How to Use Metrics for Deep Learning with Keras in Python

The Keras library provides a way to calculate and report on a suite of standard metrics when training deep learning models.

In addition to offering standard metrics for classification and regression problems, Keras also allows you to define and report on your own custom metrics when training deep learning models. This is particularly useful if you want to keep track of a performance measure that better captures the skill of your model during training.

In this tutorial, you will discover how to use the built-in metrics and how to define and use your own metrics when training deep learning models in Keras.

After completing this tutorial, you will know:

  • How Keras metrics work and how you can use them when training your models.
  • How to use regression and classification metrics in Keras with worked examples.
  • How to define and use your own custom metric in Keras with a worked example.

Let’s get started.

Metrics and How to Use Custom Metrics for Deep Learning with Keras in Python

Metrics and How to Use Custom Metrics for Deep Learning with Keras in Python
Photo by Indi Samarajiva, some rights reserved.

Tutorial Overview

This tutorial is divided into 4 parts; they are:

  1. Keras Metrics
  2. Keras Regression Metrics
  3. Keras Classification Metrics
  4. Custom Metrics in Keras

Keras Metrics

Keras allows you to list the metrics to monitor during the training of your model.

You can do this by specifying the “metrics” argument and providing a list of function names (or function name aliases) to the compile() function on your model.

For example:

The specific metrics that you list can be the names of Keras functions (like mean_squared_error) or string aliases for those functions (like ‘mse‘).

Metric values are recorded at the end of each epoch on the training dataset. If a validation dataset is also provided, then the metric recorded is also calculated for the validation dataset.

All metrics are reported in verbose output and in the history object returned from calling the fit() function. In both cases, the name of the metric function is used as the key for the metric values. In the case of metrics for the validation dataset, the “val_” prefix is added to the key.

Both loss functions and explicitly defined Keras metrics can be used as training metrics.

Keras Regression Metrics

Below is a list of the metrics that you can use in Keras on regression problems.

  • Mean Squared Error: mean_squared_error, MSE or mse
  • Mean Absolute Error: mean_absolute_error, MAE, mae
  • Mean Absolute Percentage Error: mean_absolute_percentage_error, MAPE, mape
  • Cosine Proximity: cosine_proximity, cosine

The example below demonstrates these 4 built-in regression metrics on a simple contrived regression problem.

Running the example prints the metric values at the end of each epoch.

A line plot of the 4 metrics over the training epochs is then created.

Line Plot of Built-in Keras Metrics for Regression

Line Plot of Built-in Keras Metrics for Regression

Note that the metrics were specified using string alias values [‘mse‘, ‘mae‘, ‘mape‘, ‘cosine‘] and were referenced as key values on the history object using their expanded function name.

We could also specify the metrics using their expanded name, as follows:

We can also specify the function names directly if they are imported into the script.

You can also use the loss functions as metrics.

For example, you could use the Mean squared Logarithmic Error (mean_squared_logarithmic_error, MSLE or msle) loss function as a metric as follows:

Keras Classification Metrics

Below is a list of the metrics that you can use in Keras on classification problems.

  • Binary Accuracy: binary_accuracy, acc
  • Categorical Accuracy: categorical_accuracy, acc
  • Sparse Categorical Accuracy: sparse_categorical_accuracy
  • Top k Categorical Accuracy: top_k_categorical_accuracy (requires you specify a k parameter)
  • Sparse Top k Categorical Accuracy: sparse_top_k_categorical_accuracy (requires you specify a k parameter)

Accuracy is special.

Regardless of whether your problem is a binary or multi-class classification problem, you can specify the ‘acc‘ metric to report on accuracy.

Below is an example of a binary classification problem with the built-in accuracy metric demonstrated.

Running the example reports the accuracy at the end of each training epoch.

A line plot of accuracy over epoch is created.

Line Plot of Built-in Keras Metrics for Classification

Line Plot of Built-in Keras Metrics for Classification

Custom Metrics in Keras

You can also define your own metrics and specify the function name in the list of functions for the “metrics” argument when calling the compile() function.

A metric I often like to keep track of is Root Mean Square Error, or RMSE.

You can get an idea of how to write a custom metric by examining the code for an existing metric.

For example, below is the code for the mean_squared_error loss function and metric in Keras.

K is the backend used by Keras.

From this example and other examples of loss functions and metrics, the approach is to use standard math functions on the backend to calculate the metric of interest.

For example, we can write a custom metric to calculate RMSE as follows:

You can see the function is the same code as MSE with the addition of the sqrt() wrapping the result.

We can test this in our regression example as follows. Note that we simply list the function name directly rather than providing it as a string or alias for Keras to resolve.

Running the example reports the custom RMSE metric at the end of each training epoch.

At the end of the run, a line plot of the custom RMSE metric is created.

Line Plot of Custom RMSE Keras Metric for Regression

Line Plot of Custom RMSE Keras Metric for Regression

Your custom metric function must operate on Keras internal data structures that may be different depending on the backend used (e.g. tensorflow.python.framework.ops.Tensor when using tensorflow) rather than the raw yhat and y values directly.

For this reason, I would recommend using the backend math functions wherever possible for consistency and execution speed.

Further Reading

This section provides more resources on the topic if you are looking go deeper.

Summary

In this tutorial, you discovered how to use Keras metrics when training your deep learning models.

Specifically, you learned:

  • How Keras metrics works and how you configure your models to report on metrics during training.
  • How to use classification and regression metrics built into Keras.
  • How to define and report on your own custom metrics efficiently while training your deep learning models.

Do you have any questions?
Ask your questions in the comments below and I will do my best to answer.

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34 Responses to How to Use Metrics for Deep Learning with Keras in Python

  1. Gerrit Govaerts August 9, 2017 at 5:03 pm #

    Off topic but interesting none the less :
    1) how to train an ensemble of models in the same time it takes to train 1
    http://www.kdnuggets.com/2017/08/train-deep-learning-faster-snapshot-ensembling.html

    2) when not to use deep learning
    http://www.kdnuggets.com/2017/07/when-not-use-deep-learning.html

  2. Olivier August 11, 2017 at 10:06 pm #

    Hi Jason,

    Thanks again for another great topic on keras but I’m a R user !

    I can work with keras on R, but how about to implement custom metric ‘rmse’ on keras R please ?

    Because I find something like that on the github repository :
    metric_mean_squared_error <- function(y_true, y_pred) {
    keras$metrics$mean_squared_error(y_true, y_pred)
    }
    attr(metric_mean_squared_error, "py_function_name") <- "mean_squared_error"

    and my poor

    rmse <- function(y_true, y_pred) {
    K$sqrt(K$mean(K$square(y_pred – y_true)))
    }

    is not working ("nan" is returned)

    • Olivier August 11, 2017 at 10:28 pm #

      Ok finally I make it return a value different from ‘nan’, but the result is not the same as the square root of ‘mse’ from keras ?!? Maybe due to the arg ‘axis = -1’ ?

    • Jason Brownlee August 12, 2017 at 6:46 am #

      Sorry, I have not used Keras in R, I don’t have good advice for you at this stage.

  3. John December 14, 2017 at 10:50 pm #

    hi Jason,

    Thanks for your very good topic on evaluation metrics in keras. can you please tell me how to compute macro-F and the micro-F scores?

    thanks in advance

    • Jason Brownlee December 15, 2017 at 5:33 am #

      Sorry, I am not familiar with those scores John.

      Perhaps find a definition and code them yourself?

  4. Linda Cen December 22, 2017 at 5:26 am #

    Hi Jason,

    I used your “def rmse” in my code, but it returns the same result of mse.

    # define data and target value
    X = TFIDF_Array
    Y = df[‘Shrinkage’]

    # custom metric to calculate RMSE
    def RMSE(y_true, y_pred):
    return backend.sqrt(backend.mean(backend.square(y_pred – y_true), axis=-1))

    # define base model
    def regression_model():
    # create model
    model = Sequential()
    model.add(Dense(512, input_dim=X.shape[1], kernel_initializer=’uniform’, activation=’relu’))
    model.add(Dropout(0.5))
    model.add(Dense(1, kernel_initializer=’uniform’))
    # compile model
    model.compile(loss=’mse’, optimizer=’sgd’, metrics=[RMSE])
    return model

    # evaluate model
    estimator = KerasRegressor(build_fn=regression_model, nb_epoch=100, batch_size=32, verbose=0)
    kfold = KFold(n_splits=3, random_state=1)
    reg_results = cross_val_score(estimator, X, Y, cv=kfold)

    • Jason Brownlee December 22, 2017 at 5:37 am #

      Did the example in the post – copied exactly – work for you?

      • Linda Cen December 22, 2017 at 8:58 am #

        Epoch 496/500
        0s – loss: 3.9225e-04 – rmse: 0.0170
        Epoch 497/500
        0s – loss: 3.8870e-04 – rmse: 0.0169
        Epoch 498/500
        0s – loss: 3.8518e-04 – rmse: 0.0169
        Epoch 499/500
        0s – loss: 3.8169e-04 – rmse: 0.0168
        Epoch 500/500
        0s – loss: 3.7821e-04 – rmse: 0.0167

        It gave back different values from yours.

        • Linda Cen December 22, 2017 at 9:04 am #

          Epoch 497/500
          0s – loss: 0.0198 – mean_squared_error: 0.0198
          Epoch 498/500
          0s – loss: 0.0197 – mean_squared_error: 0.0197
          Epoch 499/500
          0s – loss: 0.0197 – mean_squared_error: 0.0197
          Epoch 500/500
          0s – loss: 0.0196 – mean_squared_error: 0.0196

          and these were the result when I used:
          metrics=[‘mean_squared_error’]

          I didn’t see any difference of MSE and RMSE here.

          Please advise. Thanks.

        • Jason Brownlee December 22, 2017 at 4:15 pm #

          Yes, this is to be expected. Machine learning algorithms are stochastic meaning that the same algorithm on the same data will give different results each time it is run. See this post for more details:
          https://machinelearningmastery.com/randomness-in-machine-learning/

  5. lila January 30, 2018 at 5:19 am #

    Dear Jason,
    Thank you again for the awsome blog and clear explanations
    If I understood well, RMSE should be equal to sqrt(mse), but this is not the case for my data:
    Epoch 130/1000

    10/200 [>………………………..] – ETA: 0s – loss: 0.0989 – rmse: 0.2656
    200/200 [==============================] – 0s 64us/step – loss: 0.2856 – rmse: 0.4070

    Please sir, how can we calculate the coefficient of determination

    • Jason Brownlee January 30, 2018 at 9:56 am #

      The mse may be calculated at the end of each batch, the rmse may be calculated at the end of the epoch because it is a metric.

  6. lila January 30, 2018 at 5:26 am #

    For the determination coefficient I use this basic code

    S1, S2 = 0, 0
    for i in range(len(Y)):
    S1 = S1 + (Y_pred_array[i] – mean_y)**2
    S2 = S2 + (Y_array[i] – mean_y)**2

    R2 = S1/S2

    But this gives give bad results

    • Walid March 6, 2018 at 6:21 am #

      How can you deal with Y_pred as iterable also it is a Tensor?

      Thanks

  7. sam February 28, 2018 at 5:58 pm #

    Thanks for the article. How does Keras compute a mean statistic in a per batch fashion? Does it internally (magically) aggregate the sum and count to that point in the epoch and print the measure or does it compute the measure per batch and then again re-compute the metric at the end of each epoch over the entire data?

    • Jason Brownlee March 1, 2018 at 6:09 am #

      I believe the sum is accumulated and printed at the end of each batch or end of each epoch. I don’t recall which.

  8. Walid March 6, 2018 at 6:18 am #

    Great post and just in time as usual;

    The issue is that I am trying to calculate the loss based on IoU (Intersection over union) and I have no clue how to do it using my backend (TensorFlow)
    My output is like this(xmin,ymin,xmax,ymax)

    Thanks

    • Jason Brownlee March 6, 2018 at 6:20 am #

      Sorry, I have not implemented (or heard of) that metric.

  9. MLT March 8, 2018 at 8:39 am #

    model.compile(loss=’mse’, optimizer=’adam’, metrics=[rmse])

    Epoch 496/500
    0s – loss: 1.2992e-06 – rmse: 9.7909e-04

    loss is mse. Should mse = rmse^2? Above value (9.7909e-04)^2 is 9.6e-8, which mismatch 1.2992e-06. Did I misunderstand something? Thanks.

    • Jason Brownlee March 8, 2018 at 2:54 pm #

      The loss and metrics might not be calculated at the same time, e.g. end of batch vs end of epoch.

      • MLT March 9, 2018 at 8:06 am #

        Thanks for reply.

        history = model.fit(X, X, epochs=500, batch_size=len(X), verbose=2)
        I thought the duration of batch is equal to one epoch, since batch_size=len(X). If it is correct?

        Furthermore, it seems that the loss of epoch is also updated each iteration.

        Epoch 496/500
        0s – loss: 1.2992e-06 – rmse: 9.7909e-04

        • Jason Brownlee March 10, 2018 at 6:13 am #

          No, one epoch is comprised of 1 or more batches. Often 32 samples per batch are used as a default.

          Lear more here:
          https://machinelearningmastery.com/gentle-introduction-mini-batch-gradient-descent-configure-batch-size/

          • MLT March 10, 2018 at 7:38 am #

            Thanks a lot for your time to explain and find the link.

            I am sorry. I think I did not express my thoughts correctly.

            In the above example, history = model.fit(X, X, epochs=500, batch_size=len(X), verbose=2)

            batch_size=len(X)
            batch_size: Integer or None. Number of samples per gradient update. If unspecified, batch_size will default to 32.

            Since batch_size has been specified as the length of testset, may I consider one epoch comprises 1 batch and the end of a batch is the time when an epoch is end? Model ’mse’ loss is the rmse^2.

          • Jason Brownlee March 11, 2018 at 6:15 am #

            Yes, correct.

  10. kazim March 13, 2018 at 8:58 pm #

    Thanks for the great article, Jason. I have 2 questions;

    1) I have a pipeline which has a sequence like : Normalizer –> KerasRegressor
    Can I simply use history = pipeline.fit(..) then plot metrics ?

    2) I have a KFold crossvalidation like that:
    kfold = StratifiedKFold(n_splits=3)
    results = cross_val_score(pipeline, X, Y, cv=kfold, scoring = mape)
    How I can plot that 3 CV fits’ metrics?

    Thanks.

    • Jason Brownlee March 14, 2018 at 6:19 am #

      No, I don’t believe you can easily access history when using the sklearn wrappers.

  11. George Kibirige March 29, 2018 at 7:42 pm #

    HI Dr. Jason Brownlee

    Thanks for good tutorial.

    What is the different between these two lines
    score = model.evaluate(data2_Xscaled, data2_Yscaled, verbose=verbose)
    y_hat = model.predict(data2_Xscaled)

    objective metric is the customized one def rmse(y_true, y_pred)

    the score value should also equal to y_hat

    • Jason Brownlee March 30, 2018 at 6:35 am #

      One evaluates the model the other makes a prediction.

  12. GARCIA LOPEZ ALFONSA April 24, 2018 at 9:21 pm #

    Hello Jason,
    Thanks for your work.

    I’m using MAE as metric in a multi-class classification problem with ordered classes.
    Because, in my problem it is not the same to classify a record of class 5 in the class 4, than to assign it to the class 1.

    My model is:

    network %
    layer_dense(units = 32, activation = “relu”, input_shape = c(38)) %>%
    layer_dense(units = 5, activation = “softmax”)

    network %>% compile(
    optimizer = “rmsprop”,
    loss = “categorical_crossentropy”,
    metrics = c(“mae”)
    )

    But the model does not correctly calculate the MAE.

    It is possible to use MAE for this classification problem?

    Tanks

  13. Ashwin July 7, 2018 at 2:28 pm #

    Do you have a code written for the mean_iou metric?

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