Update README

notebooks/NATS-Bench/BayesOpt.ipynb

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+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "german-madonna",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Implementation for \"A Tutorial on Bayesian Optimization\"\n",
+    "import numpy as np\n",
+    "\n",
+    "def get_data():\n",
+    "    return np.random.random(2) * 10\n",
+    "\n",
+    "def f(x):\n",
+    "    return float(np.power((x[0] * 3 - x[1]), 3) - np.exp(x[1]) + np.power(x[0], 2))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "id": "broke-citizenship",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Kernels typically have the property that points closer in the input space are more strongly correlated\n",
+    "# i.e., if |x1 - x2| < |x1 - x3|, then sigma(x1, x2) > sigma(x1, x3).\n",
+    "# the commonly used and simple kernel is the power exponential or Gaussian kernel:\n",
+    "def sigma0(x1, x2, alpha0=1, alpha=[1,1]):\n",
+    "    \"\"\"alpha could be a vector\"\"\"\n",
+    "    power = np.array(alpha, dtype=np.float32) * np.power(np.array(x1)-np.array(x2), 2)\n",
+    "    return alpha0 * np.exp( -np.sum(power) )\n",
+    "\n",
+    "# the most common choice for the mean function is a constant value\n",
+    "def mu0(x, mu):\n",
+    "    return mu"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "id": "aerial-carnival",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "K = 5\n",
+    "X = np.array([get_data() for i in range(K)])\n",
+    "mu = np.mean(X, axis=0)\n",
+    "mu0_over_K = [mu0(x, mu) for x in X]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "id": "polished-discussion",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sigma0_over_KK = []\n",
+    "for i in range(K):\n",
+    "    sigma0_over_KK.append(np.array([sigma0(X[i], X[j]) for j in range(K)]))\n",
+    "sigma0_over_KK = np.array(sigma0_over_KK)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "id": "comic-jesus",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(20, 20)\n",
+      "1.1038803861344952e-06\n",
+      "1.1038803861344952e-06\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(sigma0_over_KK.shape)\n",
+    "print(sigma0_over_KK[1][2])\n",
+    "print(sigma0_over_KK[2][1])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "statistical-wrist",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "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": "3.8.8"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}