  This paper proposes to encode the distribution of features learned from a
convolutional neural network using a Gaussian Mixture Model. These parametric
features, called GMM-CNN, are derived from chest computed tomography and X-ray
scans of patients with Coronavirus Disease 2019. We use the proposed GMM-CNN
features as input to a robust classifier based on random forests to
differentiate between COVID-19 and other pneumonia cases. Our experiments
assess the advantage of GMM-CNN features compared to standard CNN
classification on test images. Using a random forest classifier (80\% samples
for training; 20\% samples for testing), GMM-CNN features encoded with two
mixture components provided a significantly better performance than standard
CNN classification (p\,$<$\,0.05). Specifically, our method achieved an
accuracy in the range of 96.00\,--\,96.70\% and an area under the ROC curve in
the range of 99.29\,--\,99.45\%, with the best performance obtained by
combining GMM-CNN features from both computed tomography and X-ray images. Our
results suggest that the proposed GMM-CNN features could improve the prediction
of COVID-19 in chest computed tomography and X-ray scans.
