Bagian berikut membahas kedua pertimbangan ini secara lebih mendalam.
Kehilangan Catatan
Dalam Modul regresi linear, Anda menggunakan kerugian kuadrat (juga disebut L2 (kerugian) sebagai fungsi kerugian. Kerugian kuadrat berfungsi baik untuk di mana laju perubahan nilai output konstan. Misalnya, dengan model linear $y' = b + 3x_1$, setiap kali Anda menambahkan input nilai $x_1$ sebesar 1, nilai {i>output<i} $y'$ meningkat 3.
Namun, laju perubahan model regresi logistik tidak konstan. Seperti yang Anda lihat dalam Menghitung probabilitas, Kurva sigmoid berbentuk s dan bukan linear. Ketika nilai log-peluang ($z$) lebih dekat ke 0, kecil peningkatan $z$ menghasilkan perubahan yang jauh lebih besar terhadap $y$ dibandingkan saat $z$ adalah positif atau negatif. Tabel berikut menunjukkan fungsi sigmoid output untuk nilai input dari 5 hingga 10, serta presisi yang sesuai yang diperlukan untuk menangkap perbedaan dalam hasil.
input
output logistik
digit presisi yang diperlukan
5
0,993
3
6
0,997
3
7
0,999
3
8
0,9997
4
9
0,9999
4
10
0,99998
5
Jika Anda menggunakan kerugian kuadrat untuk menghitung kesalahan fungsi sigmoid, sebagai output semakin mendekati 0 dan 1, Anda akan memerlukan lebih banyak memori untuk mempertahankan presisi yang diperlukan untuk melacak nilai ini.
Sebaliknya, fungsi kerugian untuk regresi logistik Kehilangan Log. Tujuan Persamaan Kerugian Log mengembalikan logaritma besaran perubahan, bukan dari sekedar jarak dari data ke prediksi. Kerugian Log dihitung sebagai berikut ini:
\((x,y)\in D\) adalah set data yang berisi banyak contoh berlabel, yang \((x,y)\) pasang.
\(y\) adalah label dalam contoh berlabel. Karena ini adalah regresi logistik, setiap nilai \(y\) harus 0 atau 1.
\(y'\) adalah prediksi model Anda (antara 0 dan 1), berdasarkan set di \(x\).
Regularisasi dalam regresi logistik
Regularisasi, sebuah mekanisme untuk menghukum kompleksitas model selama pelatihan, sangat penting dalam logistik pemodelan regresi. Tanpa regularisasi, sifat logistik yang asimtotik regresi akan terus mendorong kerugian menuju 0 jika model tersebut memiliki sejumlah besar fitur. Akibatnya, sebagian besar model regresi logistik menggunakan satu dari dua strategi berikut untuk mengurangi kompleksitas model:
[[["Mudah dipahami","easyToUnderstand","thumb-up"],["Memecahkan masalah saya","solvedMyProblem","thumb-up"],["Lainnya","otherUp","thumb-up"]],[["Informasi yang saya butuhkan tidak ada","missingTheInformationINeed","thumb-down"],["Terlalu rumit/langkahnya terlalu banyak","tooComplicatedTooManySteps","thumb-down"],["Sudah usang","outOfDate","thumb-down"],["Masalah terjemahan","translationIssue","thumb-down"],["Masalah kode / contoh","samplesCodeIssue","thumb-down"],["Lainnya","otherDown","thumb-down"]],["Terakhir diperbarui pada 2024-08-13 UTC."],[[["\u003cp\u003eLogistic regression models are trained similarly to linear regression models but use Log Loss instead of squared loss and require regularization.\u003c/p\u003e\n"],["\u003cp\u003eLog Loss is used in logistic regression because the rate of change isn't constant, requiring varying precision levels unlike squared loss used in linear regression.\u003c/p\u003e\n"],["\u003cp\u003eRegularization, such as L2 regularization or early stopping, is crucial in logistic regression to prevent overfitting due to the model's asymptotic nature.\u003c/p\u003e\n"]]],[],null,["[**Logistic regression**](/machine-learning/glossary#logistic_regression)\nmodels are trained using the same process as\n[**linear regression**](/machine-learning/crash-course/linear-regression)\nmodels, with two key distinctions:\n\n- Logistic regression models use [**Log Loss**](/machine-learning/glossary#Log_Loss) as the loss function instead of [**squared loss**](/machine-learning/glossary#l2-loss).\n- Applying [regularization](/machine-learning/crash-course/overfitting/regularization) is critical to prevent [**overfitting**](/machine-learning/glossary#overfitting).\n\nThe following sections discuss these two considerations in more depth.\n\nLog Loss\n\nIn the [Linear regression module](/machine-learning/crash-course/linear-regression),\nyou used [**squared loss**](/machine-learning/glossary#l2-loss) (also called\nL~2~ loss) as the\n[**loss function**](/machine-learning/glossary#loss-function).\nSquared loss works well for a linear\nmodel where the rate of change of the output values is constant. For example,\ngiven the linear model $y' = b + 3x_1$, each time you increment the input\nvalue $x_1$ by 1, the output value $y'$ increases by 3.\n\nHowever, the rate of change of a logistic regression model is *not* constant.\nAs you saw in [Calculating a probability](/machine-learning/crash-course/logistic-regression/sigmoid-function), the\n[**sigmoid**](/machine-learning/glossary#sigmoid-function) curve is s-shaped\nrather than linear. When the log-odds ($z$) value is closer to 0, small\nincreases in $z$ result in much larger changes to $y$ than when $z$ is a large\npositive or negative number. The following table shows the sigmoid function's\noutput for input values from 5 to 10, as well as the corresponding precision\nrequired to capture the differences in the results.\n\n| input | logistic output | required digits of precision |\n|-------|-----------------|------------------------------|\n| 5 | 0.993 | 3 |\n| 6 | 0.997 | 3 |\n| 7 | 0.999 | 3 |\n| 8 | 0.9997 | 4 |\n| 9 | 0.9999 | 4 |\n| 10 | 0.99998 | 5 |\n\nIf you used squared loss to calculate errors for the sigmoid function, as the\noutput got closer and closer to `0` and `1`, you would need more memory to\npreserve the precision needed to track these values.\n\nInstead, the loss function for logistic regression is\n[**Log Loss**](/machine-learning/glossary#Log_Loss). The\nLog Loss equation returns the logarithm of the magnitude of the change, rather\nthan just the distance from data to prediction. Log Loss is calculated as\nfollows:\n\n\\\\(\\\\text{Log Loss} = \\\\sum_{(x,y)\\\\in D} -y\\\\log(y') - (1 - y)\\\\log(1 - y')\\\\)\n\n\u003cbr /\u003e\n\nwhere:\n\n- \\\\((x,y)\\\\in D\\\\) is the dataset containing many labeled examples, which are \\\\((x,y)\\\\) pairs.\n- \\\\(y\\\\) is the label in a labeled example. Since this is logistic regression, every value of \\\\(y\\\\) must either be 0 or 1.\n- \\\\(y'\\\\) is your model's prediction (somewhere between 0 and 1), given the set of features in \\\\(x\\\\).\n\nRegularization in logistic regression\n\n[**Regularization**](/machine-learning/glossary#regularization), a mechanism for\npenalizing model complexity during training, is extremely important in logistic\nregression modeling. Without regularization, the asymptotic nature of logistic\nregression would keep driving loss towards 0 in cases where the model has a\nlarge number of features. Consequently, most logistic regression models use one\nof the following two strategies to decrease model complexity:\n\n- [L~2~ regularization](/machine-learning/crash-course/overfitting/regularization)\n- [Early stopping](/machine-learning/crash-course/overfitting/regularization#early_stopping_an_alternative_to_complexity-based_regularization): Limiting the number of training steps to halt training while loss is still decreasing.\n\n| **Note:** You'll learn more about regularization in the [Datasets, Generalization, and Overfitting](/machine-learning/crash-course/overfitting) module of the course.\n| **Key terms:**\n|\n| - [Gradient descent](/machine-learning/glossary#gradient-descent)\n| - [Linear regression](/machine-learning/glossary#linear_regression)\n| - [Log Loss](/machine-learning/glossary#Log_Loss)\n| - [Logistic regression](/machine-learning/glossary#logistic_regression)\n| - [Loss function](/machine-learning/glossary#loss-function)\n| - [Overfitting](/machine-learning/glossary#overfitting)\n| - [Regularization](/machine-learning/glossary#regularization)\n- [Squared loss](/machine-learning/glossary#l2-loss) \n[Help Center](https://support.google.com/machinelearningeducation)"]]
