{"id":228,"date":"2021-07-28T05:42:00","date_gmt":"2021-07-28T05:42:00","guid":{"rendered":"https:\/\/tensor.agenthub.uk\/?p=228"},"modified":"2024-05-17T06:18:03","modified_gmt":"2024-05-17T06:18:03","slug":"%e8%ae%be%e5%ae%9abias%e8%a7%a3%e5%86%b3%e6%a0%b7%e6%9c%ac%e4%b8%8d%e5%9d%87%e8%a1%a1%e9%97%ae%e9%a2%98","status":"publish","type":"post","link":"https:\/\/tensorzen.blog\/?p=228","title":{"rendered":"\u8bbe\u5b9abias\u89e3\u51b3\u6837\u672c\u4e0d\u5747\u8861\u95ee\u9898"},"content":{"rendered":"\n

\u521d\u59cb\u5316\u53c2\u6570\u76f4\u63a5\u51b3\u5b9a\u4e86\u6a21\u578b\u662f\u5426\u80fd\u5feb\u901f\u6536\u655b\uff0c\u4ece\u68af\u5ea6\u4e0b\u964d\u7684\u8fc7\u7a0b\u770b\uff0c\u521d\u59cb\u5316\u53c2\u6570$\\theta_0$\u5e94\u8be5\u662f\u5bf9$f(x;\\theta)$& \u6570\u636e\u96c6 \u4ece\u5168\u5c40\u4e0a\u8003\u8651\u4e4b\u540e\u5f97\u5230\u4e00\u4e2a\u6bd4\u8f83\u76f4\u89c9\u7684\u731c\u6d4b\u3002 \u5982\u679c\u4f60\u7684\u76f4\u89c9\u51c6\u90a3\u4e48\u6a21\u578b\u6536\u655b\u7684\u901f\u5ea6\u4f1a\u6bd4\u8f83\u5feb\uff0c\u6216\u8005\u4e0d\u81f3\u4e8e\u6389\u8fdb\u4e00\u4e2a\u5c40\u90e8\u6700\u4f18\u89e3\u722c\u4e0d\u51fa\u6765\u3002<\/p>\n\n\n\n

\u4e4b\u524d\u770b\u8fc7\u4e00\u4e2a\u8c03\u6574\u521d\u59cbbias\u5904\u7406\u4e0d\u5747\u8861\u6837\u672c\u7684\u4f8b\u5b50\uff0c\u8fd8\u633a\u6709\u8da3\u7684\uff0c\u8fd9\u91cc\u7ed9\u4e61\u4eb2\u4eec\u4ecb\u7ecd\u4e0b\u3002\u4f8b\u5b50\u6765\u81eatenosrflow\u7684tutorials\uff0c\u5730\u5740\u5728\u8fd9 https:\/\/www.tensorflow.org\/tutorials\/structured_data\/imbalanced_data<\/a><\/p>\n\n\n\n

1 \u7b80\u8ff0\u4e00\u4e0b\u4f8b\u5b50<\/h2>\n\n\n\n

\u4f8b\u5b50\u6bd4\u8f83\u7b80\u5355\uff0c\u662f\u4e00\u4e2a\u4e25\u91cd\u4e0d\u5747\u8861\u7684\u4e8c\u5206\u7c7b\u95ee\u9898\uff0c\u6570\u636e\u6765\u81eaKaggle\u7684\u4fe1\u7528\u5361\u4ea4\u6613\u8bb0\u5f55\uff0c\u76ee\u6807\u8bc6\u522b\u91cc\u9762\u4f2a\u9020\u7684\u4ea4\u6613\u8bb0\u5f55\u3002<\/p>\n\n\n\n

1.1 \u6570\u636e\u51c6\u5907<\/h3>\n\n\n\n

\u7528pandas\u52a0\u8f7d\u4e00\u4e0b\u6570\u636e\uff08\u770b\u5230URL\u91cc\u7684\u201cgoogle\u201d\u5b57\u6837\uff0c\u5927\u6982\u4e5f\u8bb8\u9700\u8981\u4e00\u628a\ud83e\ude9c\uff09\uff1a<\/p>\n\n\n\n

<\/circle><\/circle><\/circle><\/g><\/svg><\/span><\/path><\/path><\/svg><\/span>
raw_df <\/span>=<\/span> pd.<\/span>read_csv<\/span>(<\/span>'https:\/\/storage.googleapis.com\/download.tensorflow.org\/data\/creditcard.csv'<\/span>)<\/span><\/span><\/code><\/pre><\/div>\n\n\n\n
\u6837\u672c\u91cc\u7684Class\u5b57\u6bb5\u6807\u8bb0\u662f\u5426\u4e3a\u5047\u7684\u4ea4\u6613\u8bb0\u5f55\uff0cClass=1\u7684\u8868\u793a\u5047\u7684\u8bb0\u5f55\uff0c\u4ece\u6837\u672c\u6bd4\u4f8b\u4e0a\u770b\uff0c\u975e\u5e38\u4e0d\u5747\u8861<\/p>\n\n\n
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\"\"<\/figure>\n<\/div>\n\n\n
1.2 \u6784\u9020\u6a21\u578b<\/h3>\n\n\n\n
\u4e3a\u4e86\u65b9\u4fbf\u6784\u9020\u6a21\u578b\uff0c\u8fd9\u91cc\u6709\u4e2a\u51fd\u6570\uff0c\u4e5f\u662f\u6765\u81eatutorials\uff1a<\/p>\n\n\n\n
<\/circle><\/circle><\/circle><\/g><\/svg><\/span><\/path><\/path><\/svg><\/span>
def<\/span> <\/span>make_model<\/span>(metrics <\/span>=<\/span> METRICS, output_bias <\/span>=<\/span> None):<\/span><\/span>\n    if output_bias:<\/span><\/span>\n        output_bias = tf.keras.initializers.Constant(output_bias)<\/span><\/span>\n    <\/span><\/span>\n    model = keras.Sequential([<\/span><\/span>\n        <\/span>keras<\/span>.<\/span>layers<\/span>.<\/span>Dense<\/span>(<\/span>16<\/span>, activation <\/span>=<\/span> <\/span>'relu'<\/span>, input_shape <\/span>=<\/span> (train_features.shape[<\/span>-<\/span>1<\/span>], )),<\/span><\/span>\n        <\/span>keras<\/span>.<\/span>layers<\/span>.<\/span>Dropout<\/span>(<\/span>0.5<\/span>),<\/span><\/span>\n        <\/span>keras<\/span>.<\/span>layers<\/span>.<\/span>Dense<\/span>(<\/span>1<\/span>, activation <\/span>=<\/span> <\/span>'sigmoid'<\/span>, bias_initializer <\/span>=<\/span> output_bias)<\/span><\/span>\n    ])<\/span><\/span>\n    <\/span><\/span>\n    model.compile(<\/span><\/span>\n        optimizer <\/span>=<\/span> keras.optimizers.<\/span>Adam<\/span>(lr<\/span>=<\/span>1e<\/span>-<\/span>3<\/span>),<\/span><\/span>\n        loss <\/span>=<\/span> keras.losses.<\/span>BinaryCrossentropy<\/span>(),<\/span><\/span>\n        metrics<\/span>=<\/span>metrics<\/span><\/span>\n    )<\/span><\/span>\n<\/span>\n    return model<\/span><\/span><\/code><\/pre><\/div>\n\n\n\n
\u7ed3\u6784\u6bd4\u8f83\u7b80\u5355\uff0c\u6a21\u578b\u53ea\u6709\u4e00\u5c42\uff0c16\u4e2a\u795e\u7ecf\u5143\uff0c\u8f93\u51fa\u5c42\u53ea\u6709\u4e00\u4e2a\u795e\u7ecf\u5143\uff0c\u56e0\u4e3a\u662f\u4e8c\u5206\u7c7b\u95ee\u9898\uff0c\u5e26\u4e86\u4e00\u4e2asigmoid\u7684\u6fc0\u6d3b\u51fd\u6570\uff0c\u8f93\u51fa\u8be5\u6837\u672c\u662f\u4f2a\u9020\u4ea4\u6613\u7684\u6982\u7387\uff0c\u5373$P(\\hat{y}=1|x)$\u3002<\/p>\n\n\n\n
1.3 \u521d\u59cb\u6a21\u578b\u6548\u679c<\/h3>\n\n\n\n
\u73b0\u5728\u76f4\u63a5\u7528\u9ed8\u8ba4\u521d\u59cb\u5316\u7684\u6a21\u578b\uff08\u8fd8\u6ca1\u8bad\u7ec3\uff09\u8f93\u51fa\u6837\u672c\u7684\u524d1000\u4e2a\uff0c\u770b\u6982\u7387\u6570\u636e\u60c5\u51b5\uff1a<\/p>\n\n\n\n
<\/circle><\/circle><\/circle><\/g><\/svg><\/span><\/path><\/path><\/svg><\/span>
output <\/span>=<\/span> model.<\/span>predict<\/span>(train_features[<\/span>:<\/span>1000<\/span>])<\/span><\/span>\nplt.<\/span>hist<\/span>(output, bins<\/span>=<\/span>20<\/span>)<\/span><\/span><\/code><\/pre><\/div>\n\n\n
\n
\"\"<\/figure>\n<\/div>\n\n\n
\u4ece\u76f4\u65b9\u56fe\u4e0a\u770b\uff0c\u8f93\u51fa\u7684\u503c\u5927\u90fd\u96c6\u4e2d\u57280.6\u4ee5\u540e\uff0c\u56e0\u4e3a\u6a21\u578b\u8f93\u51fa\u7684\u6837\u672c\u662f\u4f2a\u9020\u4ea4\u6613\u7684\u6982\u7387\uff0c\u8fd9\u56fe\u660e\u663e\u4e0d\u7b26\u5408\u6570\u636e\u96c6\u7684\u5b9e\u9645\u5206\u5e03\uff0c\u4e8e\u662f\u4f1a\u5bfc\u81f4Loss\u975e\u5e38\u5de8\u5927\uff0c\u8981\u7ecf\u8fc7\u591a\u8f6e\u8fed\u4ee3\u624d\u80fd\u6536\u655b\uff5e<\/span><\/p>\n\n\n\n
\u6a21\u578b\u7684loss\u4f7f\u7528BinaryCrossEntropy\uff0c\u5f53\u524d\u8fd91000\u4e2a\u6837\u672c\u7684loss<\/div><\/div><\/p>\n\n\n\n
<\/circle><\/circle><\/circle><\/g><\/svg><\/span><\/path><\/path><\/svg><\/span>
tf.<\/span>reduce_mean<\/span>(tf.keras.losses.<\/span>binary_crossentropy<\/span>(y_true<\/span>=<\/span>train_labels[<\/span>:<\/span>1000<\/span>], y_pred<\/span>=<\/span>output))<\/span><\/span><\/code><\/pre><\/div>\n\n\n\n
\u6211\u8fd9\u8fb9\u8f93\u51fa:1.8788428\uff0c\u6211\u60f3\u4f60\u53ef\u80fd\u4f1a\u95ee\uff5e\u6ca1\u6709\u5bf9\u6bd4\u600e\u4e48\u77e5\u9053\u5927\u4e0d\u5927\uff1f\u662f\u76f4\u89c9\uff5e\u7eaf\u7eaf\u7684\u201c\u6211\u89c9\u5f97\u201d\uff5e\u56e0\u4e3a\u6a21\u578b\u8f93\u51fa\u7684\u5206\u5e03\u548c\u5b9e\u9645\u7684\u5206\u5e03\u5dee\u5f02\u5de8\u5927\uff0c\u6240\u4ee5\u4f60\u5c31\u60f3\uff5e\u51ed\u7a7a\u60f3\uff5e\u8fd9\u4e2aloss\u662f\u975e\u5e38\u5927\u7684\u3002<\/span><\/p>\n\n\n\n
2 \u8bbe\u5b9abias<\/h2>\n\n\n\n
\u521d\u59cb\u5316\u7684\u53c2\u6570\u8ddf\u5b9e\u9645\u6837\u672c\u7684\u6982\u7387\u5206\u5e03\u5dee\u5f02\u6bd4\u8f83\u5927\uff0c\u4f1a\u5bfc\u81f4loss\u6bd4\u8f83\u5927(Cross Entropy)\uff0c\u8fd9\u6837\u9700\u8981\u7ecf\u8fc7\u597d\u591a\u8f6e\u7684\u8fed\u4ee3\u624d\u80fd\u6536\u655b\uff0c\u6216\u8005\u6709\u53ef\u80fd\u65e0\u6cd5\u6536\u655b\u7684\u3002\u6211\u4eec\u76f4\u63a5\u7ed9\u4ed6\u4e00\u4e2a\u5927\u7684bias\uff0c\u8ba9\u6a21\u578b\u7684\u521d\u59cb\u8f93\u51fa\u5c31\u63a5\u8fd1\u771f\u5b9e\u7684\u5206\u5e03\u3002<\/p>\n\n\n\n
2.1 \u7406\u8bba\u63a8\u5bfc<\/h3>\n\n\n\n
\u4e2d\u95f4\u5c42\u7684\u795e\u7ecf\u5143\u6bd4\u8f83\u591a\uff0c\u8fd8\u5f97\u8003\u8651\u94fe\u5f0f\u6cd5\u5219\uff0c\u8c03\u6574\u8d77\u6765\u662f\u6bd4\u8f83\u9ebb\u70e6\u7684\uff0c\u8f93\u51fa\u5c42\u53ea\u6709\u4e00\u4e2a\u795e\u7ecf\u5143\u6bd4\u8f83\u597d\u8c03\u6574\uff0c\u8ba1\u7b97\u903b\u8f91\u6bd4\u8f83\u7b80\u5355<\/p>\n\n\n\n
Linear\u5c42\u7684\u5f62\u5f0f\uff08\u4e00\u4e2a\u6837\u672c\u7684\u8ba1\u7b97\u8fc7\u7a0b\uff09<\/p>\n\n\n\n
$$\\hat{y}= \\textbf{w} \\cdot \\textbf{x}+ b$$<\/p>\n\n\n\n
\u56e0\u4e3a\u4f7f\u7528\u4e86sigmoid\u6fc0\u6d3b\u51fd\u6570\uff0c\u6700\u540e\u4e00\u5c42\u7684\u8f93\u51fa\u662f<\/p>\n\n\n\n
$$\\sigma(\\hat{y}) = \\frac{1}{1 + exp( -\\textbf{w} \\cdot \\textbf{x}- b)}$$<\/p>\n\n\n\n
\u4ece\u6982\u7387\u89d2\u5ea6\u770b\u4e0a\u9762\u8f93\u51fa\u7684\u662f$P(\\hat{y}=1|\\textbf{x})$\uff0c\u90a3\u4e48$P(\\hat{y}=0|\\textbf{x})$\u662f<\/p>\n\n\n\n
$$P(\\hat{y}=0|\\textbf{x}) = \\frac{exp(-\\textbf{w} \\cdot \\textbf{x}- b))}{1 + exp(-\\textbf{w} \\cdot \\textbf{x}- b))}$$<\/p>\n\n\n\n
\u6839\u636e1.1\u4e2d\u7ed9\u51fa\u7684\u5b9e\u9645\u6837\u672c\uff0c\u8d1f\u6837\u672c\u548c\u6b63\u6837\u672c\u7684\u6bd4\u4f8b\u5e94\u8be5\u662f$$\\frac{284315}{492}$$\uff0c\u4e5f\u5c31\u662f\u8bf4\u671f\u671b\u6a21\u578b\u8f93\u51fa\u6982\u7387\u6700\u597d\u662f\u7b26\u5408\u8fd9\u4e2a\u6982\u7387\u7684<\/p>\n\n\n\n
$$\\frac{P(\\hat{y}=0|\\textbf{x})}{P(\\hat{y}=1|\\textbf{x})} \\propto \\frac{284315}{492}$$<\/p>\n\n\n\n
\u8fd9\u91cc\u6ce8\u610f\uff0c\u6211\u6ca1\u4f7f\u7528\u7b49\u53f7\uff0c\u7528\u4e86\u7b49\u6bd4$\\propto$\uff0c\u56e0\u4e3a\u6234\u5e3d\u5b50\ud83c\udfa9\u7684$\\hat{y}$\u662f\u9884\u4f30\u503c\u53ea\u662f\u54b1\u4eec\u671f\u671b\u4ed6\u8f93\u51fa\u5927\u6982\u8fd9\u4e48\u4e2a\u6982\u7387\uff0c\u628a\u4e0a\u9762\u7684\u516c\u5f0f\u4eec\u5316\u7b80\u4e00\u4e0b:<\/p>\n\n\n\n
$$\\frac{P(\\hat{y}=0|\\textbf{x})}{P(\\hat{y}=1|\\textbf{x})} =\\frac{exp(-\\textbf{w} \\cdot \\textbf{x}- b))}{1 + exp(-\\textbf{w} \\cdot \\textbf{x}- b))} \\times (1 + exp(-\\textbf{w} \\cdot \\textbf{x}- b)))=exp(-\\textbf{w} \\cdot \\textbf{x}- b)$$<\/p>\n\n\n\n
\u6700\u540e\u5269\u4e0b\u7684\u8fd9\u90e8\u5206$exp(-\\textbf{w} \\cdot \\textbf{x}- b))=exp(-\\textbf{w} \\cdot \\textbf{x})exp(-b)$,$w$\u6211\u4eec\u4e0d\u52a8\uff0c$b$\u672c\u6765\u5c31\u662fbias\u561b\uff0c\u901a\u8fc7\u8c03\u6574\u5b83\u6765\u5f71\u54cd\u6a21\u578b\u7684\u8f93\u51fa\uff0c\u4f7f\u5f97\u8f93\u51fa\u5206\u5e03\u63a5\u8fd1\u6837\u672c\u7684\u5b9e\u9645\u5206\u5e03<\/p>\n\n\n\n
$$exp(-b) = \\frac{284315}{492} \\rightarrow b = -\\log(\\frac{284315}{492}) = -6.35936$$<\/p>\n\n\n\n
2.2 \u5b9e\u8df5\u4e00\u4e0b<\/h3>\n\n\n\n
\u4e8e\u662f\u6211\u4eec\u6839\u636e\u8ba1\u7b97\u7684\u7ed3\u679c\u91cd\u65b0\u6784\u9020\u4e00\u4e2a\u6a21\u578b\uff1a<\/p>\n\n\n\n
<\/circle><\/circle><\/circle><\/g><\/svg><\/span><\/path><\/path><\/svg><\/span>
initial_bias <\/span>=<\/span> <\/span>-<\/span>np.<\/span>log<\/span>(<\/span>284315<\/span> <\/span>\/<\/span> <\/span>492<\/span>)<\/span><\/span>\nmodel2 <\/span>=<\/span> <\/span>make_model<\/span>(output_bias<\/span>=<\/span>initial_bias)<\/span><\/span><\/code><\/pre><\/div>\n\n\n\n
\u770b\u4e00\u4e0b\u8c03\u6574\u540e\u521d\u59cb\u6a21\u578b\uff08\u672a\u8bad\u7ec3\uff09\u7684\u8f93\u51fa\u60c5\u51b5<\/p>\n\n\n\n
<\/circle><\/circle><\/circle><\/g><\/svg><\/span><\/path><\/path><\/svg><\/span>
output2 <\/span>=<\/span> model2.<\/span>predict<\/span>(train_features[<\/span>:<\/span>1000<\/span>])<\/span><\/span>\nplt.<\/span>hist<\/span>(output2, bins<\/span>=<\/span>20<\/span>)<\/span><\/span><\/code><\/pre><\/div>\n\n\n
\n
\"\"<\/figure>\n<\/div>\n\n
\n
\"\"<\/figure>\n<\/div>\n\n\n
\u6bd5\u7adf\u5b9e\u9645\u7684\u6570\u636e\u96c6\u5927\u591a\u6570\u90fd\u662f0\u561b\uff0c\u8fd9\u4e5f\u7b97\u5408\u7406\u3002\u770b\u4e00\u4e0b\u5f53\u524d\u7684Loss<\/span><\/span><\/p>\n\n\n\n
<\/circle><\/circle><\/circle><\/g><\/svg><\/span><\/path><\/path><\/svg><\/span>
tf.<\/span>reduce_mean<\/span>(tf.keras.losses.<\/span>binary_crossentropy<\/span>(y_true<\/span>=<\/span>train_labels[<\/span>:<\/span>1000<\/span>], y_pred<\/span>=<\/span>output2))<\/span><\/span><\/code><\/pre><\/div>\n\n\n\n
\u77ac\u95f4\u5c31\u8dcc\u5012\u4e86\uff1a0.008621918\uff0c\u8fd9\u4e48\u770b\u6765\u76f8\u6bd4\u4e4b\u524d\u6ca1\u8c03\u6574\u7684\u521d\u59cb\u5316\u53c2\u6570\uff0c\u7f29\u5c0f\u4e86200\u591a\u500d\uff5e\uff5e<\/p>\n\n\n\n
3 \u5bf9\u6bd4<\/h2>\n\n\n\n
\u6765\u628a\u4e24\u4e2a\u6a21\u578b\u5206\u522b\u8fed\u4ee3\u4e8620\u8f6e\uff0c\u89c2\u5bdf\u4e00\u4e0bLoss\u7684\u53d8\u5316\u60c5\u51b5\uff1a<\/p>\n\n\n
\n
\"\"<\/figure>\n<\/div>\n\n\n
\u5b9e\u7ebf\u662ftrain loss\uff0c \u865a\u7ebf\u662fval loss\u3002\u84dd\u8272\u662f\u4f7f\u7528\u9ed8\u8ba4\u521d\u59cb\u5316\u53c2\u6570\u7684\u6a21\u578b\u8f93\u51fa\u7684\uff0c\u6a58\u8272\u662f\u4eba\u4e3a\u7ed9\u5b9abias\u7684\u6a21\u578b\uff0c\u660e\u663e\u6a58\u8272\u5728\u4e00\u5f00\u59cbloss\u5c31\u6bd4\u8f83\u4f4e\uff0c\u540e\u9762\u4e00\u76f4\u4e5f\u90fd\u4fdd\u6301\u7684\u6bd4\u8f83\u597d\uff5e\u84dd\u8272\u5728\u8bad\u7ec3\u4e8620\u8f6e\u540e\u4e5f\u6ca1\u6709\u8fbe\u5230\u6a58\u8272\u7684Loss\uff5e<\/p>\n\n\n\n
PS:\u611f\u6069\u8c37\u6b4c\uff5e<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
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