RegressionOutputLayer

Regression output layer

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, assembleNetwork, layerGraph, and dlnetwork functions automatically assign names to layers with the name ''.

Data Types: char | string

NumInputs — Number of inputs

1 (default)

This property is read-only.

Number of inputs of the layer. This layer accepts a single input only.

Data Types: double

InputNames — Input names

{"in"} (default)

This property is read-only.

Input names of the layer. This layer accepts a single input only.

Data Types: cell

NumOutputs — Number of outputs

0 (default)

Number of outputs of the layer. The layer has no outputs.

Data Types: double

OutputNames — Output names

{} (default)

Output names of the layer. The layer has no outputs.

Data Types: cell

Examples

Create 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