rmseMetric

Deep learning root mean squared error metric

Since R2023b

Description

Use a RMSEMetric object to track the root mean squared error (RMSE) when you train or test a deep neural network.

To specify which metrics to use during training, specify the Metrics option of the trainingOptions function. You can use this option only when you train a network using the trainnet function.

To plot the metrics during training, in the training options, specify Plots as "training-progress". If you specify the ValidationData training option, then the software also plots and records the metric values for the validation data. To output the metric values to the Command Window during training, in the training options, set Verbose to true.

You can also access the metrics after training using the TrainingHistory and ValidationHistory fields from the second output of the trainnet function.

To specify which metrics to use when you test a neural network, use the metrics argument of the testnet function.

Creation

Syntax

metric = rmseMetric

metric = rmseMetric(Name=Value)

Description

metric = rmseMetric creates a RMSEMetric object. You can then specify metric as the Metrics name-value argument in the trainingOptions function or the metrics argument of the testnet function. With no additional options specified, this syntax is equivalent to specifying the metric as "rmse".

metric = rmseMetric(Name=Value) sets the Name, NetworkOutput, and NormalizationFactor properties using name-value arguments.

Properties

Name — Metric name

"RMSE" (default) | string scalar | character vector

Metric name, specified as a string scalar or character vector. The metric name appears in the training plot, the verbose output, the training information that you can access as the second output of the trainnet function, and table output of the testnet function.

Data Types: char | string

NetworkOutput — Name of layer to apply metric to

[] (default) | string scalar | character vector

This property is read-only.

Name of the layer to apply the metric to, specified as [], a string scalar, or a character vector. When the value is [], the software passes all of the network outputs to the metric.

Note

You can apply the built-in metric to only a single output. If you have a network with multiple outputs, then you must specify the NetworkOutput name-value argument. To apply built-in metrics to multiple outputs, you must create a metric object for each output.

Data Types: char | string

NormalizationFactor — Divisor for normalizing metric sum

"all-elements" (default) | "batch-size"

This property is read-only.

Divisor for normalizing the metric sum, specified as one of these values:

• "batch-size" — Divide the metric sum by the number of elements in the targets.

• "all-elements" — Divide the metric sum by the number of observations.

Data Types: char | string

Maximize — Flag to maximize metric

0 (false)

This property is read-only.

Flag to maximize metric, specified as 0 (false) if the optimal value for the metric occurs when the metric is minimized.

For this metric, the Maximize value is always set to 0 (false).

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical

Object Functions

trainingOptions	Options for training deep learning neural network
trainnet	Train deep learning neural network

Examples

Plot and Record RMSE During Training

Plot and record the training and validation RMSE when you train a deep neural network.

Load the training and test data from the DigitsDataTrain and DigitsDataTest MAT files, respectively. The data set contains synthetic images of handwritten digits and the corresponding angles (in degrees) by which each image is rotated. The anglesTrain and anglesTest variables are the rotation angles in degrees.

load DigitsDataTrain.mat
load DigitsDataTest.mat

You can train a deep learning network to predict the rotation angle of the digit.

Create an image regression network.

layers = [
    imageInputLayer([28 28 1])
    convolution2dLayer(3,8,Padding="same")
    batchNormalizationLayer
    reluLayer
    averagePooling2dLayer(2,'Stride',2)
    convolution2dLayer(3,16,Padding="same")
    batchNormalizationLayer
    reluLayer
    averagePooling2dLayer(2,'Stride',2)
    convolution2dLayer(3,32,Padding="same")
    batchNormalizationLayer
    reluLayer
    convolution2dLayer(3,32,Padding="same")
    batchNormalizationLayer
    reluLayer
    dropoutLayer(0.2)
    fullyConnectedLayer(1)];

Create an RMSEMetric object and set the NormalizationFactor property to "batch-size". You can use this object to record and plot the training and validation RMSE.

metric = rmseMetric(NormalizationFactor="batch-size")

metric = 
  RMSEMetric with properties:

                   Name: "RMSE"
    NormalizationFactor: "batch-size"
          NetworkOutput: []
               Maximize: 0

Specify the RMSE metric in the training options. To plot the RMSE during training, set Plots to "training-progress". To output the values during training, set Verbose to true.

options = trainingOptions("adam", ...
    MaxEpochs=5, ...
    Metrics=metric, ...
    ValidationData={XTest,anglesTest}, ...
    ValidationFrequency=50, ...
    Plots="training-progress", ...
    Verbose=true);

Train the network using the trainnet function.

[net,info] = trainnet(XTrain,anglesTrain,layers,"mse",options);

    Iteration    Epoch    TimeElapsed    LearnRate    TrainingLoss    ValidationLoss    TrainingRMSE    ValidationRMSE
    _________    _____    ___________    _________    ____________    ______________    ____________    ______________
            0        0       00:00:01        0.001                            688.66                            26.242
            1        1       00:00:02        0.001          648.74                             25.47                  
           50        2       00:00:12        0.001          210.71             335.2          14.516            18.309
          100        3       00:00:19        0.001          130.55            131.78          11.426            11.479
          150        4       00:00:26        0.001          89.997            126.48          9.4867            11.246
          195        5       00:00:32        0.001          88.085            93.085          9.3854             9.648
Training stopped: Max epochs completed

Access the loss and RMSE values for the validation data.

info.ValidationHistory

ans=5×3 table
    Iteration     Loss      RMSE 
    _________    ______    ______

         0       688.66    26.242
        50        335.2    18.309
       100       131.78    11.479
       150       126.48    11.246
       195       93.085     9.648

More About

Root Mean Squared Error (RMSE)

For a set of predictions Y and a set of targets T, the software computes the RMSE using this equation:

$$\text{RMSE = }\sqrt{\frac{1}{N}{\displaystyle \sum _{i=1}^n|Y_i-T_i{|}^2}},$$

where N is the normalization factor and n is the number of observations. When the NormalizationFactor option is "all-elements", N is equal to n.

Version History

Introduced in R2023b