Explaining predictions of black-box neural networks is crucial when applied to decision-critical tasks. Thus, attribution maps are commonly used to identify important image regions, despite prior work showing that humans prefer explanations based on similar examples. To this end, ProtoPNet learns a set of class-representative feature vectors (prototypes) for case-based reasoning. During inference, similarities of latent features to prototypes are linearly classified to form predictions and attribution maps are provided to explain the similarity. In this work, we evaluate whether architectures for case-based reasoning fulfill established axioms required for faithful explanations using the example of ProtoPNet. We show that such architectures allow the extraction of faithful explanations. However, we prove that the attribution maps used to explain the similarities violate the axioms. We propose a new procedure to extract explanations for trained ProtoPNets, named ProtoPFaith. Conceptually, these explanations are Shapley values, calculated on the similarity scores of each prototype. They allow to faithfully answer which prototypes are present in an unseen image and quantify each pixel's contribution to that presence, thereby complying with all axioms. The theoretical violations of ProtoPNet manifest in our experiments on three datasets (CUB-200-2011, Stanford Dogs, RSNA) and five architectures (ConvNet, ResNet, ResNet50, WideResNet50, ResNeXt50). Our experiments show a qualitative difference between the explanations given by ProtoPNet and ProtoPFaith. Additionally, we quantify the explanations with the Area Over the Perturbation Curve, on which ProtoPFaith outperforms ProtoPNet on all experiments by a factor $>10^3$.

Alzheimer's disease (AD) has a complex and multifactorial etiology, which requires integrating information about neuroanatomy, genetics, and cerebrospinal fluid biomarkers for accurate diagnosis. Hence, recent deep learning approaches combined image and tabular information to improve diagnostic performance. However, the black-box nature of such neural networks is still a barrier for clinical applications, in which understanding the decision of a heterogeneous model is integral. We propose PANIC, a prototypical additive neural network for interpretable AD classification that integrates 3D image and tabular data. It is interpretable by design and, thus, avoids the need for post-hoc explanations that try to approximate the decision of a network. Our results demonstrate that PANIC achieves state-of-the-art performance in AD classification, while directly providing local and global explanations. Finally, we show that PANIC extracts biologically meaningful signatures of AD, and satisfies a set of desirable desiderata for trustworthy machine learning. Our implementation is available at https://github.com/ai-med/PANIC .

Deep Neural Networks (DNNs) have an enormous potential to learn from complex biomedical data. In particular, DNNs have been used to seamlessly fuse heterogeneous information from neuroanatomy, genetics, biomarkers, and neuropsychological tests for highly accurate Alzheimer's disease diagnosis. On the other hand, their black-box nature is still a barrier for the adoption of such a system in the clinic, where interpretability is absolutely essential. We propose Shapley Value Explanation of Heterogeneous Neural Networks (SVEHNN) for explaining the Alzheimer's diagnosis made by a DNN from the 3D point cloud of the neuroanatomy and tabular biomarkers. Our explanations are based on the Shapley value, which is the unique method that satisfies all fundamental axioms for local explanations previously established in the literature. Thus, SVEHNN has many desirable characteristics that previous work on interpretability for medical decision making is lacking. To avoid the exponential time complexity of the Shapley value, we propose to transform a given DNN into a Lightweight Probabilistic Deep Network without re-training, thus achieving a complexity only quadratic in the number of features. In our experiments on synthetic and real data, we show that we can closely approximate the exact Shapley value with a dramatically reduced runtime and can reveal the hidden knowledge the network has learned from the data.

We propose a versatile framework for survival analysis that combines advanced concepts from statistics with deep learning. The presented framework is based on piecewise exponential models and thereby supports various survival tasks, such as competing risks and multi-state modeling, and further allows for estimation of time-varying effects and time-varying features. To also include multiple data sources and higher-order interaction effects into the model, we embed the model class in a neural network and thereby enable the simultaneous estimation of both inherently interpretable structured regression inputs as well as deep neural network components which can potentially process additional unstructured data sources. A proof of concept is provided by using the framework to predict Alzheimer's disease progression based on tabular and 3D point cloud data and applying it to synthetic data.

We introduce a wide and deep neural network for prediction of progression from patients with mild cognitive impairment to Alzheimer's disease. Information from anatomical shape and tabular clinical data (demographics, biomarkers) are fused in a single neural network. The network is invariant to shape transformations and avoids the need to identify point correspondences between shapes. To account for right censored time-to-event data, i.e., when it is only known that a patient did not develop Alzheimer's disease up to a particular time point, we employ a loss commonly used in survival analysis. Our network is trained end-to-end to combine information from a patient's hippocampus shape and clinical biomarkers. Our experiments on data from the Alzheimer's Disease Neuroimaging Initiative demonstrate that our proposed model is able to learn a shape descriptor that augments clinical biomarkers and outperforms a deep neural network on shape alone and a linear model on common clinical biomarkers.

Neuroimaging datasets keep growing in size to address increasingly complex medical questions. However, even the largest datasets today alone are too small for training complex machine learning models. A potential solution is to increase sample size by pooling scans from several datasets. In this work, we combine 12,207 MRI scans from 15 studies and show that simple pooling is often ill-advised due to introducing various types of biases in the training data. First, we systematically define these biases. Second, we detect bias by experimentally showing that scans can be correctly assigned to their respective dataset with 73.3% accuracy. Finally, we propose to tell causal from confounding factors by quantifying the extent of confounding and causality in a single dataset using causal inference. We achieve this by finding the simplest graphical model in terms of Kolmogorov complexity. As Kolmogorov complexity is not directly computable, we employ the minimum description length to approximate it. We empirically show that our approach is able to estimate plausible causal relationships from real neuroimaging data.

Recent methods for generating novel molecules use graph representations of molecules and employ various forms of graph convolutional neural networks for inference. However, training requires solving an expensive graph isomorphism problem, which previous approaches do not address or solve only approximately. In this work, we propose LF-MolGAN, a likelihood-free approach for de novo molecule generation that avoids explicitly computing a reconstruction loss. Our approach extends generative adversarial networks by including an adversarial cycle-consistency loss to implicitly enforce the reconstruction property. To capture properties unique to molecules, such as valence, we extend Graph Isomorphism Network to multi-graphs. To quantify the performance of models, we propose to compute the distance between distributions of physicochemical properties with the 1-Wasserstein distance. We demonstrate that LF-MolGAN more accurately learns the distribution over the space of molecules than all baselines. Moreover, it can be utilized for drug discovery by efficiently searching the space of molecules using molecules' continuous latent representation.

Access to sufficient annotated data is a common challenge in training deep neural networks on medical images. As annotating data is expensive and time-consuming, it is difficult for an individual medical center to reach large enough sample sizes to build their own, personalized models. As an alternative, data from all centers could be pooled to train a centralized model that everyone can use. However, such a strategy is often infeasible due to the privacy-sensitive nature of medical data. Recently, federated learning (FL) has been introduced to collaboratively learn a shared prediction model across centers without the need for sharing data. In FL, clients are locally training models on site-specific datasets for a few epochs and then sharing their model weights with a central server, which orchestrates the overall training process. Importantly, the sharing of models does not compromise patient privacy. A disadvantage of FL is the dependence on a central server, which requires all clients to agree on one trusted central body, and whose failure would disrupt the training process of all clients. In this paper, we introduce BrainTorrent, a new FL framework without a central server, particularly targeted towards medical applications. BrainTorrent presents a highly dynamic peer-to-peer environment, where all centers directly interact with each other without depending on a central body. We demonstrate the overall effectiveness of FL for the challenging task of whole brain segmentation and observe that the proposed server-less BrainTorrent approach does not only outperform the traditional server-based one but reaches a similar performance to a model trained on pooled data.

Survival analysis is a fundamental tool in medical research to identify predictors of adverse events and develop systems for clinical decision support. In order to leverage large amounts of patient data, efficient optimisation routines are paramount. We propose an efficient training algorithm for the kernel survival support vector machine (SSVM). We directly optimise the primal objective function and employ truncated Newton optimisation and order statistic trees to significantly lower computational costs compared to previous training algorithms, which require $O(n^4)$ space and $O(p n^6)$ time for datasets with $n$ samples and $p$ features. Our results demonstrate that our proposed optimisation scheme allows analysing data of a much larger scale with no loss in prediction performance. Experiments on synthetic and 5 real-world datasets show that our technique outperforms existing kernel SSVM formulations if the amount of right censoring is high ($\geq85\%$), and performs comparably otherwise.