weighted loss function

The weighted loss function introduces weights based on the standard loss function, and is used to assign different importance to different samples or different categories when training the model.

In classification problems, the cross-entropy loss function is usually used as the standard loss function. The form of the cross-entropy loss function is as follows:

$$\mathcal{L}=-\frac{1}{N}\sum _{i=1}^N\sum _{j=1}^C{y}_{i,j}\log p_{i,j}$$

Among them, $N$ represents the sample size,$C$ represents the number of categories,$y_{i,j}$Indicates the $The\; true\; category\; of\; i$ samples is$Probability\; of\; j$ (usually 0 or 1),$p_{i,j}$Indicates that the model predicts the $i$ samples are class$The\; probability\; of\; j$ .

In the weighted loss function, a weight vector $w$ , used to give different importance to different samples or different categories. The form of the weighted cross-entropy loss function is as follows:

$$\mathcal{L}=-\frac{1}{N}\sum _{i=1}^N\sum _{j=1}^C{w}_j{y}_{i,j}\log p_{i,j}$$

Among them, $w_j$Indicates the jjthThe weights of the$j\; categories.$if$w_j$The larger the value, the higher the importance of the category, and more attention should be paid to the classification accuracy of the category when training the model. Conversely, if $w_j$The smaller the value, the lower the importance of the category, and the classification accuracy of the category can be dealt with more leniently when training the model.

In practical applications, weighted loss functions are usually used to solve the problem of class imbalance, that is, the number of samples of some classes is small, resulting in a model with low classification accuracy for these classes during training and testing. By setting appropriate weights, the classification accuracy of the model for these categories can be improved.