{"id":1390,"date":"2019-09-02T12:00:30","date_gmt":"2019-09-02T04:00:30","guid":{"rendered":"http:\/\/www.sniper97.cn\/?p=1390"},"modified":"2019-09-02T12:00:30","modified_gmt":"2019-09-02T04:00:30","slug":"%e3%80%90%e6%9c%ba%e5%99%a8%e5%ad%a6%e4%b9%a0%e3%80%91%e7%ae%97%e6%b3%95%e5%88%86%e6%9e%90%e4%b8%8e%e8%b0%83%e4%bc%98","status":"publish","type":"post","link":"http:\/\/www.sniper97.cn\/index.php\/note\/machine-learning-in-action\/1390\/","title":{"rendered":"\u3010\u5434\u6069\u8fbe\u673a\u5668\u5b66\u4e60\u3011\u7b97\u6cd5\u5206\u6790\u4e0e\u8c03\u4f18"},"content":{"rendered":"\n

\u5434\u6069\u8fbeMachine-Learning \u7b2c\u516d\u5468\uff1a\u65b9\u6cd5\u504f\u5dee\u4e0e\u65b9\u5dee\uff08bias vs variance\uff09<\/p>\n\n\n

\u4e00\u822c\u5bf9\u6570\u636e\u96c6\u7684\u533a\u5206\u5206\u4e3a\u4e24\u79cd\uff1a<\/h2>\n\n\n

\u4e00\u79cd\u662f\u5206\u4e3a\u4e24\u4efd\uff1a\u8bad\u7ec3\u96c6\u4e0e\u6d4b\u8bd5\u96c6\uff0c\u5206\u522b\u5360\u6bd470%\u548c30%\u3002<\/p>\n\n\n

\u4e0d\u8fc7\u8fd9\u79cd\u65b9\u6cd5\u4f7f\u7528\u6d4b\u8bd5\u96c6\u6765\u627e\u51fa\u6700\u4f18\u65b9\u6cd5\uff0c\u6240\u4ee5\u8fd9\u7ec4theta\u5f88\u53ef\u80fd\u53ea\u5bf9\u6d4b\u8bd5\u96c6\u6709\u5f88\u597d\u7684\u62df\u5408\u6548\u679c\uff0c\u800c\u5bf9\u5176\u4ed6\u6570\u636e\u62df\u5408\u6548\u679c\u5c31\u5dee\u4e00\u70b9\u3002\u56e0\u6b64\u6bd4\u8f83\u5efa\u8bae\u9002\u7528\u7b2c\u4e8c\u79cd\u6570\u636e\u96c6\u5206\u7c7b\u65b9\u6cd5\u3002<\/p>\n\n\n

\u7b2c\u4e8c\u79cd\uff1a\u8bad\u7ec3\u96c6\u3001\u4ea4\u53c9\u9a8c\u8bc1\u96c6\u548c\u6d4b\u8bd5\u96c6\uff0c\u5206\u522b\u5360\u6bd460%\u300120%\u300120%\u3002<\/p>\n\n\n

\u4f7f\u7528\u8fd9\u79cd\u6570\u636e\u96c6\u5212\u5206\uff0c\u9996\u5148\u4f7f\u7528\u8bad\u7ec3\u96c6\u8bad\u7ec3theta\u53c2\u6570\uff0c\u7136\u540e\u4f7f\u7528\u4ea4\u53c9\u9a8c\u8bc1\u96c6\u9009\u51fa\u6700\u4f18\u7684theta\uff0c\u6700\u540e\u4f7f\u7528\u6d4b\u8bd5\u96c6\u6d4b\u8bd5\u51fa\u7b97\u6cd5\u51c6\u786e\u7387\u3002<\/p>\n\n\n

\u504f\u5dee\u4e0e\u65b9\u5dee\uff1a<\/h2>\n\n\n

\u5bf9\u4e8e\u53c2\u6570\u7684\u7ef4\u5ea6d\uff1a<\/h3>\n\n\n

\u901a\u5e38\u5982\u679c\u6211\u4eec\u4f7f\u7528\u9ad8\u7eac\u5ea6\u7684\u53c2\u6570\u6269\u5c55\uff08\u9ad8\u9636\u53c2\u6570\uff09\uff0c\u5bf9\u4e8e\u4e0d\u540c\u7684\u9636\u6570\uff0c\u4ee3\u4ef7\u66f2\u7ebf\u5f80\u5f80\u5982\u4e0b\u56fe<\/p>\n\n\n

\"\"<\/figure><\/div>\n\n\n

\u5bf9\u4e8e\u8be5\u56fe<\/p>\n\n\n

\"\"<\/figure><\/div>\n\n\n

\u6211\u4eec\u53ef\u4ee5\u770b\u51fa\u5bf9\u4e8e\u4ea4\u53c9\u9a8c\u8bc1\u96c6\uff0c\u524d\u671f\u7684\u4e0b\u964d\u4e3a\u8bad\u7ec3\u7ed3\u679c\u504f\u5dee\u8f83\u5927\uff0c\u5f80\u5f80theta\u4e0d\u80fd\u5f88\u597d\u5730\u62df\u5408\u66f2\u7ebf\uff0c\u56e0\u6b64\u4ee3\u4ef7\u4f1a\u5f88\u9ad8\u3002\u800c\u540e\u671f\u7531\u4e8e\u7ef4\u5ea6\u8fc7\u9ad8\uff0ctheta\u5bf9\u8bad\u7ec3\u6570\u636e\u8fc7\u62df\u5408\uff0c\u53c8\u6ca1\u6709\u529e\u6cd5\u5f88\u597d\u5730\u62df\u5408\u4ea4\u53c9\u8bad\u7ec3\u96c6\uff0c\u56e0\u6b64\u5bf9\u4e8e\u4ea4\u53c9\u9a8c\u8bc1\u96c6\u7684\u4ee3\u4ef7\u53c8\u6709\u663e\u8457\u7684\u4e0a\u5347\u3002<\/p>\n\n\n

\u8fd9\u65f6\u5019\u6211\u4eec\u4e00\u822c\u53d6\u4ea4\u53c9\u9a8c\u8bc1\u96c6\u4e2d\u6700\u4f4e\u70b9\u7684d\uff0c\u4f5c\u4e3a\u6700\u4f18\u53c2\u6570\u3002<\/p>\n\n\n

\u5bf9\u4e8e\u6b63\u5219\u5316lambda\u7684\u9009\u62e9\uff1a<\/h3>\n\n\n

\u548c\u4e0a\u9762\u4e00\u6837\uff0c\u53ea\u4e0d\u8fc7\u8f83\u5927\u7684\u6b63\u5219\u5316\u53c2\u6570\u5f80\u5f80\u5bf9\u4ee3\u4ef7\u7684\u5f71\u54cd\u6210\u6b63\u76f8\u5173\u3002<\/p>\n\n\n

\"\"<\/figure><\/div>\n\n\n

\u5728\u8f83\u5c0f\u7684lambda\u7684\u60c5\u51b5\u4e0b\uff08\u6bd4\u5982\u6781\u7aef\u76840\uff0c\u8fd9\u65f6\u4e0d\u8fdb\u884c\u6b63\u5219\u5316\uff09\uff0c\u5f80\u5f80\u5f88\u5bb9\u6613\u5bf9\u8bad\u7ec3\u6570\u636e\u96c6\u8fc7\u62df\u5408\uff0c\u56e0\u6b64\u5bf9\u4e8e\u4ea4\u53c9\u9a8c\u8bc1\u96c6\u7684\u4ee3\u4ef7\u53ef\u80fd\u4f1a\u5f88\u9ad8\uff0c\u4ea7\u751f\u9ad8\u65b9\u5dee\u3002<\/p>\n\n\n

\u800c\u5728\u8f83\u5927\u7684lambda\u7684\u60c5\u51b5\u4e0b\uff0c\u53c8\u4f1a\u4ea7\u751f\u6b20\u62df\u5408\uff0c\u5373\u9ad8\u504f\u5dee\uff0c\u8fd9\u662f\u8bad\u7ec3\u96c6\u548c\u4ea4\u53c9\u9a8c\u8bc1\u96c6\u7684\u4ee3\u4ef7\u90fd\u4f1a\u4e0a\u6da8\u3002<\/p>\n\n\n

\u8fd9\u65f6\u5019\u6211\u4eec\u4e00\u822c\u4e5f\u53d6\u4ea4\u53c9\u9a8c\u8bc1\u96c6\u4e2d\u6700\u4f4e\u70b9\u7684lambda\u4f5c\u4e3a\u6700\u4f18\u53c2\u6570\u3002<\/p>\n\n\n

\u5b66\u4e60\u66f2\u7ebf\uff1a<\/h2>\n\n\n

\u5b66\u4e60\u66f2\u7ebf\u7528\u6765\u5224\u65ad\u4e00\u4e2a\u5b66\u4e60\u7b97\u6cd5\u662f\u5426\u5904\u4e8e\u504f\u5dee\u3001\u65b9\u5dee\u95ee\u9898\u3002<\/p>\n\n\n

\u5b66\u4e60\u66f2\u7ebf\u662f\u5b66\u4e60\u7b97\u6cd5\u7684\u4e00\u4e2a\u5f88\u597d\u7684\u5408\u7406\u68c0\u9a8c\u3002<\/p>\n\n\n

\u5b66\u4e60\u66f2\u7ebf\u662f\u5c06\u8bad\u7ec3\u96c6\u8bef\u5dee\u548c\u4ea4\u53c9\u9a8c\u8bc1\u96c6\u4f5c\u4e3a\u8bad\u7ec3\u5b9e\u4f8b\u6570\u91cf\u7684\u51fd\u6570\u7ed8\u5236\u7684\u56fe\u6807\u3002<\/p>\n\n\n

\u5982\u4e0b\u56fe\uff1a<\/p>\n\n\n

\"\"<\/figure><\/div>\n\n\n

\u4e0b\u56fe\u662f\u9ad8\u504f\u5dee\u60c5\u51b5\u4e0b\u7684\u4ee3\u4ef7\u56fe\uff0c\u5bf9\u4e8e\u8fd9\u79cd\u6b20\u62df\u5408\u7684\u60c5\u51b5\u4e0b\uff0c\u76f2\u76ee\u7684\u589e\u52a0\u8bad\u7ec3\u6570\u636e\u91cf\u662f\u6ca1\u6709\u4ec0\u4e48\u660e\u663e\u4f5c\u7528\u7684\uff0c\u5f80\u5f80\u9700\u8981\u51cf\u5c0flambda\uff08\u5373\u51cf\u5c11\u6b63\u5219\u5316\u5f3a\u5ea6\uff09\u6216\u8005\u589e\u52a0theta\u7684\u7ef4\u5ea6\uff0c\u6765\u589e\u5f3atheta\u5bf9\u6570\u636e\u7684\u62df\u5408\uff1a<\/p>\n\n\n

\"\"<\/figure><\/div>\n\n\n

\u4e0b\u9762\u662f\u9ad8\u65b9\u5dee\u7684\u60c5\u51b5\u4e0b\u7684\u4ee3\u4ef7\u56fe\uff0c\u800c\u8fd9\u79cd\u60c5\u51b5\uff0c\u589e\u52a0\u8bad\u7ec3\u6570\u636e\u91cf\u53ef\u4ee5\u53d6\u5f97\u8f83\u597d\u7684\u7ed3\u679c\uff1a<\/p>\n\n\n

\"\"<\/figure><\/div>\n\n\n

\u4e0b\u9762\u9488\u5bf9\u5177\u4f53\u7684\u4f8b\u5b50\u8fdb\u884c\u4e3e\u4f8b\uff1a<\/h2>\n\n\n

\u6570\u636e\u9884\u89c8\uff1a<\/p>\n\n\n

\"\"<\/figure><\/div>\n\n\n

\u7ebf\u6027\u56de\u5f52\u8bbe\u7f6e\u540e\u7684\u5206\u754c\u7ebf\uff1a<\/p>\n\n\n

\"\"<\/figure><\/div>\n\n\n

\u5b66\u4e60\u66f2\u7ebf\uff1a<\/h3>\n\n\n

\u4e0d\u540c\u8bad\u7ec3\u96c6\u957f\u5ea6\u5bf9\u8bad\u7ec3\u4ee3\u4ef7\u4ee5\u53ca\u4ea4\u53c9\u9a8c\u8bc1\u96c6\u4ee3\u4ef7\u4ea7\u751f\u7684\u5f71\u54cd\uff0c\u53ef\u4ee5\u770b\u5230\u8fd9\u4e2a\u6a21\u578b\u5e76\u6ca1\u6709\u5f88\u597d\u5730\u62df\u5408\u8bad\u7ec3\u6570\u636e\uff08\u6700\u7ec8\u4e24\u6761\u66f2\u7ebf\u572825\u9644\u8fd1\u7684\u9ad8\u4ee3\u4ef7\u9644\u8fd1\u9760\u8fd1\uff0c\u9ad8\u504f\u5dee\uff0c\u6709\u4e00\u70b9\u6b20\u62df\u5408\uff09\uff1a<\/p>\n\n\n

\"\"<\/figure><\/div>\n\n\n

\u5bf9lambda\u7684\u9009\u62e9\uff1a<\/h3>\n\n\n

\u4e0d\u540clambda\u4e0b\u8bad\u7ec3\u4ee3\u4ef7\u548c\u4ea4\u53c9\u6821\u9a8c\u4ee3\u4ef7\u7684\u53d8\u5316\uff0c\u53ef\u4ee5\u770b\u5230\u5927\u6982\u57281\u9644\u8fd1\u53d6\u5230\u6700\u4f4e\uff1a<\/p>\n\n\n

\"\"<\/figure><\/div>\n\n\n

lambda = 0\uff0c\u8bad\u7ec3\u4ee3\u4ef7\u4f4e\u7684\u4e0d\u771f\u5b9e\uff0c\u8fc7\u62df\u5408\uff1a<\/p>\n\n\n

\"\"<\/figure><\/div>\n\n\n

lambda = 1\uff0c\u8bad\u7ec3\u6210\u672c\u6709\u4e00\u70b9\u4e0a\u5347\uff0c\u6211\u4eec\u5047\u8bbe\u6709\u4e00\u70b9\u4e0d\u662f\u90a3\u4e48\u8fc7\u62df\u5408\uff08\u548c0\u6bd4\uff09\uff1a<\/p>\n\n\n

\"\"<\/figure><\/div>\n\n\n

lambda = 100,\uff0c\u8fc7\u591a\u7684\u6b63\u5219\u5316\uff1a<\/p>\n\n\n

\"\"<\/figure><\/div>\n\n\n

\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n\n\n

# -*- coding:utf-8 -*-\nimport numpy as np\nimport scipy.io as sio\nimport scipy.optimize as opt\nimport pandas as pd\nimport matplotlib.pyplot as plt\nimport seaborn as sns\ndef load_data():\n    \"\"\"\n    \u6587\u4ef6\u8bfb\u53d6\n    :return:\n    \"\"\"\n    d = sio.loadmat('.\/data\/ex5data1.mat')\n    return map(np.ravel, [d['X'], d['y'], d['Xval'], d['yval'], d['Xtest'], d['ytest']])\n# \u8bfb\u53d6\u6570\u636e\u4e0e\u753b\u51fa\u521d\u59cb\u6570\u636e\u56fe\nX, y, Xval, yval, Xtest, ytest = load_data()\ndf = pd.DataFrame({'water_level': X, 'flow': y})\nsns.lmplot('water_level', 'flow', data=df, fit_reg=False, size=7)\nplt.show()\n# \u5bf9X\u3001Xval\u3001Xtest\u6dfb\u52a0Ones\u504f\u7f6e\u5217\nX, Xval, Xtest = [np.insert(x.reshape(x.shape[0], 1), 0, np.ones(x.shape[0]), axis=1) for x in (X, Xval, Xtest)]\ndef cost(theta, X, y):\n    \"\"\"\n    \u8ba1\u7b97\u4ee3\u4ef7\uff08\u5e73\u65b9\u5dee\uff09\n    :param theta:\n    :param X:\n    :param y:\n    :return:\n    \"\"\"\n    m = X.shape[0]\n    inner = X @ theta - y  # R(m*1)\n    # 1*m @ m*1 = 1*1 in matrix multiplication\n    # but you know numpy didn't do transpose in 1d array, so here is just a\n    # vector inner product to itselves\n    square_sum = inner.T @ inner\n    cost = square_sum \/ (2 * m)\n    return cost\ntheta = np.ones(X.shape[1])\n# 303.951525554\nprint(cost(theta, X, y))\ndef gradient(theta, X, y):\n    \"\"\"\n    \u4e0b\u964d\u7b97\u6cd5\n    :param theta:\n    :param X:\n    :param y:\n    :return:\n    \"\"\"\n    m = X.shape[0]\n    inner = X.T @ (X @ theta - y)  # (m,n).T @ (m, 1) -> (n, 1)\n    return inner \/ m\n# [ -15.30301567  598.16741084]\nprint(gradient(theta, X, y))\ndef regularized_gradient(theta, X, y, l=1):\n    \"\"\"\n    \u6b63\u5219\u5316\u68af\u5ea6\u4e0b\u964d\n    :param theta:\n    :param X:\n    :param y:\n    :param l:\n    :return:\n    \"\"\"\n    m = X.shape[0]\n    # \u4e0d\u60e9\u7f5a\u7b2c\u4e00\u9879\n    regularized_term = theta.copy()  # same shape as theta\n    regularized_term[0] = 0  # don't regularize intercept theta\n    regularized_term = (l \/ m) * regularized_term\n    return gradient(theta, X, y) + regularized_term\n# [ -15.30301567  598.16741084]\nprint(regularized_gradient(theta, X, y))\ndef linear_regression_np(X, y, l=1):\n    \"\"\"\n    \u7ebf\u6027\u56de\u5f52\n    linear regression\n    args:\n        X: feature matrix, (m, n+1) # with incercept x0=1\n        y: target vector, (m, )\n        l: lambda constant for regularization\n    return: trained parameters\n    \"\"\"\n    # init theta\n    theta = np.ones(X.shape[1])\n    # train it\n    res = opt.minimize(fun=regularized_cost,\n                       x0=theta,\n                       args=(X, y, l),\n                       method='TNC',\n                       jac=regularized_gradient,\n                       options={'disp': True})\n    return res\ndef regularized_cost(theta, X, y, l=1):\n    \"\"\"\n    \u6b63\u5219\u5316\u4ee3\u4ef7\u51fd\u6570\n    :param theta:\n    :param X:\n    :param y:\n    :param l:\n    :return:\n    \"\"\"\n    # \u4e0d\u60e9\u7f5a\u7b2c\u4e00\u9879\n    m = X.shape[0]\n    regularized_term = (l \/ (2 * m)) * np.power(theta[1:], 2).sum()\n    return cost(theta, X, y) + regularized_term\ntheta = np.ones(X.shape[0])\n# \u83b7\u5f97\u8bad\u7ec3\u597d\u7684theta [ 13.08790362   0.36777923]\nfinal_theta = linear_regression_np(X, y, l=0).get('x')\nb = final_theta[0]  # intercept\nm = final_theta[1]  # slope\n# \u753b\u51fa\u8bad\u7ec3\u597d\u7684\u56fe\u50cf\nplt.scatter(X[:, 1], y, label=\"Training data\")\nplt.plot(X[:, 1], X[:, 1] * m + b, label=\"Prediction\")\nplt.legend(loc=2)\nplt.show()\ntraining_cost, cv_cost = [], []\nm = X.shape[0]\n# \u4e0d\u540c\u8bad\u7ec3\u96c6\u5927\u5c0f\u5bf9\u4ee3\u4ef7\u7684\u53d8\u5316\u4ea7\u751f\u7684\u5f71\u54cd\nfor i in range(1, m + 1):\n    #     print('i={}'.format(i))\n    res = linear_regression_np(X[:i, :], y[:i], l=0)\n    tc = regularized_cost(res.x, X[:i, :], y[:i], l=0)\n    cv = regularized_cost(res.x, Xval, yval, l=0)\n    #     print('tc={}, cv={}'.format(tc, cv))\n    training_cost.append(tc)\n    cv_cost.append(cv)\n# \u7ed8\u5236\u4e0d\u540c\u8bad\u7ec3\u96c6\u5927\u5c0f\u4e0b\u7684\u4ee3\u4ef7\u53d8\u5316\u56fe\nplt.plot(np.arange(1, m + 1), training_cost, label='training cost')\nplt.plot(np.arange(1, m + 1), cv_cost, label='cv cost')\nplt.legend(loc=1)\nplt.show()\ndef prepare_poly_data(*args, power):\n    \"\"\"\n    args: keep feeding in X, Xval, or Xtest\n        will return in the same order\n    \"\"\"\n    def prepare(x):\n        # expand feature\n        # \u7279\u5f81\u6269\u5c55\n        df = poly_features(x, power=power)\n        # normalization\n        # \u6807\u51c6\u5316\u6570\u636e\n        ndarr = normalize_feature(df).as_matrix()\n        # add intercept term\n        # \u589e\u52a0Ones\u504f\u7f6e\u9879\n        return np.insert(ndarr, 0, np.ones(ndarr.shape[0]), axis=1)\n    return [prepare(x) for x in args]\ndef poly_features(x, power, as_ndarray=False):\n    \"\"\"\n    \u8fd4\u56dex\u7684\u9ad8\u9636\n    :param x:\n    :param power:\n    :param as_ndarray:\n    :return:\n    \"\"\"\n    data = {'f{}'.format(i): np.power(x, i) for i in range(1, power + 1)}\n    df = pd.DataFrame(data)\n    return df.as_matrix() if as_ndarray else df\nX, y, Xval, yval, Xtest, ytest = load_data()\npoly_features(X, power=3)\ndef normalize_feature(df):\n    \"\"\"Applies function along input axis(default 0) of DataFrame.\"\"\"\n    \"\"\"\n    lambda\u8868\u8fbe\u5f0f\u548cdef\u5f88\u50cf\uff0c\u53ea\u4e0d\u8fc7\u662f\u4e00\u4e2a\u8f7b\u91cf\u7ea7\u7684def\n    lambda\u540e\u9762\u7684\u53d8\u91cf\u4e3a\u53c2\u6570\uff0c\u591a\u9910\u7528\u9017\u53f7\u9694\u5f00\u3002\n    \u7d27\u63a5\u7740\u4e3a\u8868\u8fbe\u5f0f\uff0c\u7528\u6765\u6267\u884c\u5bf9\u53c2\u6570\u7684\u76f8\u5173\u64cd\u4f5c\u3002\n    \u5982\u4e0b\u9762\u7684lambda\u53c2\u6570\u7b49\u4ef7\u4e8e\n    def xxx(column):\n        (column - column.mean()) \/ column.std()\n    \u4e5f\u5c31\u662f\u6267\u884c\u6570\u636e\u7684\u6807\u51c6\u5316\u7684\u52a8\u4f5c\n    \"\"\"\n    return df.apply(lambda column: (column - column.mean()) \/ column.std())\nX_poly, Xval_poly, Xtest_poly = prepare_poly_data(X, Xval, Xtest, power=8)\nprint(X_poly[:3, :])\ndef plot_learning_curve(X, y, Xval, yval, l=0):\n    \"\"\"\n    \u5b66\u4e60\u66f2\u7ebf\n    :param X:\n    :param y:\n    :param Xval:\n    :param yval:\n    :param l:\n    :return:\n    \"\"\"\n    training_cost, cv_cost = [], []\n    m = X.shape[0]\n    # \u4e0d\u540c\u8bad\u7ec3\u96c6\u5927\u5c0f\u4e0b\u7684\u5b66\u4e60\u4ee3\u4ef7\u53d8\u5316\n    for i in range(1, m + 1):\n        # regularization applies here for fitting parameters\n        res = linear_regression_np(X[:i, :], y[:i], l=l)\n        # remember, when you compute the cost here, you are computing\n        # non-regularized cost. Regularization is used to fit parameters only\n        # \u8bb0\u4f4f\uff0c\u5f53\u4f60\u5728\u8fd9\u8ba1\u7b97\u4ee3\u4ef7\u65f6\uff0c\u4e0d\u8981\u4f7f\u7528\u6b63\u5219\u8ba1\u7b97\u3002\u6b63\u5219\u8ba1\u7b97\u53ea\u7528\u6765\u5bfb\u627e\u53c2\u6570\n        tc = cost(res.x, X[:i, :], y[:i])\n        cv = cost(res.x, Xval, yval)\n        training_cost.append(tc)\n        cv_cost.append(cv)\n    plt.plot(np.arange(1, m + 1), training_cost, label='training cost')\n    plt.plot(np.arange(1, m + 1), cv_cost, label='cv cost')\n    plt.legend(loc=1)\n# \u7ed8\u5236\u4e09\u79cd\u4e0d\u540clambda\u5bf9\u7528\u7684\u56fe\u50cf\nplot_learning_curve(X_poly, y, Xval_poly, yval, l=0)\nplt.show()\nplot_learning_curve(X_poly, y, Xval_poly, yval, l=1)\nplt.show()\nplot_learning_curve(X_poly, y, Xval_poly, yval, l=100)\nplt.show()\n# \u8bbe\u7f6e\u4e86\u51e0\u79cdlambda\u7684\u503c\nl_candidate = [0, 0.001, 0.003, 0.01, 0.03, 0.1, 0.3, 1, 3, 10]\ntraining_cost, cv_cost = [], []\n# \u5bf9\u6bcf\u4e00\u79cdlambda\u8fdb\u884c\u8ba1\u7b97\u5e76\u4e14\u753b\u56fe\nfor l in l_candidate:\n    res = linear_regression_np(X_poly, y, l)\n    tc = cost(res.x, X_poly, y)\n    cv = cost(res.x, Xval_poly, yval)\n    training_cost.append(tc)\n    cv_cost.append(cv)\nplt.plot(l_candidate, training_cost, label='training')\nplt.plot(l_candidate, cv_cost, label='cross validation')\nplt.legend(loc=2)\nplt.xlabel('lambda')\nplt.ylabel('cost')\nplt.show()\n# best cv I got from all those candidates\nprint(l_candidate[np.argmin(cv_cost)])\n# use test data to compute the cost\nfor l in l_candidate:\n    theta = linear_regression_np(X_poly, y, l).x\n    print('test cost(l={}) = {}'.format(l, cost(theta, Xtest_poly, ytest)))\n<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"
\u5434\u6069\u8fbeMachine-Learning \u7b2c\u516d\u5468\uff1a\u65b9\u6cd5\u504f\u5dee\u4e0e\u65b9\u5dee\uff08bias vs variance\uff09  […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"_mi_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[6,10],"tags":[],"views":5085,"_links":{"self":[{"href":"http:\/\/www.sniper97.cn\/index.php\/wp-json\/wp\/v2\/posts\/1390"}],"collection":[{"href":"http:\/\/www.sniper97.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.sniper97.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.sniper97.cn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.sniper97.cn\/index.php\/wp-json\/wp\/v2\/comments?post=1390"}],"version-history":[{"count":0,"href":"http:\/\/www.sniper97.cn\/index.php\/wp-json\/wp\/v2\/posts\/1390\/revisions"}],"wp:attachment":[{"href":"http:\/\/www.sniper97.cn\/index.php\/wp-json\/wp\/v2\/media?parent=1390"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.sniper97.cn\/index.php\/wp-json\/wp\/v2\/categories?post=1390"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.sniper97.cn\/index.php\/wp-json\/wp\/v2\/tags?post=1390"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}