Machine learning loss function (Loss Function)

Loss Function is a key concept in machine learning and deep learning. It is used to measure the difference or error between the prediction of the model and the actual target. The choice of loss function is crucial for model training and performance evaluation, and different tasks and problems usually require different loss functions.

Here are some common loss functions and their applications in different tasks:

1. Mean Squared Error (MSE) :

   • Used in regression problems, it measures the average of the squared errors between the model's predicted values ​​and the actual values.
   • MSE = (1/n) * Σ(yi - ŷi)², where yi is the actual value, ŷi is the predicted value, and n is the sample size.

2. Mean Absolute Error (MAE) :

   • Used in regression problems, it measures the average of the absolute errors between the model's predicted values ​​and the actual values.
   • MAE = (1/n) * Σ|this - ŷi|。

3. Cross-Entropy Loss :

   • Used for classification problems, measuring the difference between the model's classification probability distribution and the actual labels.
   • For binary classification problems: Binary Cross-Entropy Loss.
   • For multi-classification problems: Categorical Cross-Entropy Loss.

4. Log Loss :

   • Typically used in binary classification problems, it is a form of cross-entropy loss.
   • Log Loss = -Σ(this * log(i) + (1 - this) * log(1 - i)).

5. Winner takes all loss (Hinge Loss) :

   • Used in classification problems such as support vector machines (SVM) to encourage the model to have a larger margin of correct classification.
   • Hinge Loss = Σmax(0, 1 - yi * ŷi), where yi is the true label and ŷi is the prediction of the model.

6. Huber loss :

   • Used for regression problems, it is a mixture of mean square error (MSE) and mean absolute error (MAE) and is insensitive to outliers.

7. Custom loss :

   • For specific problems, custom loss functions can be defined to meet the special needs of the task.

Choosing an appropriate loss function depends on your problem type and task goals. During the training process, the optimization algorithm attempts to minimize the loss function to adjust the model parameters so that it can better fit the training data and generalize to new data. Different loss functions will lead to different training behavior and model performance, so choosing an appropriate loss function is very important.