Loss Functions

Loss functions are crucial in machine learning as they quantify the difference between predicted and actual values, serving as a guide for the model to optimize its parameters. Here are various loss functions implemented in Mojo's machine learning library.

Provided Functions

Function mse (Mean Squared Error)

• Function Signature:

  fn mse(predicted: Tensor, expected: Tensor) raises -> Tensor

• Brief Explanation: Computes the Mean Squared Error (MSE) between the predicted and expected tensors. MSE is a common loss function for regression problems, measuring the average squared difference between corresponding elements.

Function mae (Mean Absolute Error)

• Function Signature:

  fn mae(predicted: Tensor, expected: Tensor) raises -> Tensor

• Brief Explanation: Computes the Mean Absolute Error (MAE) between the predicted and expected tensors. MAE is another loss function for regression, measuring the average absolute difference between corresponding elements.

Function mape (Mean Absolute Percentage Error)

• Function Signature:

  fn mape(predicted: Tensor, expected: Tensor) raises -> Tensor

• Brief Explanation: Computes the Mean Absolute Percentage Error (MAPE) between the predicted and expected tensors. MAPE is a loss function suitable for regression tasks, measuring the average percentage difference between corresponding elements.

Function msle (Mean Squared Logarithmic Error)

• Function Signature:

  fn msle(predicted: Tensor, expected: Tensor) raises -> Tensor

• Brief Explanation: Computes the Mean Squared Logarithmic Error (MSLE) between the predicted and expected tensors. MSLE is often used when the scale of the target variable varies widely.

Function bce (Binary Cross-Entropy)

• Function Signature:

  fn bce(predicted: Tensor, expected: Tensor) raises -> Tensor

• Brief Explanation: Computes the Binary Cross-Entropy (BCE) between the predicted and expected tensors. BCE is a common loss function for binary classification problems, measuring the cross-entropy between the predicted probabilities and true labels.

Function cce (Categorical Cross-Entropy)

• Function Signature:

  fn cce(predicted: Tensor, expected: Tensor) raises -> Tensor

• Brief Explanation: Computes the Categorical Cross-Entropy (CCE) between the predicted and expected tensors. CCE is a widely used loss function for multi-class classification problems, measuring the cross-entropy between predicted class probabilities and true one-hot encoded labels.

Function cfce (Center-Focused Categorical Cross-Entropy)

• Function Signature:

  fn cfce(predicted: Tensor, expected: Tensor) raises -> Tensor

• Brief Explanation: Computes the Center-Focused Categorical Cross-Entropy (CFCE) between the predicted and expected tensors. This may be a custom loss function designed to focus on center classes in multi-class classification problems.

These loss functions provide a diverse set of options for different types of machine learning tasks, helping to guide the training process towards optimal model parameters.