Class MeanBiasErrorLoss<T>

Namespace

AiDotNet.LossFunctions

Assembly

AiDotNet.dll

Implements the Mean Bias Error (MBE) loss function.

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

Type Parameters

T

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

Inheritance

object

LossFunctionBase<T>

MeanBiasErrorLoss<T>

Implements

ILossFunction<T>

Inherited Members

LossFunctionBase<T>.NumOps

LossFunctionBase<T>.Engine

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

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 Bias Error is a diagnostic metric that reveals systematic bias in predictions. Unlike MSE or MAE which measure error magnitude, MBE tells you the *direction* of errors.

The formula is: MBE = (1/n) * Σ(actual - predicted)

Think of MBE like this:

• MBE = 0: Your model is unbiased (errors cancel out)
• MBE > 0: Your model tends to under-predict (predictions are too low)
• MBE < 0: Your model tends to over-predict (predictions are too high)

Example scenarios:

• Weather forecasting: MBE = +2°C means you're consistently predicting 2 degrees too cold
• Price predictions: MBE = -$5,000 means you're consistently overestimating by $5,000
• Medical diagnostics: MBE helps detect if a test systematically over/under-estimates values

Key properties:

• Can be positive, negative, or zero (unlike MSE/RMSE which are always non-negative)
• Errors of opposite signs cancel each other out
• Not sensitive to the magnitude of individual errors
• Useful for detecting systematic bias, not for measuring overall accuracy
• Often used alongside RMSE or MAE for a complete error analysis

MBE is ideal for:

• Diagnosing systematic prediction bias
• Calibrating models that consistently over/under-predict
• Quality control in measurement systems
• Understanding if your model needs adjustment in a specific direction

Important: MBE should not be used alone for model evaluation, as positive and negative errors cancel out. A model with large errors in both directions could have MBE ≈ 0. Always use MBE together with metrics like RMSE or MAE.

Methods

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

Calculates the derivative of the Mean Bias 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 MBE for each prediction.

Remarks

The derivative is constant: d(MBE)/d(predicted) = -1/n for all elements. This means each prediction contributes equally to reducing bias, regardless of the current error.

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

Calculates the Mean Bias 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 bias error value. Positive values indicate under-prediction, negative values indicate over-prediction.