RegressionOutputLayer

Regression output layer

regressionLayer is not recommended. Use the trainnet function and set the loss function to "mse" instead. For more information, see Version History.

Description

A regression layer computes the half-mean-squared-error loss for regression tasks.

Creation

Create a regression output layer using regressionLayer.

Properties

Regression Output

ResponseNames — Names of responses

{} (default) | cell array of character vectors | string array

Names of the responses, specified a cell array of character vectors or a string array. At training time, the software automatically sets the response names according to the training data. The default is {}.

Data Types: cell

LossFunction — Loss function for training

'mean-squared-error'

Loss function the software uses for training, specified as 'mean-squared-error'.

Layer

Name — Layer name

"" (default) | character vector | string scalar

Layer name, specified as a character vector or a string scalar. For Layer array input, the trainNetwork function automatically assigns names to layers with the name "".

The RegressionOutputLayer object stores this property as a character vector.

Data Types: char | string

NumInputs — Number of inputs

1 (default)

Number of inputs to the layer, returned as 1. This layer accepts a single input only.

Data Types: double

InputNames — Input names

{'in'} (default)

Input names, returned as {'in'}. This layer accepts a single input only.

Data Types: cell

NumOutputs — Number of outputs

0 (default)

Number of outputs of the layer, returned as 0. This layer has no outputs.

Data Types: double

OutputNames — Output names

{} (default)

Output names of the layer, returned as {}. This layer has no outputs.

Data Types: cell

Examples

Create Regression Output Layer

Create a regression output layer.

Create a regression output layer with the name 'routput'.

layer = regressionLayer('Name','routput')

layer = 
  RegressionOutputLayer with properties:

             Name: 'routput'
    ResponseNames: {}

   Hyperparameters
     LossFunction: 'mean-squared-error'

The default loss function for regression is mean-squared-error.

Include a regression output layer in a Layer array.

layers = [ ...
    imageInputLayer([28 28 1])
    convolution2dLayer(12,25)
    reluLayer
    fullyConnectedLayer(1)
    regressionLayer]

layers = 
  5x1 Layer array with layers:

     1   ''   Image Input         28x28x1 images with 'zerocenter' normalization
     2   ''   2-D Convolution     25 12x12 convolutions with stride [1  1] and padding [0  0  0  0]
     3   ''   ReLU                ReLU
     4   ''   Fully Connected     1 fully connected layer
     5   ''   Regression Output   mean-squared-error

More About

Regression Output Layer

A regression layer computes the half-mean-squared-error loss for regression tasks. For typical regression problems, a regression layer must follow the final fully connected layer.

For a single observation, the mean-squared-error is given by:

$$\text{MSE}={\displaystyle \sum }_{i=1}^R\frac{{(t_i-y_i)}^2}{R},$$

where R is the number of responses, t_i is the target output, and y_i is the network’s prediction for response i.

For image and sequence-to-one regression networks, the loss function of the regression layer is the half-mean-squared-error of the predicted responses, not normalized by R:

$$\text{loss}=\frac{1}{2}{\displaystyle \sum }_{i=1}^R{(t_i-y_i)}^2.$$

For image-to-image regression networks, the loss function of the regression layer is the half-mean-squared-error of the predicted responses for each pixel, not normalized by R:

$$\text{loss}=\frac{1}{2}{\displaystyle \sum }_{p=1}^{HWC}{(t_p-y_p)}^2,$$

where H, W, and C denote the height, width, and number of channels of the output respectively, and p indexes into each element (pixel) of t and y linearly.

For sequence-to-sequence regression networks, the loss function of the regression layer is the half-mean-squared-error of the predicted responses for each time step, not normalized by R:

$$\text{loss}=\frac{1}{2S}{\displaystyle \sum }_{i=1}^S{\displaystyle \sum }_{j=1}^R{(t_{ij}-y_{ij})}^2,$$

where S is the sequence length.

When training, the software calculates the mean loss over the observations in the mini-batch.

Version History

Introduced in R2017a

R2024a: Not recommended

Starting in R2024a, RegressionOutputLayer objects are not recommended, use the trainnet and set the loss function to "mse" instead.

There are no plans to remove support for RegressionOutputLayer objects. However, the trainnet function has these advantages and is recommended instead:

• trainnet supports dlnetwork objects, which support a wider range of network architectures that you can create or import from external platforms.

• trainnet enables you to easily specify loss functions. You can select from built-in loss functions or specify a custom loss function.

• trainnet outputs a dlnetwork object, which is a unified data type that supports network building, prediction, built-in training, visualization, compression, verification, and custom training loops.

• trainnet is typically faster than trainNetwork.

This table shows some typical usages of the trainNetwork function with RegressionOutputLayer objects and how to update your code to use the trainnet function instead.

Not Recommended	Recommended
net = trainNetwork(X,T,layers,options), where layers contains a RegressionOutputLayer object.	net = trainnet(X,T,layers,"mse",options); In this example, layers specifies same network without a RegressionOutputLayer object.
net = trainNetwork(data,layers,options), where layers contains a RegressionOutputLayer object.	net = trainnet(data,layers,"mse",options); In this example, layers specifies same network without a RegressionOutputLayer object.