Class MeanSquaredErrorLoss<T>

Namespace

AiDotNet.LossFunctions

Assembly

AiDotNet.dll

Implements the Mean Squared Error (MSE) loss function.

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

Type Parameters

T

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

Inheritance

object

LossFunctionBase<T>

MeanSquaredErrorLoss<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 Squared Error is one of the most common loss functions used in regression problems. It measures the average squared difference between predicted and actual values.

The formula is: MSE = (1/n) * ?(predicted - actual)²

MSE has these key properties:

• It heavily penalizes large errors due to the squaring operation
• It treats all data points equally
• It's differentiable everywhere, making it suitable for gradient-based optimization
• It's always positive, with perfect predictions giving a value of zero

MSE is ideal for problems where:

• You're predicting continuous values (like prices, temperatures, etc.)
• Outliers should be given extra attention (due to the squaring)
• The prediction errors follow a normal distribution

Methods

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

Calculates the derivative of the Mean Squared 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 MSE for each prediction.

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

Calculates the Mean Squared 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 squared error value.

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

Calculates both MSE 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.