Log-Cosh Loss is a loss function commonly used in regression problems within the field of machine learning. It is particularly appreciated for its smoothness, which makes it less sensitive to outliers compared to traditional loss functions like Mean Squared Error (MSE) and Mean Absolute Error (MAE).
The Log-Cosh Loss is defined mathematically as the logarithm of the hyperbolic cosine of the prediction error. Specifically, it can be expressed as:
Log-Cosh(y, ŷ) = Σ log(cosh(ŷ - y))
Where:
- y is the true value.
- ŷ is the predicted value.
Unlike the MSE, which squares the error, the Log-Cosh Loss does not excessively penalize larger errors, thereby providing a more balanced approach to training models. This characteristic allows it to behave like MSE when the error is small but transitions to behave like MAE when the error is larger, effectively combining the strengths of both loss functions.
Log-Cosh Loss is particularly useful in scenarios where robustness to outliers is desired, making it a popular choice for various regression tasks in machine learning applications, such as predicting real estate prices or stock market trends. Its smooth gradient also facilitates optimization during the training phase, leading to potentially faster convergence of learning algorithms.