Once you fit a deep learning neural network model, you must evaluate its performance on a test dataset.

This is critical, as the reported performance allows you to both choose between candidate models and to communicate to stakeholders about how good the model is at solving the problem.

The Keras deep learning API model is very limited in terms of the metrics that you can use to report the model performance.

I am frequently asked questions, such as:How can I calculate the precision and recall for my model?And:How can I calculate the F1-score or confusion matrix for my model?In this tutorial, you will discover how to calculate metrics to evaluate your deep learning neural network model with a step-by-step example.

After completing this tutorial, you will know:Let’s get started.

How to Calculate Precision, Recall, F1, and More for Deep Learning ModelsPhoto by John, some rights reserved.

This tutorial is divided into three parts; they are:We will use a standard binary classification problem as the basis for this tutorial, called the “two circles” problem.

It is called the two circles problem because the problem is comprised of points that when plotted, show two concentric circles, one for each class.

As such, this is an example of a binary classification problem.

The problem has two inputs that can be interpreted as x and y coordinates on a graph.

Each point belongs to either the inner or outer circle.

The make_circles() function in the scikit-learn library allows you to generate samples from the two circles problem.

The “n_samples” argument allows you to specify the number of samples to generate, divided evenly between the two classes.

The “noise” argument allows you to specify how much random statistical noise is added to the inputs or coordinates of each point, making the classification task more challenging.

The “random_state” argument specifies the seed for the pseudorandom number generator, ensuring that the same samples are generated each time the code is run.

The example below generates 1,000 samples, with 0.

1 statistical noise and a seed of 1.

Once generated, we can create a plot of the dataset to get an idea of how challenging the classification task is.

The example below generates samples and plots them, coloring each point according to the class, where points belonging to class 0 (outer circle) are colored blue and points that belong to class 1 (inner circle) are colored orange.

Running the example generates the dataset and plots the points on a graph, clearly showing two concentric circles for points belonging to class 0 and class 1.

Scatter Plot of Samples From the Two Circles ProblemWe will develop a Multilayer Perceptron, or MLP, model to address the binary classification problem.

This model is not optimized for the problem, but it is skillful (better than random).

After the samples for the dataset are generated, we will split them into two equal parts: one for training the model and one for evaluating the trained model.

Next, we can define our MLP model.

The model is simple, expecting 2 input variables from the dataset, a single hidden layer with 100 nodes, and a ReLU activation function, then an output layer with a single node and a sigmoid activation function.

The model will predict a value between 0 and 1 that will be interpreted as to whether the input example belongs to class 0 or class 1.

The model will be fit using the binary cross entropy loss function and we will use the efficient Adam version of stochastic gradient descent.

The model will also monitor the classification accuracy metric.

We will fit the model for 300 training epochs with the default batch size of 32 samples and evaluate the performance of the model at the end of each training epoch on the test dataset.

At the end of training, we will evaluate the final model once more on the train and test datasets and report the classification accuracy.

Finally, the performance of the model on the train and test sets recorded during training will be graphed using a line plot, one for each of the loss and the classification accuracy.

Tying all of these elements together, the complete code listing of training and evaluating an MLP on the two circles problem is listed below.

Running the example fits the model very quickly on the CPU (no GPU is required).

The model is evaluated, reporting the classification accuracy on the train and test sets of about 83% and 85% respectively.

Note, your specific results may vary given the stochastic nature of the training algorithm.

A figure is created showing two line plots: one for the learning curves of the loss on the train and test sets and one for the classification on the train and test sets.

The plots suggest that the model has a good fit on the problem.

Line Plot Showing Learning Curves of Loss and Accuracy of the MLP on the Two Circles Problem During TrainingPerhaps you need to evaluate your deep learning neural network model using additional metrics that are not supported by the Keras metrics API.

The Keras metrics API is limited and you may want to calculate metrics such as precision, recall, F1, and more.

One approach to calculating new metrics is to implement them yourself in the Keras API and have Keras calculate them for you during model training and during model evaluation.

For help with this approach, see the tutorial:This can be technically challenging.

A much simpler alternative is to use your final model to make a prediction for the test dataset, then calculate any metric you wish using the scikit-learn metrics API.

Three metrics, in addition to classification accuracy, that are commonly required for a neural network model on a binary classification problem are:In this section, we will calculate these three metrics, as well as classification accuracy using the scikit-learn metrics API, and we will also calculate three additional metrics that are less common but may be useful.

They are:This is not a complete list of metrics for classification models supported by scikit-learn; nevertheless, calculating these metrics will show you how to calculate any metrics you may require using the scikit-learn API.

For a full list of supported metrics, see:The example in this section will calculate metrics for an MLP model, but the same code for calculating metrics can be used for other models, such as RNNs and CNNs.

We can use the same code from the previous sections for preparing the dataset, as well as defining and fitting the model.

To make the example simpler, we will put the code for these steps into simple function.

First, we can define a function called get_data() that will generate the dataset and split it into train and test sets.

Next, we will define a function called get_model() that will define the MLP model and fit it on the training dataset.

We can then call the get_data() function to prepare the dataset and the get_model() function to fit and return the model.

Now that we have a model fit on the training dataset, we can evaluate it using metrics from the scikit-learn metrics API.

First, we must use the model to make predictions.

Most of the metric functions require a comparison between the true class values (e.

g.

testy) and the predicted class values (yhat_classes).

We can predict the class values directly with our model using the predict_classes() function on the model.

Some metrics, like the ROC AUC, require a prediction of class probabilities (yhat_probs).

These can be retrieved by calling the predict() function on the model.

For more help with making predictions using a Keras model, see the post:We can make the class and probability predictions with the model.

The predictions are returned in a two-dimensional array, with one row for each example in the test dataset and one column for the prediction.

The scikit-learn metrics API expects a 1D array of actual and predicted values for comparison, therefore, we must reduce the 2D prediction arrays to 1D arrays.

We are now ready to calculate metrics for our deep learning neural network model.

We can start by calculating the classification accuracy, precision, recall, and F1 scores.

Notice that calculating a metric is as simple as choosing the metric that interests us and calling the function passing in the true class values (testy) and the predicted class values (yhat_classes).

We can also calculate some additional metrics, such as the Cohen’s kappa, ROC AUC, and confusion matrix.

Notice that the ROC AUC requires the predicted class probabilities (yhat_probs) as an argument instead of the predicted classes (yhat_classes).

Now that we know how to calculate metrics for a deep learning neural network using the scikit-learn API, we can tie all of these elements together into a complete example, listed below.

Running the example prepares the dataset, fits the model, then calculates and reports the metrics for the model evaluated on the test dataset.

Your specific results may vary given the stochastic nature of the training algorithm.

If you need help interpreting a given metric, perhaps start with the “Classification Metrics Guide” in the scikit-learn API documentation: Classification Metrics GuideAlso, checkout the Wikipedia page for your metric; for example: Precision and recall, Wikipedia.

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

In this tutorial, you discovered how to calculate metrics to evaluate your deep learning neural network model with a step-by-step example.

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

…with just a few lines of PythonDiscover how in my new Ebook: Deep Learning With PythonIt covers self-study tutorials and end-to-end projects on topics like: Multilayer Perceptrons, Convolutional Nets and Recurrent Neural Nets, and more…Skip the Academics.

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