Class MeanAbsoluteErrorLoss<T>

Namespace

AiDotNet.LossFunctions

Assembly

AiDotNet.dll

Implements the Mean Absolute Error (MAE) loss function.

public class MeanAbsoluteErrorLoss<T> : LossFunctionBase<T>, ILossFunction<T>

Type Parameters

T

The numeric type used for calculations (e.g., float, double).

Inheritance

object

LossFunctionBase<T>

MeanAbsoluteErrorLoss<T>

Implements

ILossFunction<T>

Inherited Members

LossFunctionBase<T>.NumOps

LossFunctionBase<T>.Engine

LossFunctionBase<T>.ValidateVectorLengths(Vector<T>, Vector<T>)

object.Equals(object)

object.Equals(object, object)

object.GetHashCode()

object.GetType()

object.MemberwiseClone()

object.ReferenceEquals(object, object)

object.ToString()

Extension Methods

LossFunctionExtensions.ComputeGradient<T>(ILossFunction<T>, Tensor<T>, Tensor<T>)

LossFunctionExtensions.ComputeLoss<T>(ILossFunction<T>, Tensor<T>, Tensor<T>)

Remarks

For Beginners: Mean Absolute Error measures the average absolute difference between predicted and actual values.

The formula is: MAE = (1/n) * ?|predicted - actual|

MAE has these key properties:

• It treats all errors linearly (unlike MSE which squares errors)
• It's less sensitive to outliers than MSE
• It's simple to understand as the average magnitude of errors
• It's always positive, with perfect predictions giving a value of zero

MAE is ideal for problems where:

• You're predicting continuous values
• You want all errors to be treated equally (not emphasizing large errors)
• The prediction errors follow a Laplace distribution
• Outliers should not have a disproportionate influence on the model

Methods

CalculateDerivative(Vector<T>, Vector<T>)

Calculates the derivative of the Mean Absolute Error loss function.

public override Vector<T> CalculateDerivative(Vector<T> predicted, Vector<T> actual)

Parameters

predicted Vector<T>

The predicted values from the model.

actual Vector<T>

The actual (target) values.

Returns

Vector<T>

A vector containing the derivatives of MAE for each prediction.

Remarks

The derivative of MAE is sign(predicted-actual)/n where:

• sign(x) = 1 if x > 0
• sign(x) = -1 if x < 0
• sign(x) = 0 if x = 0 (subgradient at the kink point)

CalculateLoss(Vector<T>, Vector<T>)

Calculates the Mean Absolute Error between predicted and actual values.

public override T CalculateLoss(Vector<T> predicted, Vector<T> actual)

Parameters

predicted Vector<T>

The predicted values from the model.

actual Vector<T>

The actual (target) values.

Returns

T

The mean absolute error value.

CalculateLossAndGradientGpu(IGpuTensor<T>, IGpuTensor<T>)

Calculates both MAE loss and gradient on GPU in a single efficient pass.

public override (T Loss, IGpuTensor<T> Gradient) CalculateLossAndGradientGpu(IGpuTensor<T> predicted, IGpuTensor<T> actual)

Parameters

predicted IGpuTensor<T>

The predicted GPU tensor from the model.

actual IGpuTensor<T>

The actual (target) GPU tensor.

Returns

(T Loss, IGpuTensor<T> Gradient)

A tuple containing the loss value and gradient tensor.