Open Access

Outcomes with a natural order commonly occur in prediction problems and often the available input data are a mixture of complex data like images and tabular predictors. Deep Learning (DL) models are state-of-the-art for image classification tasks but frequently treat ordinal outcomes as unordered and lack interpretability. In contrast, classical ordinal regression models consider the outcome’s order and yield interpretable predictor effects but are limited to tabular data. We present ordinal neural network transformation models (ontrams), which unite DL with classical ordinal regression approaches. ontrams are a special case of transformation models and trade off flexibility and interpretability by additively decomposing the transformation function into terms for image and tabular data using jointly trained neural networks. The performance of the most flexible ontram is by definition equivalent to a standard multi-class DL model trained with cross-entropy while being faster in training when facing ordinal outcomes. Lastly, we discuss how to interpret model components for both tabular and image data on two publicly available datasets.

Rheumatoid arthritis is an autoimmune disease that causes chronic inflammation of synovial joints, often resulting in irreversible structural damage. The activity of the disease is evaluated by clinical examinations, laboratory tests, and patient self-assessment. The long-term course of the disease is assessed with radiographs of hands and feet. The evaluation of the X-ray images performed by trained medical staff requires several minutes per patient. We demonstrate that deep convolutional neural networks can be leveraged for a fully automated, fast, and reproducible scoring of X-ray images of patients with rheumatoid arthritis. A comparison of the predictions of different human experts and our deep learning system shows that there is no significant difference in the performance of human experts and our deep learning model.

Deep neural networks (DNNs) are known for their high prediction performance, especially in perceptual tasks such as object recognition or autonomous driving. Still, DNNs are prone to yield unreliable predictions when encountering completely new situations without indicating their uncertainty. Bayesian variants of DNNs (BDNNs), such as MC dropout BDNNs, do provide uncertainty measures. However, BDNNs are slow during test time because they rely on a sampling approach. Here we present a single shot MC dropout approximation that preserves the advantages of BDNNs without being slower than a DNN. Our approach is to analytically approximate for each layer in a fully connected network the expected value and the variance of the MC dropout signal. We evaluate our approach on different benchmark datasets and a simulated toy example. We demonstrate that our single shot MC dropout approximation resembles the point estimate and the uncertainty estimate of the predictive distribution that is achieved with an MC approach, while being fast enough for real-time deployments of BDNNs.

Deep convolutional neural networks show outstanding performance in image-based phenotype classification given that all existing phenotypes are presented during the training of the network. However, in real-world high-content screening (HCS) experiments, it is often impossible to know all phenotypes in advance. Moreover, novel phenotype discovery itself can be an HCS outcome of interest. This aspect of HCS is not yet covered by classical deep learning approaches. When presenting an image with a novel phenotype to a trained network, it fails to indicate a novelty discovery but assigns the image to a wrong phenotype. To tackle this problem and address the need for novelty detection, we use a recently developed Bayesian approach for deep neural networks called Monte Carlo (MC) dropout to define different uncertainty measures for each phenotype prediction. With real HCS data, we show that these uncertainty measures allow us to identify novel or unclear phenotypes. In addition, we also found that the MC dropout method results in a significant improvement of classification accuracy. The proposed procedure used in our HCS case study can be easily transferred to any existing network architecture and will be beneficial in terms of accuracy and novelty detection.