mse

Half mean squared error

Syntax

dlY = mse(dlX,targets)

dlY = mse(dlX,targets,'DataFormat',FMT)

Description

The half mean squared error operation computes the half mean squared error loss between network predictions and target values for regression tasks.

The loss is calculated using the following formula

$$\text{loss}=\frac{1}{2N}{\displaystyle \sum _{i=1}^M{(X_i-T_i)}^2}$$

where X_i is the network response, T_i is the target value, M is the total number of responses in X (across all observations), and N is the total number of observations in X.

Note

This function computes the half mean squared error loss between predictions and targets stored as dlarray data. If you want to calculate the half mean squared error loss within a layerGraph object or Layer array for use with trainNetwork, use the following layer:

• regressionLayer

dlY = mse(dlX,targets) computes the half mean squared error loss between the predictions dlX and the target values targets for regression problems. The input dlX is a formatted dlarray with dimension labels. The output dlY is an unformatted scalar dlarray with no dimension labels.

dlY = mse(dlX,targets,'DataFormat',FMT) also specifies the dimension format FMT when dlX is not a formatted dlarray.

Examples

Find Half Mean Squared Error Between Predicted and Target Values

The half mean squared error evaluates how well the network predictions correspond to the target values.

Create the input predictions as a single observation of random values with a height and width of six and a single channel.

height = 6;
width = 6;
channels = 1;
observations = 1;

X = rand(height,width,channels,observations);
dlX = dlarray(X,'SSCB')

Create the target values as a numeric array with the same dimension order as the input data dlX.

targets = ones(height,width,channels,observations);

Compute the half mean squared error between the predictions and the targets.

dlY = mse(dlX,targets)

dlY =

  1x1 dlarray

    5.2061

Input Arguments

dlX — Predictions

dlarray | numeric array

Predictions, specified as a dlarray with or without dimension labels or a numeric array. When dlX is not a formatted dlarray, you must specify the dimension label format using 'DataFormat',FMT. If dlX is a numeric array, targets must be a dlarray.

Data Types: single | double

targets — Target values

dlarray | numeric array

Target values, specified as a formatted or unformatted dlarray or a numeric array.

If targets is a formatted dlarray, its dimension format must be the same as the format of X, or the same as 'DataFormat' if X is unformatted

If targets is an unformatted dlarray or a numeric array, the size of targets must exactly match the size of X. The format of X or the value of 'DataFormat' is implicitly applied to targets.

Data Types: single | double

FMT — Dimension order of unformatted data

char array | string

Dimension order of unformatted input data, specified as the comma-separated pair consisting of 'DataFormat' and a character array or string FMT that provides a label for each dimension of the data. Each character in FMT must be one of the following:

• 'S' — Spatial

• 'C' — Channel

• 'B' — Batch (for example, samples and observations)

• 'T' — Time (for example, sequences)

• 'U' — Unspecified

You can specify multiple dimensions labeled 'S' or 'U'. You can use the labels 'C', 'B', and 'T' at most once.

You must specify 'DataFormat',FMT when the input data dlX is not a formatted dlarray.

Example: 'DataFormat','SSCB'

Data Types: char | string

Output Arguments

dlY — Half mean squared error loss

dlarray scalar

Half mean squared error loss, returned as a dlarray scalar without dimension labels. The output dlY has the same underlying data type as the input dlX.

More About

Half Mean Squared Error Loss

The mse function computes the half-mean-squared-error loss for regression problems. For more information, see the definition of Regression Output Layer on the RegressionOutputLayer reference page.

Extended Capabilities

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Usage notes and limitations:

• When at least one of the following input arguments is a gpuArray or a dlarray with underlying data of type gpuArray, this function runs on the GPU:

  • dlX

  • targets

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).