update bayesian optimization wip
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ritchie46 committed
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1 file changed
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@@ -2,7 +2,7 @@
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 336,
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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@@ -58,27 +58,49 @@
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" 0, & \\text{otherwise}\n",
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"\\end{cases}$$\n",
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"\n",
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"$$\\text{EI}(x) = (\\delta) \\Phi(Z) + \\sigma \\phi(Z)$$\n",
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"$$\\text{EI}(x) = (\\delta) \\Phi(Z) + \\sigma(x^*) \\phi(Z)$$\n",
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"\n",
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"Recommendation value for $\\xi = 0.01$. \n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 391,
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"execution_count": 5,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Randomly selected hyper parameters: {'x': 9.545454545454545}\n"
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]
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}
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],
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"outputs": [],
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"source": [
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"\n",
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"def select_hyperparams_random(param_ranges):\n",
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" \"\"\"\n",
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" Select hyperparameters at random.\n",
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" \n",
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" Parameters\n",
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" ----------\n",
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" param_ranges : dict\n",
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" Named parameter ranges.\n",
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"\n",
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" Example:\n",
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" \n",
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" {\n",
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" 'foo': {\n",
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" 'range': [1, 10],\n",
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" 'type': 'float'\n",
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" }\n",
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" 'bar': {\n",
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" 'range': [10, 1000],\n",
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" 'type': 'int'\n",
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" }\n",
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" }\n",
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"\n",
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" Returns\n",
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" -------\n",
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" selection : dict\n",
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" Randomly selected hyperparameters within given boundaries.\n",
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" \n",
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" Example:\n",
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" {'foo': 4.213, 'bar': 935}\n",
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"\n",
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" \"\"\"\n",
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" selection = {}\n",
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" for k in param_ranges:\n",
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" val = np.random.choice(\n",
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@@ -101,17 +123,14 @@
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"\n",
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" f : GP predict function\n",
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" y_current : float\n",
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" Current best score\n",
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" Current best evaluation f(x+)\n",
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" x_proposed : np.array\n",
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" Proposal parameters. Shape: (1, 1)\n",
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" xi : float\n",
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" Exploration parameter\n",
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"\n",
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" Returns\n",
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" -------\n",
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" expected_improvement : float\n",
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" E(max(f_proposed - f_current), 0)\n",
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" \n",
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" \"\"\"\n",
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" mu, var = f(x_proposed)\n",
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" std = var ** 0.5\n",
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@@ -122,25 +141,49 @@
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" z = delta / std\n",
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" unit_norm = stats.norm()\n",
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" return delta * unit_norm.cdf(z) + std * unit_norm.pdf(z)\n",
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"\n",
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"\n",
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"\n",
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"hp = select_hyperparams_random(param_ranges)\n",
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"print('Randomly selected hyper parameters:', hp)\n"
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"\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 401,
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"execution_count": 18,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"{'foo': 4.545454545454545, 'bar': 580}"
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]
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},
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"execution_count": 18,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"param_ranges = {\n",
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" 'foo': {\n",
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" 'range': [1, 10],\n",
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" 'type': 'float'\n",
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" },\n",
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" 'bar': {\n",
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" 'range': [10, 1000],\n",
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" 'type': 'int'\n",
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" }\n",
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"}\n",
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"\n",
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"select_hyperparams_random(param_ranges)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 263,
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"metadata": {},
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"outputs": [],
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"source": [
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"class BayesOpt:\n",
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" def __init__(self, \n",
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" param_ranges, \n",
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" f, \n",
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" random_trials=5, \n",
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" optimization_trials=30,\n",
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" def __init__(\n",
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" self, param_ranges, f, random_trials=5, optimization_trials=20, kernel=None\n",
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" ):\n",
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" \"\"\"\n",
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" Parameters\n",
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@@ -148,6 +191,15 @@
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"\n",
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" param_ranges : dict\n",
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" f : function\n",
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" black box function to evaluate\n",
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" random_trials : int\n",
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" Number of random trials to run before optimization starts\n",
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" optimization_trials : int\n",
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" Number of optimization trials to run.\n",
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" Together with the random_trials this is the total budget\n",
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" kernel: GPy.kern.src.kern.Kern\n",
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" GPy kernel for the Gaussian Process.\n",
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" If None given, RBF kernel is used\n",
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" \"\"\"\n",
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" self.param_ranges = param_ranges\n",
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" self.f = f\n",
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@@ -156,14 +208,25 @@
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" self.n_trials = random_trials + optimization_trials\n",
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" self.x = np.zeros((self.n_trials, len(param_ranges)))\n",
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" self.y = np.zeros((self.n_trials, 1))\n",
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" self.kernel = GPy.kern.RBF(input_dim=self.x.shape[1], \n",
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" variance=1,\n",
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" lengthscale=1) \n",
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"\n",
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" if kernel is None:\n",
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" self.kernel = GPy.kern.RBF(\n",
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" input_dim=self.x.shape[1], variance=1, lengthscale=1\n",
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" )\n",
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" else:\n",
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" self.kernel = kernel\n",
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" self.gp = None\n",
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" self.bounds = np.array([pr['range'] for pr in param_ranges.values()])\n",
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" self.bounds = np.array([pr[\"range\"] for pr in param_ranges.values()])\n",
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"\n",
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" @property\n",
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" def best_params(self):\n",
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" \"\"\"\n",
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" Select best parameters.\n",
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"\n",
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" Returns\n",
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" -------\n",
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" best_parameters : dict\n",
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" \"\"\"\n",
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" return self._prepare_kwargs(self.x[self.y.argmax()])\n",
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"\n",
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" def fit(self):\n",
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@@ -171,75 +234,129 @@
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" self._bayesian_search()\n",
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"\n",
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" def _random_search(self):\n",
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" print(f'Starting {self.random_trials} random trials...')\n",
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" \"\"\"\n",
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" Run the random trials budget\n",
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" \"\"\"\n",
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" print(f\"Starting {self.random_trials} random trials...\")\n",
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" for i in tqdm(range(self.random_trials)):\n",
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" hp = select_hyperparams_random(self.param_ranges)\n",
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" self.x[i] = np.array(list(hp.values()))\n",
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" self.y[i] = evaluate_params(hp)\n",
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" self.y[i] = self.f(hp)\n",
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"\n",
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" def _bayesian_search(self):\n",
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" print(f'Starting {self.optimization_trials} optimization trials...')\n",
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" for i in tqdm(range(self.random_trials, \n",
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" self.random_trials + self.optimization_trials)):\n",
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" \"\"\"\n",
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" Run the Bayesian Optimization budget\n",
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" \"\"\"\n",
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" print(f\"Starting {self.optimization_trials} optimization trials...\")\n",
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" for i in tqdm(\n",
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" range(self.random_trials, self.random_trials + self.optimization_trials)\n",
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" ):\n",
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" self.x[i], self.y[i] = self._single_iter()\n",
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"\n",
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" def _single_iter(self):\n",
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" def _single_iter(self, x=None):\n",
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" \"\"\"\n",
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" Fit a GP and retrieve and evaluate a new\n",
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" parameter proposal.\n",
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"\n",
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" Returns\n",
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" -------\n",
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" out : tuple[np.array[flt], np.array[flt]]\n",
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" (x, f(x))\n",
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"\n",
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" \"\"\"\n",
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" self._fit_gp()\n",
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" if x is None:\n",
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" x = self._new_proposal()\n",
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" y = evaluate_params(self._prepare_kwargs(x))\n",
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" y = self.f(self._prepare_kwargs(x))\n",
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" return x, y\n",
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"\n",
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" \n",
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" def _fit_gp(self, noise_var=0):\n",
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" \"\"\"\n",
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" Fit a GP on the currently observed data points.\n",
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"\n",
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" Parameters\n",
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" ----------\n",
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" noise_var : flt\n",
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" GPY argmument noise_var\n",
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" \"\"\"\n",
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" mask = self.x.sum(axis=1) != 0\n",
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" self.gp = GPy.models.GPRegression(bo.x[mask], \n",
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" bo.y[mask], \n",
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" self.gp = GPy.models.GPRegression(\n",
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" self.x[mask],\n",
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" self.y[mask],\n",
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" normalizer=True,\n",
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" kernel=self.kernel,\n",
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" noise_var=noise_var)\n",
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" noise_var=noise_var,\n",
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" )\n",
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" self.gp.optimize()\n",
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"\n",
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" def _new_proposal(self, n=25):\n",
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" \"\"\"\n",
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" Get a new parameter proposal by maximizing\n",
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" the acquisition function.\n",
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"\n",
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" Parameters\n",
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" ----------\n",
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" n : int\n",
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" Number of retries.\n",
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" Each new retry the optimization is\n",
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" started in another parameter location.\n",
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" This improves the chance of finding a global optimum.\n",
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"\n",
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" Returns\n",
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" -------\n",
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" proposal : dict\n",
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" Example:\n",
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" {'foo': 4.213, 'bar': 935}\n",
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" \"\"\"\n",
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"\n",
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" def f(x):\n",
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" return -expected_improvement(\n",
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" f=self.gp.predict,\n",
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" y_current=self.y.max(),\n",
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" x_proposed=x[None, :]\n",
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" f=self.gp.predict, y_current=self.y.max(), x_proposed=x[None, :]\n",
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" )\n",
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"\n",
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" x0 = np.random.uniform(\n",
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" low=self.bounds[:, 0],\n",
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" high=self.bounds[:, 1],\n",
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" size=(n, self.x.shape[1])\n",
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" low=self.bounds[:, 0], high=self.bounds[:, 1], size=(n, self.x.shape[1])\n",
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" )\n",
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" proposal = None\n",
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" best_ei = np.inf\n",
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" for x0_ in x0:\n",
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" res = optimize.minimize(f, \n",
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" x0_, \n",
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" bounds=self.bounds)\n",
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" res = optimize.minimize(f, x0_, bounds=self.bounds)\n",
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" if res.success and res.fun < best_ei:\n",
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" best_ei = res.fun\n",
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" proposal = res.x\n",
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" if np.isnan(res.fun):\n",
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" raise ValueError('NaN within bounds')\n",
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" raise ValueError(\"NaN within bounds\")\n",
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" return proposal\n",
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"\n",
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" def _prepare_kwargs(self, x):\n",
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" \"\"\"\n",
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" Create a dictionary with named parameters\n",
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" and the proper python types.\n",
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"\n",
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" Parameters\n",
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" ----------\n",
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" x : np.array\n",
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" Example:\n",
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" [4.213, 935.03]\n",
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"\n",
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" Returns\n",
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" -------\n",
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" hyperparameters : dict\n",
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"\n",
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" Example:\n",
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" {'foo': 4.213, 'bar': 935}\n",
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" \"\"\"\n",
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" # create hyper parameter dict\n",
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" hp = dict(zip(self.param_ranges.keys(), x))\n",
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" # cast values\n",
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" for k in self.param_ranges:\n",
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" if self.param_ranges[k]['type'] == 'int':\n",
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" if self.param_ranges[k][\"type\"] == \"int\":\n",
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" hp[k] = int(hp[k])\n",
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" elif self.param_ranges[k]['type'] == 'float':\n",
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" elif self.param_ranges[k][\"type\"] == \"float\":\n",
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" hp[k] = float(hp[k])\n",
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" else:\n",
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" raise ValueError('Parameter type not known')\n",
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" return hp\n",
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"\n",
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" \n",
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"bo = BayesOpt(param_ranges, evaluate_params)\n",
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"# bo.fit()"
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" raise ValueError(\"Parameter type not known\")\n",
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" return hp"
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]
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},
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{
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@@ -251,12 +368,22 @@
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},
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{
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"cell_type": "code",
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"execution_count": 402,
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"execution_count": 284,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"[<matplotlib.lines.Line2D at 0x7f9ef1f369b0>]"
|
||||
]
|
||||
},
|
||||
"execution_count": 284,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": "iVBORw0KGgoAAAANSUhEUgAAA7MAAAEXCAYAAAB/DBO+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvnQurowAAIABJREFUeJzs3Xd4lFXi9vHvSSchpIcAIbTQO4SOYBdUsCsWBEEB+7prWd3VXV1XXd1iARVUELAiggUVC1U6obdAQuiQBiSkkH7ePxL3Zf2pBEjmmUnuz3VxZWbyPDP3KCX3nPOcY6y1iIiIiIiIiHgSL6cDiIiIiIiIiJwplVkRERERERHxOCqzIiIiIiIi4nFUZkVERERERMTjqMyKiIiIiIiIx1GZFREREREREY+jMisiIiIiIiIeR2VWRETkFMaYvcaYi53OURXGmLbGmA3GmFxjzAMufu1txpjza+i5o4wx3xtjjhtj3qmJ1xAREc/n43QAERGRqjLGLAa6AjHW2iKH47iDR4HF1truNfkixpi9wJ3W2h9+esxa27EGX/JxINlae0kNvoaIiHg4jcyKiIhHMMY0B84DLDDc0TDuoxmwzekQNeBi4BOnQ4iIiHtTmRUREU9xO7AKeBcY9VsHGmOsMSb+lPvvGmOerby91xjzsDFmszEmxxjzsTEm4Feep50xZo8xZsTpzjXGtDfGLDbGZFdOwR1+yvPcYYz58pT7KcaYWafcP2CM6XaG2RYCFwATjTF5xpg2v/W+q5C/qTFmjjEm0xhz1BgzsfLxmUAc8GXl6zx6ynNdXIX3fibvyc8YkwN0rny9Lb90nIiICKjMioiI57gdeL/y12XGmIbn8Fw3AkOAFkAXYPTPDzDG9AC+A+631n70W+caY3yBLyuPjwbuB943xrStPGcJcJ4xxssY0wjwBQZUvk5LoD6wuarZAKy1FwI/AvdZa+tba3ed7Xs3xngD84B9QHOgCfBR5euMBPYDwypf58Wf/Xc63Xs/k/dUDPQDMipfq3MV35OIiNRBKrMiIuL2jDEDqZhSO8tauw7YDdxyDk/5qrX2sLX2GBVFrNvPvn8e8AUwylo7rwrn9qWikL5grS221i6kohzeDGCtTQVyK48dDHwLHDLGtKu8/6O1tryK2c7VLz1/b6Ax8Ii1Nt9aW2itXVbF5/vN9/4br/lrugGbzvA9iYhIHaQyKyIinmAU8J21Nqvy/gecZqrxaaSdcruAijJ2qgnACmvtoiqe2xg4cEohhYpRzian3F8CnA8Mqry9mIoiO7jyflWznatfev6mwD5rbelZPF9V3vuZvCeVWRERqRKVWRERcWvGmHpUTFMdbIxJM8akAQ8BXY0xXX/ltAIg8JT7MWf4shOAOGPMf6p4/GGgqTHm1H9X44BDp9z/qcyeV3l7Cb9cZs/F2b7vA1S831/b5cD+xrlVee9noisqsyIiUgUqsyIi4u6uBsqADlSM2nUD2lNxvejtv3LORuAWY4y3MWYIFYXxTORScY3nIGPMC1U4fjWQDzxqjPGt3H91GJXXnVZaQsWCTfWstQcr8w8BIoANZ5jv15zt+14DHAFeMMYEGWMCjDEDTvl+OtDyV86tyns/EyqzIiJSJSqzIiLi7kYB06y1+621aT/9AiYCt/7KaOKDVBSqbOBW4LMzfVFrbTZwCTDUGPO30xxbTMV2QUOBLOB14HZrbdIpx+wC8qgosVhrTwCpwHJrbdmZ5vsVZ/W+K19/GBBPxWJPB4GbTjnkeeDPlasVP/yzc0/73qvKGBMDhAFnfK6IiNQ9xtrfmjkkIiIiIiIi4n40MisiIiIiIiIeR2VWREREREREPI7KrIiIiIiIiHgclVkRERERERHxOL+2n5zbioyMtM2bN3c6hoiIiIiIiNSAdevWZVlro053nMeV2ebNm5OYmOh0DBEREREREakBxph9VTlO04xFRERERETE46jMioiIiIiIiMdRmRURERERERGPozIrIiIiIiIiHkdlVkRERERERDyOyqyIiIiIiIh4HJdtzWOM2QvkAmVAqbU2wRjzEjAMKAZ2A3dYa7NdlUlEREREREQ8k6tHZi+w1naz1iZU3v8e6GSt7QLsAh53cR4REREREZE6Yf3+40xeshtrrdNRqoWj04yttd9Za0sr764CYp3MIyIiIiIiUhulZOQx5t21fLBmP3lFpac/wQO4ssxa4DtjzDpjzLhf+P4Y4JtfOtEYM84Yk2iMSczMzKzRkCIiIiIiIrVJ+olCRk1dg4+XYcaY3gQH+DodqVq4sswOsNb2AIYC9xpjBv30DWPMn4BS4P1fOtFaO8Vam2CtTYiKinJNWhEREREREQ93orCE0dPWcrygmGmje9MsIsjpSNXGZWXWWnu48msGMBfoDWCMGQVcCdxqa8vkbREREREREYcVlZYxfsY6ktNzefO2nnSODXE6UrVySZk1xgQZY4J/ug1cCmw1xgwBHgOGW2sLXJFFRERERESktisvt/x+1iZWph7lxeu7MKhN7Zvh6qqteRoCc40xP73mB9ba+caYFMAf+L7ye6ustRNclElERERERKTWsdbyt6+289XmIzw+tB3X9qid6+y6pMxaa1OBrr/weLwrXl9ERERERKSumLI0lWnL9zJmQAvGDWrpdJwa4+jWPCIiIiIiIlJ95qw/yPPfJHFll0b8+Yr2VM6ArZVUZkVERERERGqBJbsyeXT2Zvq1jOBfN3bFy6v2FllQmRUREREREfF4mw9mc/d762jdMJjJt/fE38fb6Ug1TmVWRERERETEg+3NyueOaWsJC/Rj+h29aBDg63Qkl1CZFRERERER8VCZuUWMmraGcmuZMbY30Q0CnI7kMq7amkdERERERESqUX5RKWPeXUv6iUI+vKsvraLqOx3JpVRmRUREREREPExxaTkT3lvH9iMnmDKyJ93jwpyO5HKaZiwiIiIiIuJBysstj326mR+Ts3j+ms5c1L6h05EcoTIrIiIiIiLiQf7xbRJzNxzi4UvbcGOvpk7HcYzKrIiIiIiIiIeYumwPk5ekMrJvM+69IN7pOI5SmRUREREREfEAX246zN++2s6QjjH8dXhHjDFOR3KUyqyIiIiIiIib23Qgmz/M2kSvZuG8PKIb3l51u8iCyqyIiIiIiIhbyzlZwn0fricq2J8pt/ckwNfb6UhuQVvziIiIiIiIuClrLY/P2czh7EJmje9HaKCf05HchkZmRURERERE3NT7q/fz9ZY0HrmsLT2b1b29ZH+LyqyIiIiIiIgb2n74BM/M287gNlGMO6+l03HcjsqsiIiIiIiIm8kvKuW+D9YTWs+Xf9/YFS8t+PR/6JpZERERERERN/Pk51vZezSf9+/sS0R9f6fjuCWNzIqIiIiIiLiR2esOMmf9IR64qDX9WkU4HcdtqcyKiIiIiIi4iZSMXJ78bCt9W4Zz/4WtnY7j1lRmRURERERE3EBhSRn3vr+Ben7evDKiO966TvY36ZpZERERERERN/DMvO3sTM/l3Tt60bBBgNNx3J5GZkVERERERBz25abDfLB6P+MHt+T8ttFOx/EIKrMiIiIiIiIO2nc0n8fnbKF7XCgPX9rW6TgeQ2VWRERERETEIUWlZdz3wQa8DLx2c3d8vVXRqkrXzIqIiIiIiDjkH9/sZMuhHCaP7ElsWKDTcTyKar+IiIiIiIgDvt+eztTlexjdvzmXdYxxOo7HUZkVERERERFxsUPZJ3n4k010atKAxy9v53Qcj6QyKyIiIiIi4kIlZeU88OEGSsvKee3mHvj7eDsdySO5rMwaY/YaY7YYYzYaYxIrH7vBGLPNGFNujElwVRYRERERERGn/Of7Xazbd5znru1Mi8ggp+N4LFcvAHWBtTbrlPtbgWuByS7OISIiIiIi4nJLd2XyxpLdjOjVlKu6NXE6jkdzdDVja+0OAGOMkzFERERERERqXMaJQn4/ayOto+vzl2EdnY7j8Vx5zawFvjPGrDPGjDuTE40x44wxicaYxMzMzBqKJyIiIiIiUjPKyi2/+3gjeUWlTLqlB/X8dJ3suXJlmR1gre0BDAXuNcYMquqJ1top1toEa21CVFRUzSUUERERERGpAW8sTmHF7qM8M7wTrRsGOx2nVnBZmbXWHq78mgHMBXq76rVFREREREScsvlgNi//kMywro25ISHW6Ti1hkvKrDEmyBgT/NNt4FIqFn8SERERERGptQpLyvj9rE1E1vfn2as6ab2gauSqkdmGwDJjzCZgDfCVtXa+MeYaY8xBoB/wlTHmWxflERERERERqXEvzt9JSkYeL93QhZBAX6fj1CouWc3YWpsKdP2Fx+dSMeVYRERERESkVlmxO4upy/dwe79mnNdaa/9UN1cuACUiIiIiIlInnCgs4ZFPNtMiMog/Dm3ndJxaydF9ZkVERERERGqjZ77czpGck3x6d38C/VS7aoJGZkVERERERKrRt9vSmL3uIPdeEE/3uDCn49RaKrMiIiIiIiLVJCuviCfmbKFj4wbcf2Frp+PUahrvFhERERERqQbWWh6fs4XcolI+vKkbfj4aO6xJ+q8rIiIiIiJSDWavO8j329N59LK2tGkY7HScWk9lVkRERERE5BwdPF7A019up0+LcMYMaOF0nDpBZVZEREREROQclJdbHv5kE9Za/nlDV7y8jNOR6gSVWRERERERkXMwbcVeVqUe4y/DOtI0PNDpOHWGyqyIiIiIiMhZSk7P5R/zk7i4fUNuSIh1Ok6dojIrIiIiIiJyFkrKynlo1kbq+/vw/LWdMUbTi11JW/OIiIiIiIichdcWprD10AnevK0nUcH+TsepczQyKyIiIiIicoY2Hshm0qIUru3RhCGdYpyOUyepzIqIiIiIiJyBk8Vl/H7WRhoG+/PX4R2djlNnaZqxiIiIiIjIGfjH/CRSM/P54M4+NAjwdTpOnaWRWRERERERkSpalpzFuyvLine truncated
|
||||
"text/plain": [
|
||||
"<Figure size 1152x288 with 1 Axes>"
|
||||
]
|
||||
@@ -274,15 +401,15 @@
|
||||
" return np.sin(2 * x) + (x / 3)**2 - x + 50\n",
|
||||
"\n",
|
||||
"plt.figure(figsize=(16, 4))\n",
|
||||
"plt.plot(x, func(x))\n",
|
||||
"\n",
|
||||
"np.random.seed(1)\n",
|
||||
"bo = BayesOpt(param_ranges, evaluate_params)\n"
|
||||
"plt.title('A unknown function $f$')\n",
|
||||
"plt.xlabel('$x$')\n",
|
||||
"plt.ylabel('$f(x)$')\n",
|
||||
"plt.plot(x, func(x))\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 403,
|
||||
"execution_count": 259,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
@@ -291,7 +418,7 @@
|
||||
"\n",
|
||||
"param_ranges = {\n",
|
||||
" 'x': {\n",
|
||||
" 'range': [1, 10],\n",
|
||||
" 'range': [0, 10],\n",
|
||||
" 'type': 'float'\n",
|
||||
" }\n",
|
||||
"}\n"
|
||||
@@ -299,14 +426,14 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 438,
|
||||
"execution_count": 285,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stderr",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"100%|██████████| 2/2 [00:00<00:00, 5210.32it/s]"
|
||||
"100%|██████████| 2/2 [00:00<00:00, 2374.36it/s]"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -320,19 +447,373 @@
|
||||
"name": "stderr",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"\n"
|
||||
"\n",
|
||||
" /opt/miniconda3/lib/python3.7/site-packages/paramz/transformations.py:111: RuntimeWarning:divide by zero encountered in log\n",
|
||||
" /opt/miniconda3/lib/python3.7/site-packages/paramz/transformations.py:108: RuntimeWarning:invalid value encountered in greater\n",
|
||||
" /opt/miniconda3/lib/python3.7/site-packages/GPy/kern/src/stationary.py:168: RuntimeWarning:overflow encountered in true_divide\n",
|
||||
" /opt/miniconda3/lib/python3.7/site-packages/GPy/kern/src/rbf.py:54: RuntimeWarning:invalid value encountered in multiply\n",
|
||||
" /opt/miniconda3/lib/python3.7/site-packages/paramz/transformations.py:113: RuntimeWarning:invalid value encountered in greater\n",
|
||||
" /opt/miniconda3/lib/python3.7/site-packages/GPy/kern/src/rbf.py:51: RuntimeWarning:overflow encountered in square\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<Figure size 1440x288 with 2 Axes>"
|
||||
]
|
||||
},
|
||||
"metadata": {
|
||||
"needs_background": "light"
|
||||
},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"data": {
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||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<Figure size 1440x288 with 2 Axes>"
|
||||
]
|
||||
},
|
||||
"metadata": {
|
||||
"needs_background": "light"
|
||||
},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"data": {
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||||
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truncated
|
||||
"text/plain": [
|
||||
"<Figure size 1440x288 with 2 Axes>"
|
||||
]
|
||||
},
|
||||
"metadata": {
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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||||
"data": {
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truncated
|
||||
"text/plain": [
|
||||
"<Figure size 1440x288 with 2 Axes>"
|
||||
]
|
||||
},
|
||||
"metadata": {
|
||||
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|
||||
},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"data": {
|
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|
||||
"text/plain": [
|
||||
"<Figure size 1440x288 with 2 Axes>"
|
||||
]
|
||||
},
|
||||
"metadata": {
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||||
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|
||||
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||||
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|
||||
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|
||||
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||||
"data": {
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|
||||
"text/plain": [
|
||||
"<Figure size 1440x288 with 2 Axes>"
|
||||
]
|
||||
},
|
||||
"metadata": {
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
{
|
||||
"data": {
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||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<Figure size 1440x288 with 2 Axes>"
|
||||
]
|
||||
},
|
||||
"metadata": {
|
||||
"needs_background": "light"
|
||||
},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<Figure size 1440x288 with 2 Axes>"
|
||||
]
|
||||
},
|
||||
"metadata": {
|
||||
"needs_background": "light"
|
||||
},
|
||||
"output_type": "display_data"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"np.random.seed(3)\n",
|
||||
"bo = BayesOpt(param_ranges, evaluate_params, random_trials=2)\n",
|
||||
"bo._random_search()\n",
|
||||
"bo._fit_gp()\n",
|
||||
"new_proposal = bo._new_proposal()\n",
|
||||
"x_, y_ = bo._single_iter(new_proposal)\n",
|
||||
"\n",
|
||||
"for i in range(2, 10):\n",
|
||||
" new_proposal = bo._new_proposal()\n",
|
||||
" ei = expected_improvement(\n",
|
||||
" f=bo.gp.predict, y_current=bo.y.max(), x_proposed=x[:, None]\n",
|
||||
" )\n",
|
||||
" x_, y_ = bo._single_iter(new_proposal)\n",
|
||||
" bo.x[i], bo.y[i] = x_, y_\n",
|
||||
"\n",
|
||||
" quants = bo.gp.predict_quantiles(x[:, None], quantiles=(10, 90))\n",
|
||||
" mu, var = bo.gp.predict(x[:, None])\n",
|
||||
"\n",
|
||||
" plt.figure(figsize=(20, 4))\n",
|
||||
" plt.suptitle(f\"Iteration {i - 1}\")\n",
|
||||
" plt.subplot(1, 2, 1)\n",
|
||||
" plt.title(\"$f(x^*)$\")\n",
|
||||
" plt.plot(x, mu, color=\"C0\", label=\"Mean\")\n",
|
||||
" plt.fill_between(\n",
|
||||
" x,\n",
|
||||
" quants[0].flatten(),\n",
|
||||
" quants[1].flatten(),\n",
|
||||
" alpha=0.15,\n",
|
||||
" edgecolor=\"C1\",\n",
|
||||
" label=\"Confidence\",\n",
|
||||
" )\n",
|
||||
" plt.scatter(\n",
|
||||
" bo.x[: bo.random_trials],\n",
|
||||
" bo.y[: bo.random_trials],\n",
|
||||
" color=\"r\",\n",
|
||||
" label=\"random trials\",\n",
|
||||
" )\n",
|
||||
" plt.xlim(x.min() - 1, x.max() + 1)\n",
|
||||
" mask = bo.x.sum(axis=1) != 0\n",
|
||||
" plt.scatter(\n",
|
||||
" bo.x[mask][bo.random_trials : -1],\n",
|
||||
" bo.y[mask][bo.random_trials : -1],\n",
|
||||
" color=\"g\",\n",
|
||||
" label=\"BO trials\",\n",
|
||||
" )\n",
|
||||
"\n",
|
||||
" plt.legend()\n",
|
||||
" plt.subplot(1, 2, 2)\n",
|
||||
" plt.title(\"$EI(x)$\")\n",
|
||||
" plt.plot(x, ei, color=\"C1\")\n",
|
||||
" plt.vlines(new_proposal, 0, ei.max(), linestyle=\"--\", label=\"New proposal\")\n",
|
||||
" plt.xlim(x.min() - 1, x.max() + 1)\n",
|
||||
" plt.legend()\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 234,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"array([5.69161243])"
|
||||
]
|
||||
},
|
||||
"execution_count": 234,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"bo._new_proposal()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 235,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"<matplotlib.legend.Legend at 0x7f9ef1bdc7b8>"
|
||||
]
|
||||
},
|
||||
"execution_count": 235,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<Figure size 1440x288 with 2 Axes>"
|
||||
]
|
||||
},
|
||||
"metadata": {
|
||||
"needs_background": "light"
|
||||
},
|
||||
"output_type": "display_data"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"quants = bo.gp.predict_quantiles(x[:, None], quantiles=(10, 90))\n",
|
||||
"mu, var = bo.gp.predict(x[:, None])\n",
|
||||
"\n",
|
||||
"ei = expected_improvement(\n",
|
||||
" f=bo.gp.predict,\n",
|
||||
" y_current=bo.y.max(),\n",
|
||||
" x_proposed=x[:, None])\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"plt.figure(figsize=(20, 4))\n",
|
||||
"plt.suptitle(f'Iteration {i}')\n",
|
||||
"plt.subplot(1, 2, 1)\n",
|
||||
"plt.title('$f(x^*)$')\n",
|
||||
"plt.plot(x, mu, color='C0', label='Mean')\n",
|
||||
"plt.fill_between(x, quants[0].flatten(), quants[1].flatten(), alpha=0.15, edgecolor='C1', label='Confidence')\n",
|
||||
"plt.scatter(bo.x[:bo.random_trials], bo.y[:bo.random_trials], color='r', label='random trials')\n",
|
||||
"\n",
|
||||
"mask = bo.x.sum(axis=1) != 0\n",
|
||||
"plt.scatter(bo.x[mask][bo.random_trials:], bo.y[mask][bo.random_trials:], color='g', label='BO trials')\n",
|
||||
"\n",
|
||||
"plt.legend()\n",
|
||||
"\n",
|
||||
"plt.subplot(1, 2, 2)\n",
|
||||
"plt.title('$EI(x)$')\n",
|
||||
"plt.plot(x, ei, color='C1')\n",
|
||||
"plt.vlines(bo._new_proposal(), 0, ei.max(), linestyle='--', label='New proposal')\n",
|
||||
"plt.legend()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 206,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"ename": "ValueError",
|
||||
"evalue": "Array 'cov' must be square if it is two dimensional, but cov.shape = (50, 1).",
|
||||
"output_type": "error",
|
||||
"traceback": [
|
||||
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
|
||||
"\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
|
||||
"\u001b[0;32m<ipython-input-206-b3e1a5540454>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0ma\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mstats\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmultivariate_normal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmu\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mflatten\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcov\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrvs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m75\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 2\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfigure\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfigsize\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m16\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m4\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0malpha\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.5\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||
"\u001b[0;32m/opt/miniconda3/lib/python3.7/site-packages/scipy/stats/_multivariate.py\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self, mean, cov, allow_singular, seed)\u001b[0m\n\u001b[1;32m 361\u001b[0m return multivariate_normal_frozen(mean, cov,\n\u001b[1;32m 362\u001b[0m \u001b[0mallow_singular\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mallow_singular\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 363\u001b[0;31m seed=seed)\n\u001b[0m\u001b[1;32m 364\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 365\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_process_parameters\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdim\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmean\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcov\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||
"\u001b[0;32m/opt/miniconda3/lib/python3.7/site-packages/scipy/stats/_multivariate.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, mean, cov, allow_singular, seed, maxpts, abseps, releps)\u001b[0m\n\u001b[1;32m 733\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_dist\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmultivariate_normal_gen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mseed\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 734\u001b[0m self.dim, self.mean, self.cov = self._dist._process_parameters(\n\u001b[0;32m--> 735\u001b[0;31m None, mean, cov)\n\u001b[0m\u001b[1;32m 736\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcov_info\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_PSD\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcov\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mallow_singular\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mallow_singular\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 737\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mmaxpts\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||
"\u001b[0;32m/opt/miniconda3/lib/python3.7/site-packages/scipy/stats/_multivariate.py\u001b[0m in \u001b[0;36m_process_parameters\u001b[0;34m(self, dim, mean, cov)\u001b[0m\n\u001b[1;32m 419\u001b[0m \" but 'mean' is a vector of length %d.\")\n\u001b[1;32m 420\u001b[0m \u001b[0mmsg\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmsg\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcov\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmean\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 421\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmsg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 422\u001b[0m \u001b[0;32melif\u001b[0m \u001b[0mcov\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 423\u001b[0m raise ValueError(\"Array 'cov' must be at most two-dimensional,\"\n",
|
||||
"\u001b[0;31mValueError\u001b[0m: Array 'cov' must be square if it is two dimensional, but cov.shape = (50, 1)."
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"a = stats.multivariate_normal(mu.flatten(), cov).rvs(75)\n",
|
||||
"\n",
|
||||
"plt.figure(figsize=(16, 4))\n",
|
||||
"for i in range(a.shape[0]):\n",
|
||||
" plt.plot(x, a[i, :], alpha=0.5)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 143,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"{'gpmean': [[<matplotlib.lines.Line2D at 0x7f9ef3c11240>],\n",
|
||||
" [<matplotlib.lines.Line2D at 0x7f9ef3ae7eb8>],\n",
|
||||
" [<matplotlib.lines.Line2D at 0x7f9ef3aa18d0>],\n",
|
||||
" [<matplotlib.lines.Line2D at 0x7f9ef3aa1160>],\n",
|
||||
" [<matplotlib.lines.Line2D at 0x7f9ef3aa1da0>],\n",
|
||||
" [<matplotlib.lines.Line2D at 0x7f9ef3aa1e80>],\n",
|
||||
" [<matplotlib.lines.Line2D at 0x7f9ef3aa9470>],\n",
|
||||
" [<matplotlib.lines.Line2D at 0x7f9ef3aa97b8>],\n",
|
||||
" [<matplotlib.lines.Line2D at 0x7f9ef3aa9b00>],\n",
|
||||
" [<matplotlib.lines.Line2D at 0x7f9ef3aa9e48>],\n",
|
||||
" [<matplotlib.lines.Line2D at 0x7f9ef3aa9f28>],\n",
|
||||
" [<matplotlib.lines.Line2D at 0x7f9ef3ab2518>],\n",
|
||||
" [<matplotlib.lines.Line2D at 0x7f9ef3ab2860>],\n",
|
||||
" [<matplotlib.lines.Line2D at 0x7f9ef3ab2ba8>],\n",
|
||||
" [<matplotlib.lines.Line2D at 0x7f9ef3ab2ef0>],\n",
|
||||
" [<matplotlib.lines.Line2D at 0x7f9ef3ab2fd0>],\n",
|
||||
" [<matplotlib.lines.Line2D at 0x7f9ef3abd5c0>],\n",
|
||||
" [<matplotlib.lines.Line2D at 0x7f9ef3abd908>],\n",
|
||||
" [<matplotlib.lines.Line2D at 0x7f9ef3abdc50>],\n",
|
||||
" [<matplotlib.lines.Line2D at 0x7f9ef3abdf98>]]}"
|
||||
]
|
||||
},
|
||||
"execution_count": 143,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<Figure size 432x288 with 1 Axes>"
|
||||
]
|
||||
},
|
||||
"metadata": {
|
||||
"needs_background": "light"
|
||||
},
|
||||
"output_type": "display_data"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"bo.gp.plot_samples(samples=20)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 12,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stderr",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"100%|██████████| 2/2 [00:00<00:00, 1279.92it/s]"
|
||||
]
|
||||
},
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Starting 2 random trials...\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"name": "stderr",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"\n",
|
||||
" /opt/miniconda3/lib/python3.7/site-packages/paramz/transformations.py:111: RuntimeWarning:divide by zero encountered in log\n",
|
||||
" /opt/miniconda3/lib/python3.7/site-packages/paramz/transformations.py:108: RuntimeWarning:invalid value encountered in greater\n",
|
||||
" /opt/miniconda3/lib/python3.7/site-packages/GPy/kern/src/stationary.py:168: RuntimeWarning:overflow encountered in true_divide\n",
|
||||
" /opt/miniconda3/lib/python3.7/site-packages/GPy/kern/src/rbf.py:54: RuntimeWarning:invalid value encountered in multiply\n",
|
||||
" /opt/miniconda3/lib/python3.7/site-packages/paramz/transformations.py:113: RuntimeWarning:invalid value encountered in greater\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"[<matplotlib.lines.Line2D at 0x7f7eb2e6b668>]"
|
||||
"[<matplotlib.lines.Line2D at 0x7f9f04d91860>]"
|
||||
]
|
||||
},
|
||||
"execution_count": 438,
|
||||
"execution_count": 12,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
},
|
||||
{
|
||||
"name": "stderr",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
" /opt/miniconda3/lib/python3.7/site-packages/matplotlib/figure.py:2369: UserWarning:This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
@@ -361,14 +842,14 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 436,
|
||||
"execution_count": 13,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stderr",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"100%|██████████| 2/2 [00:00<00:00, 1687.17it/s]\n",
|
||||
"100%|██████████| 2/2 [00:00<00:00, 1929.75it/s]\n",
|
||||
" 0%| | 0/5 [00:00<?, ?it/s]"
|
||||
]
|
||||
},
|
||||
@@ -384,22 +865,23 @@
|
||||
"name": "stderr",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"100%|██████████| 5/5 [00:01<00:00, 3.41it/s]\n"
|
||||
" 20%|██ | 1/5 [00:00<00:01, 2.33it/s] /opt/miniconda3/lib/python3.7/site-packages/GPy/kern/src/rbf.py:51: RuntimeWarning:overflow encountered in square\n",
|
||||
"100%|██████████| 5/5 [00:01<00:00, 3.23it/s]\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"<matplotlib.collections.PathCollection at 0x7f7eb2ef96a0>"
|
||||
"<matplotlib.collections.PathCollection at 0x7f9f04a61400>"
|
||||
]
|
||||
},
|
||||
"execution_count": 436,
|
||||
"execution_count": 13,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
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truncated
|
||||
"image/png": "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 truncated
|
||||
"text/plain": [
|
||||
"<Figure size 1152x288 with 1 Axes>"
|
||||
]
|
||||
@@ -421,7 +903,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 437,
|
||||
"execution_count": 14,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
@@ -430,7 +912,7 @@
|
||||
"{'x': 10.0}"
|
||||
]
|
||||
},
|
||||
"execution_count": 437,
|
||||
"execution_count": 14,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
@@ -441,16 +923,16 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 407,
|
||||
"execution_count": 15,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"array([4.47201616])"
|
||||
"array([9.82811278])"
|
||||
]
|
||||
},
|
||||
"execution_count": 407,
|
||||
"execution_count": 15,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
|
||||
Reference in new issue
Block a user