# mse

Half mean squared error

## Description

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

The loss is calculated using the following formula

$\text{loss}=\frac{1}{2N}\sum _{i=1}^{M}{\left({X}_{i}-{T}_{i}\right)}^{2}$

where Xi is the network response, Ti 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:

example

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 labels FMT when dlX is not a formatted dlarray.

## Examples

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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

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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

Target values, specified as a dlarray with or without dimension labels or a numeric array. If targets is an unformatted dlarray or a numeric array, it must have the same dimension order as the input dlX. The size of each dimension of targets must match the size of each corresponding dimension in dlX.

Data Types: single | double

Dimension order of unformatted input data, specified as the comma-separated pair consisting of 'DataFormat' and a character array or string 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', or 'T' at most once.

You must specify 'DataFormat' when the input data dlX is an unformatted dlarray.

Example: 'DataFormat','SSCB'

Data Types: char | string

## Output Arguments

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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.

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### 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.