared Error (e)', fontsize=12)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### 2 dimensional error manifold"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[[144 121 100 81 64 49 36 25 16 9 4]\n",
" [121 100 81 64 49 36 25 16 9 4 1]\n",
" [100 81 64 49 36 25 16 9 4 1 0]\n",
" [ 81 64 49 36 25 16 9 4 1 0 1]\n",
" [ 64 49 36 25 16 9 4 1 0 1 4]\n",
" [ 49 36 25 16 9 4 1 0 1 4 9]\n",
" [ 36 25 16 9 4 1 0 1 4 9 16]\n",
" [ 25 16 9 4 1 0 1 4 9 16 25]\n",
" [ 16 9 4 1 0 1 4 9 16 25 36]\n",
" [ 9 4 1 0 1 4 9 16 25 36 49]\n",
" [ 4 1 0 1 4 9 16 25 36 49 64]]\n"
]
}
],
"source": [
"error_matrix = []\n",
"iterator = -1\n",
"for c in intercepts:\n",
" error_matrix.append([])\n",
" iterator += 1\n",
" for m in slopes:\n",
" error_matrix[iterator].append((Y - (m*X+c))**2)\n",
"\n",
"error_matrix = np.array(error_matrix)\n",
"print(error_matrix)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We use both the 'slopes' array and the 'intercepts' array for the 2D example.\n",
"As can be observed in the graph underneath, in this case, we have minima for a set of values:\n",
"\n",
"- m=6, c=-2\n",
"- m=5, c=-1\n",
"- m=4, c=0\n",
"- m=3, c=1\n",
"- m=2, c=2\n",
"- m=1, c=3\n",
"- m=0, c=4\n",
"- m=-1, c=5\n",
"- m=-2, c=6"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 504x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"X = np.array(slopes)\n",
"Y = np.array(intercepts)\n",
"Z = error_matrix\n",
"\n",
"fig = plt.figure(figsize=(7, 5))\n",
"ax = plt.axes(projection='3d')\n",
"ax.contour3D(X, Y, Z, 1200, cmap='viridis')\n",
"ax.title.set_fontsize(16)\n",
"ax.title.set_text(\"Error Manifold 2D\")\n",
"ax.set_xlabel('intercept', fontsize=12)\n",
"ax.set_ylabel('slope', fontsize=12)\n",
"ax.set_zlabel('squared error', fontsize=12);\n",
"plt.show()"
]
}
],
"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": "3.6.9"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment