{
"cells": [
{
"cell_type": "markdown",
"id": "20fce00f",
"metadata": {},
"source": [
"### Machine Learning\n",
"#### Maximum likelihood estimation (MLE) for multivariate normal (Gaussian) distirbution\n",
"Having a sample of $n$ i.i.d. (independent and identically distributed) random vectors from a multivariate normal distribution $N(\\boldsymbol{\\mu},\\Sigma)$, we can estimate its parameters $\\boldsymbol{\\mu}$ and $\\Sigma$ by the **MLE** method. The details are given in the **Pinterest** page mentioned below. In summary, we can estimate the mean vector $\\boldsymbol{\\mu}$ and coviarance matrix $\\Sigma$ by:\n",
" \n",
" $\\boldsymbol{\\mu}=\\frac{1}{n}\\sum_{i=1}^{n}\\boldsymbol{x}_i$\n",
" $\\Sigma=\\frac{1}{n}\\sum_{i=1}^{n}(\\boldsymbol{x}_i-\\boldsymbol{\\mu})(\\boldsymbol{x}_i-\\boldsymbol{\\mu})^T$\n",
" \n",
" In the following, we state an example of the MLE for estimating the parameters of the normal distribution from the given samples. Also, we display the ellipse of the estimated convariance matrix along with the samples.\n",
" \n",
" https://github.com/ostad-ai/Machine-Learning\n",
" Explanation: https://www.pinterest.com/HamedShahHosseini/Machine-Learning/background-knowledge"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "84c6d039",
"metadata": {},
"outputs": [],
"source": [
"# importing the required modules\n",
"from matplotlib import pyplot as plt\n",
"import numpy as np\n",
"from numpy.linalg import eig"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "74ae0061",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The real mean vector of samples: [1, 2]\n",
"The estimated mean vector of samples: [0.97276985 2.02631888]\n",
"-----------------\n",
"The real covariance matrix of samples:\n",
" [[2, 2], [2, 7]]\n",
"The estimated covariance matrix of samples:\n",
" [[1.8317566478731837, 1.830567701477496], [1.830567701477496, 6.497817868585885]]\n"
]
}
],
"source": [
"# example\n",
"# parameters of multivariate normal\n",
"mean,sigma,n=[1,2],[[2,2],[2,7]],1000\n",
"# n sampels taken from the normal distribution\n",
"xs=np.random.multivariate_normal(mean,sigma,n)\n",
"# lets estimate the parameters by the MLE formulae\n",
"mean_hat=1/n*np.sum(xs,axis=0)\n",
"sigma_hat=1/n*((xs-mean_hat).T@(xs-mean_hat))\n",
"print(f'The real mean vector of samples: {mean}')\n",
"print(f'The estimated mean vector of samples: {mean_hat}')\n",
"print('-----------------')\n",
"print(f'The real covariance matrix of samples:\\n {sigma}')\n",
"print(f'The estimated covariance matrix of samples:\\n {sigma_hat.tolist()}')"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "b82ca68c",
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# showing the samples along the ellipse of the estimated covariance amtrix\n",
"ts = np.linspace(0, 2*np.pi, 100);\n",
"eigvals,eigvecs=eig(sigma_hat)\n",
"points = (np.sqrt(eigvals[np.newaxis,:]) * eigvecs) @ [np.cos(ts), np.sin(ts)]\n",
"plt.plot(mean_hat[0]+points[0], mean_hat[1]+points[1],c='blue')\n",
"plt.plot(xs[:,0],xs[:,1],'.',alpha=.2,c='orange')\n",
"plt.title('Samples are the orange dots. The ellipse of the estimated covariance matrix is in blue')\n",
"plt.axis('equal')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "194d60cb",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"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": "3.11.1"
}
},
"nbformat": 4,
"nbformat_minor": 5
}