# Accuracy and error rate

In the previous chapter, we used SVM to predict the handwritten digits in the mnist dataset. In this chapter, we will evaluate the quality of our model.

The most commonly used method to check the quality of a model is accuracy. This is also used a lot in our lives. For example, in our exams, students get scores if they answer correctly, but they don’t get scores if they don’t answer it correctly. In the end, students' scores determine their academic performance. The score here is the accuracy.

```python
model_pred = [
    7, 0, 1, 0, 4, 1, 9, 4, 1, 9,
    0, 1, 9, 0, 1, 9, 7, 7, 2, 4,
    9, 6, 1, 5, 4, 0, 7, 4, 0, 1,
    3, 1, 3, 4, 9, 5, 7, 1, 1, 1
    ]

ture_label = [
    7, 2, 1, 0, 4, 1, 4, 9, 5, 9,
    0, 6, 9, 0, 1, 5, 9, 7, 3, 4,
    9, 6, 6, 5, 4, 0, 7, 4, 0, 1,
    3, 1, 3, 4, 7, 2, 7, 1, 2, 1
    ]
```

For example, the above is the predicted label obtained by the model and the real label of the item. The method of testing the accuracy is to compare the predicted label and the real label one by one. If it is correct, add one to the correct number, and do nothing if it is wrong. Finally get the correct number, and then divide the correct number by the total to get the correct rate.

```python
model_pred = [
    7, 0, 1, 0, 4, 1, 9, 4, 1, 9,
    0, 1, 9, 0, 1, 9, 7, 7, 2, 4,
    9, 6, 1, 5, 4, 0, 7, 4, 0, 1,
    3, 1, 3, 4, 9, 5, 7, 1, 1, 1
    ]

ture_label = [
    7, 2, 1, 0, 4, 1, 4, 9, 5, 9,
    0, 6, 9, 0, 1, 5, 9, 7, 3, 4,
    9, 6, 6, 5, 4, 0, 7, 4, 0, 1,
    3, 1, 3, 4, 7, 2, 7, 1, 2, 1
    ]

acc = 0
for i in range(len(model_pred)):
    if model_pred[i] == ture_label[i]:
        acc += 1

acc_rate = acc/len(model_pred)
print('acc_rate =', acc_rate)
print('error_rate =', 1-acc_rate)
```

Of course, accuracy rate and error rate are antonyms, so the error rate is equal to 1 minus the accuracy rate. Run the program, you can get the following results:

```python
acc_rate = 0.7
error_rate = 0.30000000000000004
>>> 
```

Of course, python provides functions for calculating accuracy and error rates, we only need to call them. For details, please refer to the confusion matrix in the next chapter.

## Statistics

Start time of this page: December 26, 2021

Completion time of this page: December 26, 2021


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