Christian Fischer Pedersen

Christian Marius Lillelund, Henrik Bagger Jensen, Christian Fischer Pedersen

Cloud K-SVD is a dictionary learning algorithm that can train at multiple nodes and hereby produce a mutual dictionary to represent low-dimensional geometric structures in image data. We present a novel application of the algorithm as we use it to recover both noiseless and noisy images from overlapping patches. We implement a node network in Kubernetes using Docker containers to facilitate Cloud K-SVD. Results show that Cloud K-SVD can recover images approximately and remove quantifiable amounts of noise from benchmark gray-scaled images without sacrificing accuracy in recovery; we achieve an SSIM index of 0.88, 0.91 and 0.95 between clean and recovered images for noise levels ($μ$ = 0, $σ^{2}$ = 0.01, 0.005, 0.001), respectively, which is similar to SOTA in the field. Cloud K-SVD is evidently able to learn a mutual dictionary across multiple nodes and remove AWGN from images. The mutual dictionary can be used to recover a specific image at any of the nodes in the network.

Christian Marius Lillelund, Fernando Pannullo, Morten Opprud Jakobsen et al.

Ball bearings find widespread use in various manufacturing and mechanical domains, and methods based on machine learning have been widely adopted in the field to monitor wear and spot defects before they lead to failures. Few studies, however, have addressed the problem of censored data, in which failure is not observed. In this paper, we propose a novel approach to predict the time to failure in ball bearings using survival analysis. First, we analyze bearing data in the frequency domain and annotate when a bearing fails by comparing the Kullback-Leibler divergence and the standard deviation between its break-in frequency bins and its break-out frequency bins. Second, we train several survival models to estimate the time to failure based on the annotated data and covariates extracted from the time domain, such as skewness, kurtosis and entropy. The models give a probabilistic prediction of risk over time and allow us to compare the survival function between groups of bearings. We demonstrate our approach on the XJTU and PRONOSTIA datasets. On XJTU, the best result is a 0.70 concordance-index and 0.21 integrated Brier score. On PRONOSTIA, the best is a 0.76 concordance-index and 0.19 integrated Brier score. Our work motivates further work on incorporating censored data in models for predictive maintenance.

Jimmi Agerskov, Kristian Nielsen, Christian Marius Lillelund et al.

An abundance of information about cancer exists online, but categorizing and extracting useful information from it is difficult. Almost all research within healthcare data processing is concerned with formal clinical data, but there is valuable information in non-clinical data too. The present study combines methods within distributed computing, text retrieval, clustering, and classification into a coherent and computationally efficient system, that can clarify cancer patient trajectories based on non-clinical and freely available information. We produce a fully-functional prototype that can retrieve, cluster and present information about cancer trajectories from non-clinical forum posts. We evaluate three clustering algorithms (MR-DBSCAN, DBSCAN, and HDBSCAN) and compare them in terms of Adjusted Rand Index and total run time as a function of the number of posts retrieved and the neighborhood radius. Clustering results show that neighborhood radius has the most significant impact on clustering performance. For small values, the data set is split accordingly, but high values produce a large number of possible partitions and searching for the best partition is hereby time-consuming. With a proper estimated radius, MR-DBSCAN can cluster 50000 forum posts in 46.1 seconds, compared to DBSCAN (143.4) and HDBSCAN (282.3). We conduct an interview with the Danish Cancer Society and present our software prototype. The organization sees a potential in software that can democratize online information about cancer and foresee that such systems will be required in the future.

Christian Marius Lillelund, Martin Magris, Christian Fischer Pedersen

Variational Inference (VI) is a commonly used technique for approximate Bayesian inference and uncertainty estimation in deep learning models, yet it comes at a computational cost, as it doubles the number of trainable parameters to represent uncertainty. This rapidly becomes challenging in high-dimensional settings and motivates the use of alternative techniques for inference, such as Monte Carlo Dropout (MCD) or Spectral-normalized Neural Gaussian Process (SNGP). However, such methods have seen little adoption in survival analysis, and VI remains the prevalent approach for training probabilistic neural networks. In this paper, we investigate how to train deep probabilistic survival models in large datasets without introducing additional overhead in model complexity. To achieve this, we adopt three probabilistic approaches, namely VI, MCD, and SNGP, and evaluate them in terms of their prediction performance, calibration performance, and model complexity. In the context of probabilistic survival analysis, we investigate whether non-VI techniques can offer comparable or possibly improved prediction performance and uncertainty calibration compared to VI. In the MIMIC-IV dataset, we find that MCD aligns with VI in terms of the concordance index (0.748 vs. 0.743) and mean absolute error (254.9 vs. 254.7) using hinge loss, while providing C-calibrated uncertainty estimates. Moreover, our SNGP implementation provides D-calibrated survival functions in all datasets compared to VI (4/4 vs. 2/4, respectively). Our work encourages the use of techniques alternative to VI for survival analysis in high-dimensional datasets, where computational efficiency and overhead are of concern.

Lena Todnem Bach Christensen, Dikte Straadt, Stratos Vassis et al.

Juvenile idiopathic arthritis (JIA) is the most common rheumatic disease during childhood and adolescence. The temporomandibular joints (TMJ) are among the most frequently affected joints in patients with JIA, and mandibular growth is especially vulnerable to arthritic changes of the TMJ in children. A clinical examination is the most cost-effective method to diagnose TMJ involvement, but clinicians find it difficult to interpret and inaccurate when used only on clinical examinations. This study implemented an explainable artificial intelligence (AI) model that can help clinicians assess TMJ involvement. The classification model was trained using Random Forest on 6154 clinical examinations of 1035 pediatric patients (67% female, 33% male) and evaluated on its ability to correctly classify TMJ involvement or not on a separate test set. Most notably, the results show that the model can classify patients within two years of their first examination as having TMJ involvement with a precision of 0.86 and a sensitivity of 0.7. The results show promise for an AI model in the assessment of TMJ involvement in children and as a decision support tool.

Christian Marius Lillelund, Fernando Pannullo, Morten Opprud Jakobsen et al.

Predicting the remaining useful life (RUL) of ball bearings is an active area of research, where novel machine learning techniques are continuously being applied to predict degradation trends and anticipate failures before they occur. However, few studies have explicitly addressed the challenge of handling censored data, where information about a specific event (\eg mechanical failure) is incomplete or only partially observed. To address this issue, we introduce a novel and flexible method for early fault detection using Kullback-Leibler (KL) divergence and RUL estimation using survival analysis that naturally supports censored data. We demonstrate our approach in the XJTU-SY dataset using a 5-fold cross-validation strategy across three different operating conditions. When predicting the time to failure for bearings under the highest load (C1, 12.0 kN and 2100 RPM) with 25% random censoring, our approach achieves a mean absolute error (MAE) of 14.7 minutes (95% CI = 13.6-15.8) using a linear CoxPH model, and an MAE of 12.6 minutes (95% CI = 11.8-13.4) using a nonlinear Random Survival Forests model, compared to an MAE of 18.5 minutes (95% CI = 17.4-19.6) using a linear LASSO model that does not support censoring. Moreover, our approach achieves a mean cumulative relative accuracy (CRA) of 0.7586 over 5 bearings under the highest load, which improves over several state-of-the-art baselines. Our work highlights the importance of considering censored data as part of the model design when building predictive models for early fault detection and RUL estimation.

Christian Marius Lillelund, Shi-ang Qi, Russell Greiner et al.

We argue that many survival analysis and time-to-event models are incorrectly evaluated. First, we survey many examples of evaluation approaches in the literature and find that most rely on concordance (C-index). However, the C-index only measures a model's discriminative ability and does not assess other important aspects, such as the accuracy of the time-to-event predictions or the calibration of the model's probabilistic estimates. Next, we present a set of key desiderata for choosing the right evaluation metric and discuss their pros and cons. These are tailored to the challenges in survival analysis, such as sensitivity to miscalibration and various censoring assumptions. We hypothesize that the current development of survival metrics conforms to a double-helix ladder, and that model validity and metric validity must stand on the same rung of the assumption ladder. Finally, we discuss the appropriate methods for evaluating a survival model in practice and summarize various viewpoints opposing our analysis.

Friedrich Dörmann, Osvald Frisk, Lars Nørvang Andersen et al.

Learning often involves sensitive data and as such, privacy preserving extensions to Stochastic Gradient Descent (SGD) and other machine learning algorithms have been developed using the definitions of Differential Privacy (DP). In differentially private SGD, the gradients computed at each training iteration are subject to two different types of noise. Firstly, inherent sampling noise arising from the use of minibatches. Secondly, additive Gaussian noise from the underlying mechanisms that introduce privacy. In this study, we show that these two types of noise are equivalent in their effect on the utility of private neural networks, however they are not accounted for equally in the privacy budget. Given this observation, we propose a training paradigm that shifts the proportions of noise towards less inherent and more additive noise, such that more of the overall noise can be accounted for in the privacy budget. With this paradigm, we are able to improve on the state-of-the-art in the privacy/utility tradeoff of private end-to-end CNNs.

Osvald Frisk, Friedrich Dörmann, Christian Marius Lillelund et al.

The combination of deep neural networks and Differential Privacy has been of increasing interest in recent years, as it offers important data protection guarantees to the individuals of the training datasets used. However, using Differential Privacy in the training of neural networks comes with a set of shortcomings, like a decrease in validation accuracy and a significant increase in the use of resources and time in training. In this paper, we examine super-convergence as a way of greatly increasing training speed of differentially private neural networks, addressing the shortcoming of high training time and resource use. Super-convergence allows for acceleration in network training using very high learning rates, and has been shown to achieve models with high utility in orders of magnitude less training iterations than conventional ways. Experiments in this paper show that this order-of-magnitude speedup can also be seen when combining it with Differential Privacy, allowing for higher validation accuracies in much fewer training iterations compared to non-private, non-super convergent baseline models. Furthermore, super-convergence is shown to improve the privacy guarantees of private models.