Error Function

What is an Error function? Error Function Explained

An error function, also known as a loss function or objective function, is a mathematical function that quantifies the discrepancy between the predicted output of a machine learning model and the true or desired output. This function is a crucial component of the training process as it guides the model toward minimizing the error and improving its predictive performance.

The choice of an error function depends on the type of machine learning task, such as classification, regression, or sequence generation. Here are some commonly used error functions for different tasks:

Mean Squared Error (MSE): MSE is popular for regression tasks. It measures the average squared difference between the predicted values and the true values. Minimizing MSE encourages the model to reduce both large and small errors. It is computed as the mean of the squared differences between the predicted and true values.

Mean Absolute Error (MAE): MAE is another function for regression tasks. It measures the average absolute difference between the predicted values and the true values. MAE is less sensitive to outliers compared to MSE as it does not square the differences.

Binary Cross-Entropy Loss: Binary cross-entropy is commonly used for binary classification tasks. It calculates the average negative logarithm of the predicted probabilities for the correct class. Minimizing binary cross-entropy encourages the model to assign high probabilities to the correct class and low probabilities to the incorrect class.

Categorical Cross-Entropy Loss: Categorical cross-entropy is used for multi-class classification tasks. It extends binary cross-entropy to handle multiple classes. It calculates the average negative logarithm of the predicted probabilities for the true class label. Similar to binary cross-entropy, minimizing categorical cross-entropy encourages the model to assign high probabilities to the correct class and low probabilities to the incorrect classes.

Hinge Loss: Hinge loss is commonly used for training models in support vector machines (SVMs) and is also employed in some models for binary classification tasks. It aims to maximize the margin between the decision boundary and the data points. Hinge loss penalizes misclassifications and encourages the model to correctly classify instances with a margin.

Log Loss (Cross-Entropy Loss): Log loss, or cross-entropy loss, is used in probabilistic models such as logistic regression or deep neural networks for classification tasks. It measures the discrepancy between the predicted probabilities and the true class labels. Minimizing log loss encourages the model to output high probabilities for the true class and low probabilities for the other classes.

The selection of an appropriate error function depends on the characteristics of the problem, the nature of the data, and the objectives of the model. It is essential to choose an error function that aligns with the specific requirements of the task and guides the model toward achieving the desired behavior.

It’s worth noting that this function is optimized during the training process by adjusting the model’s parameters using optimization techniques like gradient descent. The optimization process iteratively updates the model parameters to minimize the error function and improve the model’s performance on the training data.