[{'role': 'system', 'content': "You are an expert in machine learning and your task is to classify the code snippets into categories from the provided list of categories. List of categories: ['helper_functions', 'load_data', 'data_exploration', 'data_preprocessing', 'evaluation', 'modelling', 'prediction', 'result_visualization', 'save_results', 'comment_only']"}, {'role': 'user', 'content': "Identify to which category the provided code belongs and assign the code snippet to at least 1 but up to 5 categories based on the probabilities, ignore if the probability of the category is negligible. Strictly provide your response as a list. Avoid providing any additional information, commentary, or personal opinions.\\nPython Code:def posterior(bo, xmin=-2, xmax=10):\nxmin, xmax = -2, 10\nbo.gp.fit(bo.X, bo.Y)\nmu, sigma2 = bo.gp.predict(np.linspace(xmin, xmax, 1000).reshape(-1, 1), eval_MSE=True)\nreturn mu, np.sqrt(sigma2)\ndef plot_gp(bo, x, y):\nfig = plt.figure(figsize=(16, 10))\nfig.suptitle('Gaussian Process and Utility Function After {} Steps'.format(len(bo.X)), fontdict={'size':30})\ngs = gridspec.GridSpec(2, 1, height_ratios=[3, 1])\naxis = plt.subplot(gs[0])\nacq = plt.subplot(gs[1])\nmu, sigma = posterior(bo)\naxis.plot(x, y, linewidth=3, label='Target')\naxis.plot(bo.X.flatten(), bo.Y, 'D', markersize=8, label=u'Observations', color='r')\naxis.plot(x, mu, '--', color='k', label='Prediction')\naxis.fill(np.concatenate([x, x[::-1]]),\nnp.concatenate([mu - 1.9600 * sigma, (mu + 1.9600 * sigma)[::-1]]),\nalpha=.6, fc='c', ec='None', label='95% confidence interval')\naxis.set_xlim((-2, 10))\naxis.set_ylim((None, None))\naxis.set_ylabel('f(x)', fontdict={'size':20})\naxis.set_xlabel('x', fontdict={'size':20})\nutility = bo.util.utility(x.reshape((-1, 1)), bo.gp, 0)\nacq.plot(x, utility, label='Utility Function', color='purple')\nacq.plot(x[np.argmax(utility)], np.max(utility), '*', markersize=15,\nlabel=u'Next Best Guess', markerfacecolor='gold', markeredgecolor='k', markeredgewidth=1)\nacq.set_xlim((-2, 10))\nacq.set_ylim((0, np.max(utility) + 0.5))\nacq.set_ylabel('Utility', fontdict={'size':20})\nacq.set_xlabel('x', fontdict={'size':20})\naxis.legend(loc=2, bbox_to_anchor=(1.01, 1), borderaxespad=0.)\nacq.legend(loc=2, bbox_to_anchor=(1.01, 1), borderaxespad=0.)"}, {'role': 'assistant', 'content': "['modelling', 'prediction', 'result_visualization']"}]