Model Evaluation and loss of function

 Model Evaluation

Chapter II: Evaluation and loss function model

• A point: prediction logistic regression model of the sample depends on the weight vector and bias .

• concept:

  No.	concept	Explanation
  1	Training set	Sample set contains real class labels
  2	training	According to the training process to find the optimal set of parameters
  3	Loss function	It is a function of the model parameters used to measure the pros and cons of the model parameters

   

• Logistic regression prediction sample X = (X . 1 , X 2 , X . 3 , ......, X n- ) T probability of belonging to the positive class P :

  f(x) = ​ ​

  • Which, w and b are parameters of the model, the training process is to find these two parameters.

 

• Confusion matrix

  	Forecast negative class	Predicted positive class
  Negative real class	TN	FP
  Real positive class	FN	TP

   

• Correct rate

  • Accuracy of calculation formula:

    accuracy = ​

    The correct rate is the correct ratio of the number of samples and the total number of sample models predict. It is not always reliable, such as n Example: 99 = Negative Example: 1, positive for the whole prediction result, then the accuracy was 99%.

• Precision:

  • Also known accuracy (precision), using the following formula:

    (N-type)

    (Negative type)

    Seen from the formula, the number of samples correctly predicted positive class and the total number of samples predicted positive class ratio. Negative similar.

• Recall:

  • Recall, also known as the recall: recall

    ​

    This formula means that the number of samples predicted positive class and all classes than the number of positive samples. Also known as the true positive rate ( TPR , to true positive Rate) Correspondingly, there are false positive rate ( FPR , false positive Rate):

    ​

• ROC curve

  • In the logistic regression, assume we've got a set of w and B, so we can test set data into f (x) for predicting, after substituting the function we get a value from a number between 0 and 1 in order to achieve the forecast, we need a threshold, we will f (x) is greater than the threshold value of the test data as a positive class, otherwise negative category.

  • So threshold selection will directly affect the quality of our logistic regression model.

  • FPR false positive rate and positive real rate of this index with the threshold value changes with the rise with the fall. TPR high and low FPR is our hope.

  • ROC curve in FIG.

  • 

  • FPR in the horizontal axis, TPR vertical axis, drawn to a different threshold corresponding ROC curve. The higher the arch curve ROC, have described higher in the lower region of the FPR TPR.

  • The area under the ROC curve, AUC (area under curve) can measure the quality of the model.

 

 

The next section will publish calculation of loss function

There are follow-up gradient descent method to solve the logistic regression, the gradient descent method improvement of content, then offer logistic regression handwritten codes

Thanks for attention