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This paper explores the growing impact of AI and NLP in bank marketing, highlighting their evolving roles in enhancing marketing strategies, improving customer engagement, and creating value within this sector. While AI and NLP have been widely studied in general marketing, there is a notable gap in understanding their specific applications and potential within the banking sector. This research addresses this specific gap by providing a systematic review and strategic analysis of AI and NLP applications in bank marketing, focusing on their integration across the customer journey and operational excellence. Employing the PRISMA methodology, this study systematically reviews existing literature to assess the current landscape of AI and NLP in bank marketing. Additionally, it incorporates semantic mapping using Sentence Transformers and UMAP for strategic gap analysis to identify underexplored areas and opportunities for future research. The systematic review reveals limited research specifically focused on NLP applications in bank marketing. The strategic gap analysis identifies key areas where NLP can further enhance marketing strategies, including customer-centric applications like acquisition, retention, and personalized engagement, offering valuable insights for both academic research and practical implementation. This research contributes to the field of bank marketing by mapping the current state of AI and NLP applications and identifying strategic gaps. The findings provide actionable insights for developing NLP-driven growth and innovation frameworks and highlight the role of NLP in improving operational efficiency and regulatory compliance. This work has broader implications for enhancing customer experience, profitability, and innovation in the banking industry.

Energy is a critical driver of modern economic systems. Accurate energy price forecasting plays an important role in supporting decision-making at various levels, from operational purchasing decisions at individual business organizations to policy-making. A significant body of literature has looked into energy price forecasting, investigating a wide range of methods to improve accuracy and inform these critical decisions. Given the evolving landscape of forecasting techniques, the literature lacks a thorough empirical comparison that systematically contrasts these methods. This paper provides an in-depth review of the evolution of forecasting modeling frameworks, from well-established econometric models to machine learning methods, early sequence learners such LSTMs, and more recent advancements in deep learning with transformer networks, which represent the cutting edge in forecasting. We offer a detailed review of the related literature and categorize forecasting methodologies into four model families. We also explore emerging concepts like pre-training and transfer learning, which have transformed the analysis of unstructured data and hold significant promise for time series forecasting. We address a gap in the literature by performing a comprehensive empirical analysis on these four family models, using data from the EU energy markets, we conduct a large-scale empirical study, which contrasts the forecasting accuracy of different approaches, focusing especially on alternative propositions for time series transformers.

Nonlinear causal discovery from observational data imposes strict identifiability assumptions on the formulation of structural equations utilized in the data generating process. The evaluation of structure learning methods under assumption violations requires a rigorous and interpretable approach, which quantifies both the structural similarity of the estimation with the ground truth and the capacity of the discovered graphs to be used for causal inference. Motivated by the lack of unified performance assessment framework, we introduce an interpretable, six-dimensional evaluation metric, i.e., distance to optimal solution (DOS), which is specifically tailored to the field of causal discovery. Furthermore, this is the first research to assess the performance of structure learning algorithms from seven different families on increasing percentage of non-identifiable, nonlinear causal patterns, inspired by real-world processes. Our large-scale simulation study, which incorporates seven experimental factors, shows that besides causal order-based methods, amortized causal discovery delivers results with comparatively high proximity to the optimal solution. In addition to the findings from our sensitivity analysis, we explore interactions effects between the experimental factors of our simulation framework in order to provide transparency about the expected performance of causal discovery techniques in different scenarios.

Matching cancer patients to clinical trials is essential for advancing treatment and patient care. However, the inconsistent format of medical free text documents and complex trial eligibility criteria make this process extremely challenging and time-consuming for physicians. We investigated whether the entire trial matching process - from identifying relevant trials among 105,600 oncology-related clinical trials on clinicaltrials.gov to generating criterion-level eligibility matches - could be automated using Large Language Models (LLMs). Using GPT-4o and a set of 51 synthetic Electronic Health Records (EHRs), we demonstrate that our approach identifies relevant candidate trials in 93.3% of cases and achieves a preliminary accuracy of 88.0% when matching patient-level information at the criterion level against a baseline defined by human experts. Utilizing LLM feedback reveals that 39.3% criteria that were initially considered incorrect are either ambiguous or inaccurately annotated, leading to a total model accuracy of 92.7% after refining our human baseline. In summary, we present an end-to-end pipeline for clinical trial matching using LLMs, demonstrating high precision in screening and matching trials to individual patients, even outperforming the performance of qualified medical doctors. Our fully end-to-end pipeline can operate autonomously or with human supervision and is not restricted to oncology, offering a scalable solution for enhancing patient-trial matching in real-world settings., Comment: 149 pages, including Supplements. 3 Main Figures

Scoring models support decision-making in financial institutions. Their estimation and evaluation are based on the data of previously accepted applicants with known repayment behavior. This creates sampling bias: the available labeled data offers a partial picture of the distribution of candidate borrowers, which the model is supposed to score. The paper addresses the adverse effect of sampling bias on model training and evaluation. To improve scorecard training, we propose bias-aware self-learning - a reject inference framework that augments the biased training data by inferring labels for selected rejected applications. For scorecard evaluation, we propose a Bayesian framework that extends standard accuracy measures to the biased setting and provides a reliable estimate of future scorecard performance. Extensive experiments on synthetic and real-world data confirm the superiority of our propositions over various benchmarks in predictive performance and profitability. By sensitivity analysis, we also identify boundary conditions affecting their performance. Notably, we leverage real-world data from a randomized controlled trial to assess the novel methodologies on holdout data that represent the true borrower population. Our findings confirm that reject inference is a difficult problem with modest potential to improve scorecard performance. Addressing sampling bias during scorecard evaluation is a much more promising route to improve scoring practices. For example, our results suggest a profit improvement of about eight percent, when using Bayesian evaluation to decide on acceptance rates.

Deep convolutional neural networks are widely used in medical image segmentation but require many labeled images for training. Annotating three-dimensional medical images is a time-consuming and costly process. To overcome this limitation, we propose a novel semi-supervised segmentation method that leverages mostly unlabeled images and a small set of labeled images in training. Our approach involves assessing prediction uncertainty to identify reliable predictions on unlabeled voxels from the teacher model. These voxels serve as pseudo-labels for training the student model. In voxels where the teacher model produces unreliable predictions, pseudo-labeling is carried out based on voxel-wise embedding correspondence using reference voxels from labeled images. We applied this method to automate hip bone segmentation in CT images, achieving notable results with just 4 CT scans. The proposed approach yielded a Hausdorff distance with 95th percentile (HD95) of 3.30 and IoU of 0.929, surpassing existing methods achieving HD95 (4.07) and IoU (0.927) at their best., Comment: 13 pages, MIDL2024 oral

This paper introduces a novel approach for efficiently distilling LLMs into smaller, application-specific models, significantly reducing operational costs and manual labor. Addressing the challenge of deploying computationally intensive LLMs in specific applications or edge devices, this technique utilizes LLMs' reasoning capabilities to generate labels and natural language rationales for unlabeled data. Our approach enhances both finetuning and distillation by employing a multi-task training framework where student models mimic these rationales alongside teacher predictions. Key contributions include the employment of zero-shot prompting to elicit teacher model rationales, reducing the necessity for handcrafted few-shot examples and lowering the overall token count required, which directly translates to cost savings given the pay-per-token billing model of major tech companies' LLM APIs. Additionally, the paper investigates the impact of explanation properties on distillation efficiency, demonstrating that minimal performance loss occurs even when rationale augmentation is not applied across the entire dataset, facilitating further reductions of tokens. This research marks a step toward the efficient training of task-specific models with minimal human intervention, offering substantial cost-savings while maintaining, or even enhancing, performance.

In many business applications, including online marketing and customer churn prevention, randomized controlled trials (RCT's) are conducted to investigate on the effect of specific treatment (coupon offers, advertisement mailings,...). Such RCT's allow for the estimation of average treatment effects as well as the training of (uplift) models for the heterogeneity of treatment effects between individuals. The problem with these RCT's is that they are costly and this cost increases with the number of individuals included into the RCT. For this reason, there is research how to conduct experiments involving a small number of individuals while still obtaining precise treatment effect estimates. We contribute to this literature a heteroskedasticity-aware stratified sampling (HS) scheme, which leverages the fact that different individuals have different noise levels in their outcome and precise treatment effect estimation requires more observations from the "high-noise" individuals than from the "low-noise" individuals. By theory as well as by empirical experiments, we demonstrate that our HS-sampling yields significantly more precise estimates of the ATE, improves uplift models and makes their evaluation more reliable compared to RCT data sampled completely randomly. Due to the relative ease of application and the significant benefits, we expect HS-sampling to be valuable in many real-world applications.

There are various applications, where companies need to decide to which individuals they should best allocate treatment. To support such decisions, uplift models are applied to predict treatment effects on an individual level. Based on the predicted treatment effects, individuals can be ranked and treatment allocation can be prioritized according to this ranking. An implicit assumption, which has not been doubted in the previous uplift modeling literature, is that this treatment prioritization approach tends to bring individuals with high treatment effects to the top and individuals with low treatment effects to the bottom of the ranking. In our research, we show that heteroskedastictity in the training data can cause a bias of the uplift model ranking: individuals with the highest treatment effects can get accumulated in large numbers at the bottom of the ranking. We explain theoretically how heteroskedasticity can bias the ranking of uplift models and show this process in a simulation and on real-world data. We argue that this problem of ranking bias due to heteroskedasticity might occur in many real-world applications and requires modification of the treatment prioritization to achieve an efficient treatment allocation., Comment: 10 pages, 4 figures

We introduce novel approaches to cryptocurrency price forecasting, leveraging Machine Learning (ML) and Natural Language Processing (NLP) techniques, with a focus on Bitcoin and Ethereum. By analysing news and social media content, primarily from Twitter and Reddit, we assess the impact of public sentiment on cryptocurrency markets. A distinctive feature of our methodology is the application of the BART MNLI zero-shot classification model to detect bullish and bearish trends, significantly advancing beyond traditional sentiment analysis. Additionally, we systematically compare a range of pre-trained and fine-tuned deep learning NLP models against conventional dictionary-based sentiment analysis methods. Another key contribution of our work is the adoption of local extrema alongside daily price movements as predictive targets, reducing trading frequency and portfolio volatility. Our findings demonstrate that integrating textual data into cryptocurrency price forecasting not only improves forecasting accuracy but also consistently enhances the profitability and Sharpe ratio across various validation scenarios, particularly when applying deep learning NLP techniques. The entire codebase of our experiments is made available via an online repository: https://anonymous.4open.science/r/crypto-forecasting-public

Transfer learning leverages pre-trained model features from a large dataset to save time and resources when training new models for various tasks, potentially enhancing performance. Due to the lack of large datasets in the medical imaging domain, transfer learning from one medical imaging model to other medical imaging models has not been widely explored. This study explores the use of transfer learning to improve the performance of deep convolutional neural networks for organ segmentation in medical imaging. A base segmentation model (3D U-Net) was trained on a large and sparsely annotated dataset; its weights were used for transfer learning on four new down-stream segmentation tasks for which a fully annotated dataset was available. We analyzed the training set size's influence to simulate scarce data. The results showed that transfer learning from the base model was beneficial when small datasets were available, providing significant performance improvements; where fine-tuning the base model is more beneficial than updating all the network weights with vanilla transfer learning. Transfer learning with fine-tuning increased the performance by up to 0.129 (+28\%) Dice score than experiments trained from scratch, and on average 23 experiments increased the performance by 0.029 Dice score in the new segmentation tasks. The study also showed that cross-modality transfer learning using CT scans was beneficial. The findings of this study demonstrate the potential of transfer learning to improve the efficiency of annotation and increase the accessibility of accurate organ segmentation in medical imaging, ultimately leading to improved patient care. We made the network definition and weights publicly available to benefit other users and researchers.

In this study, we introduce a deep learning approach for segmenting kidney parenchyma and kidney abnormalities to support clinicians in identifying and quantifying renal abnormalities such as cysts, lesions, masses, metastases, and primary tumors. Our end-to-end segmentation method was trained on 215 contrast-enhanced thoracic-abdominal CT scans, with half of these scans containing one or more abnormalities. We began by implementing our own version of the original 3D U-Net network and incorporated four additional components: an end-to-end multi-resolution approach, a set of task-specific data augmentations, a modified loss function using top-$k$, and spatial dropout. Furthermore, we devised a tailored post-processing strategy. Ablation studies demonstrated that each of the four modifications enhanced kidney abnormality segmentation performance, while three out of four improved kidney parenchyma segmentation. Subsequently, we trained the nnUNet framework on our dataset. By ensembling the optimized 3D U-Net and the nnUNet with our specialized post-processing, we achieved marginally superior results. Our best-performing model attained Dice scores of 0.965 and 0.947 for segmenting kidney parenchyma in two test sets (20 scans without abnormalities and 30 with abnormalities), outperforming an independent human observer who scored 0.944 and 0.925, respectively. In segmenting kidney abnormalities within the 30 test scans containing them, the top-performing method achieved a Dice score of 0.585, while an independent second human observer reached a score of 0.664, suggesting potential for further improvement in computerized methods. All training data is available to the research community under a CC-BY 4.0 license on https://doi.org/10.5281/zenodo.8014289

The increasing usage of new data sources and machine learning (ML) technology in credit modeling raises concerns with regards to potentially unfair decision-making that rely on protected characteristics (e.g., race, sex, age) or other socio-economic and demographic data. The authors demonstrate the impact of such algorithmic bias in the microfinance context. Difficulties in assessing credit are disproportionately experienced among vulnerable groups, however, very little is known about inequities in credit allocation between groups defined, not only by single, but by multiple and intersecting social categories. Drawing from the intersectionality paradigm, the study examines intersectional horizontal inequities in credit access by gender, age, marital status, single parent status and number of children. This paper utilizes data from the Spanish microfinance market as its context to demonstrate how pluralistic realities and intersectional identities can shape patterns of credit allocation when using automated decision-making systems. With ML technology being oblivious to societal good or bad, we find that a more thorough examination of intersectionality can enhance the algorithmic fairness lens to more authentically empower action for equitable outcomes and present a fairer path forward. We demonstrate that while on a high-level, fairness may exist superficially, unfairness can exacerbate at lower levels given combinatorial effects; in other words, the core fairness problem may be more complicated than current literature demonstrates. We find that in addition to legally protected characteristics, sensitive attributes such as single parent status and number of children can result in imbalanced harm. We discuss the implications of these findings for the financial services industry.

In response to growing FinTech competition and the need for improved operational efficiency, this research focuses on understanding the potential of advanced document analytics, particularly using multimodal models, in banking processes. We perform a comprehensive analysis of the diverse banking document landscape, highlighting the opportunities for efficiency gains through automation and advanced analytics techniques in the customer business. Building on the rapidly evolving field of natural language processing (NLP), we illustrate the potential of models such as LayoutXLM, a cross-lingual, multimodal, pre-trained model, for analyzing diverse documents in the banking sector. This model performs a text token classification on German company register extracts with an overall F1 score performance of around 80\%. Our empirical evidence confirms the critical role of layout information in improving model performance and further underscores the benefits of integrating image information. Interestingly, our study shows that over 75% F1 score can be achieved with only 30% of the training data, demonstrating the efficiency of LayoutXLM. Through addressing state-of-the-art document analysis frameworks, our study aims to enhance process efficiency and demonstrate the real-world applicability and benefits of multimodal models within banking., Comment: A Preprint

This paper presents a large publicly available multi-center lumbar spine magnetic resonance imaging (MRI) dataset with reference segmentations of vertebrae, intervertebral discs (IVDs), and spinal canal. The dataset includes 447 sagittal T1 and T2 MRI series from 218 patients with a history of low back pain and was collected from four different hospitals. An iterative data annotation approach was used by training a segmentation algorithm on a small part of the dataset, enabling semi-automatic segmentation of the remaining images. The algorithm provided an initial segmentation, which was subsequently reviewed, manually corrected, and added to the training data. We provide reference performance values for this baseline algorithm and nnU-Net, which performed comparably. Performance values were computed on a sequestered set of 39 studies with 97 series, which were additionally used to set up a continuous segmentation challenge that allows for a fair comparison of different segmentation algorithms. This study may encourage wider collaboration in the field of spine segmentation and improve the diagnostic value of lumbar spine MRI., Comment: Published in Scientific Data

We propose a novel method for predicting time-to-event in the presence of cure fractions based on flexible survivals models integrated into a deep neural network framework. Our approach allows for non-linear relationships and high-dimensional interactions between covariates and survival and is suitable for large-scale applications. Furthermore, we allow the method to incorporate an identified predictor formed of an additive decomposition of interpretable linear and non-linear effects and add an orthogonalization layer to capture potential higher dimensional interactions. We demonstrate the usefulness and computational efficiency of our method via simulations and apply it to a large portfolio of US mortgage loans. Here, we find not only a better predictive performance of our framework but also a more realistic picture of covariate effects.

We propose MCLFIQ: Mobile Contactless Fingerprint Image Quality, the first quality assessment algorithm for mobile contactless fingerprint samples. To this end, we re-trained the NIST Fingerprint Image Quality (NFIQ) 2 method, which was originally designed for contact-based fingerprints, with a synthetic contactless fingerprint database. We evaluate the predictive performance of the resulting MCLFIQ model in terms of Error-vs.-Discard Characteristic (EDC) curves on three real-world contactless fingerprint databases using three recognition algorithms. In experiments, the MCLFIQ method is compared against the original NFIQ 2.2 method, a sharpness-based quality assessment algorithm developed for contactless fingerprint images \rev{and the general purpose image quality assessment method BRISQUE. Furthermore, benchmarks on four contact-based fingerprint datasets are also conducted.} Obtained results show that the fine-tuning of NFIQ 2 on synthetic contactless fingerprints is a viable alternative to training on real databases. Moreover, the evaluation shows that our MCLFIQ method works more accurate and robust compared to all baseline methods on contactless fingerprints. We suggest considering the proposed MCLFIQ method as a \rev{starting point for the development of} a new standard algorithm for contactless fingerprint quality assessment.

Many forecasting applications have a limited distributed target variable, which is zero for most observations and positive for the remaining observations. In the econometrics literature, there is much research about statistical model building for limited distributed target variables. Especially, there are two component model approaches, where one model is build for the probability of the target to be positive and one model for the actual value of the target, given that it is positive. However, the econometric literature focuses on effect estimation and does not provide theory for predictive modeling. Nevertheless, some concepts like the two component model approach and Heckmann's sample selection correction also appear in the predictive modeling literature, without a sound theoretical foundation. In this paper, we theoretically analyze predictive modeling for limited dependent variables and derive best practices. By analyzing various real-world data sets, we also use the derived theoretical results to explain which predictive modeling approach works best on which application., Comment: 15 pages, 2 figures

Carbon dioxide removal (CDR) moves atmospheric carbon to geological or land-based sinks. In a first-best setting, the optimal use of CDR is achieved by a removal subsidy that equals the optimal carbon tax and marginal damages. We derive second-best policy rules for CDR subsidies and carbon taxes when no global carbon price exists but a national government implements a unilateral climate policy. We find that the optimal carbon tax differs from an optimal CDR subsidy because of carbon leakage and a balance of resource trade effect. First, the optimal removal subsidy tends to be larger than the carbon tax because of lower supply-side leakage on fossil resource markets. Second, net carbon exporters exacerbate this wedge to increase producer surplus of their carbon resource producers, implying even larger removal subsidies. Third, net carbon importers may set their removal subsidy even below their carbon tax when marginal environmental damages are small, to appropriate producer surplus from carbon exporters.

There has been intensive research regarding machine learning models for predicting bankruptcy in recent years. However, the lack of interpretability limits their growth and practical implementation. This study proposes a data-driven explainable case-based reasoning (CBR) system for bankruptcy prediction. Empirical results from a comparative study show that the proposed approach performs superior to existing, alternative CBR systems and is competitive with state-of-the-art machine learning models. We also demonstrate that the asymmetrical feature similarity comparison mechanism in the proposed CBR system can effectively capture the asymmetrically distributed nature of financial attributes, such as a few companies controlling more cash than the majority, hence improving both the accuracy and explainability of predictions. In addition, we delicately examine the explainability of the CBR system in the decision-making process of bankruptcy prediction. While much research suggests a trade-off between improving prediction accuracy and explainability, our findings show a prospective research avenue in which an explainable model that thoroughly incorporates data attributes by design can reconcile the dilemma.

Estimating treatment effects is one of the most challenging and important tasks of data analysts. In many applications, like online marketing and personalized medicine, treatment needs to be allocated to the individuals where it yields a high positive treatment effect. Uplift models help select the right individuals for treatment and maximize the overall treatment effect (uplift). A major challenge in uplift modeling concerns model evaluation. Previous literature suggests methods like the Qini curve and the transformed outcome mean squared error. However, these metrics suffer from variance: their evaluations are strongly affected by random noise in the data, which renders their signals, to a certain degree, arbitrary. We theoretically analyze the variance of uplift evaluation metrics and derive possible methods of variance reduction, which are based on statistical adjustment of the outcome. We derive simple conditions under which the variance reduction methods improve the uplift evaluation metrics and empirically demonstrate their benefits on simulated and real-world data. Our paper provides strong evidence in favor of applying the suggested variance reduction procedures by default when evaluating uplift models on RCT data.

In this paper, we describe an experiment measuring low-$Q^2$ elastic electron-proton scattering using a newly developed cryogenic supersonic gas jet target in the A1 three-spectrometer facility at the Mainz Microtron. We measured the proton electric form factor within the four-momentum transfer range of $0.01\le Q^2 \le 0.045(\text{GeV/c})^2$. The experiment showed consistent results with the existing measurements. The data we collected demonstrated the feasibility of the gas jet target and the potential of future scattering experiments using high-resolution spectrometers with this gas jet target., Comment: 10 pages, 8 figures

Anticipating price developments in financial markets is a topic of continued interest in forecasting. Funneled by advancements in deep learning and natural language processing (NLP) together with the availability of vast amounts of textual data in form of news articles, social media postings, etc., an increasing number of studies incorporate text-based predictors in forecasting models. We contribute to this literature by introducing weak learning, a recently proposed NLP approach to address the problem that text data is unlabeled. Without a dependent variable, it is not possible to finetune pretrained NLP models on a custom corpus. We confirm that finetuning using weak labels enhances the predictive value of text-based features and raises forecast accuracy in the context of predicting cryptocurrency returns. More fundamentally, the modeling paradigm we present, weak labeling domain-specific text and finetuning pretrained NLP models, is universally applicable in (financial) forecasting and unlocks new ways to leverage text data., Comment: 29 pages

Generative models for images have gained significant attention in computer vision and natural language processing due to their ability to generate realistic samples from complex data distributions. To leverage the advances of image-based generative models for the time series domain, we propose a two-dimensional image representation for time series, the Extended Intertemporal Return Plot (XIRP). Our approach captures the intertemporal time series dynamics in a scale-invariant and invertible way, reducing training time and improving sample quality. We benchmark synthetic XIRPs obtained by an off-the-shelf Wasserstein GAN with gradient penalty (WGAN-GP) to other image representations and models regarding similarity and predictive ability metrics. Our novel, validated image representation for time series consistently and significantly outperforms a state-of-the-art RNN-based generative model regarding predictive ability. Further, we introduce an improved stochastic inversion to substantially improve simulation quality regardless of the representation and provide the prospect of transfer potentials in other domains.

Image registration is a fundamental medical image analysis task, and a wide variety of approaches have been proposed. However, only a few studies have comprehensively compared medical image registration approaches on a wide range of clinically relevant tasks. This limits the development of registration methods, the adoption of research advances into practice, and a fair benchmark across competing approaches. The Learn2Reg challenge addresses these limitations by providing a multi-task medical image registration data set for comprehensive characterisation of deformable registration algorithms. A continuous evaluation will be possible at https://learn2reg.grand-challenge.org. Learn2Reg covers a wide range of anatomies (brain, abdomen, and thorax), modalities (ultrasound, CT, MR), availability of annotations, as well as intra- and inter-patient registration evaluation. We established an easily accessible framework for training and validation of 3D registration methods, which enabled the compilation of results of over 65 individual method submissions from more than 20 unique teams. We used a complementary set of metrics, including robustness, accuracy, plausibility, and runtime, enabling unique insight into the current state-of-the-art of medical image registration. This paper describes datasets, tasks, evaluation methods and results of the challenge, as well as results of further analysis of transferability to new datasets, the importance of label supervision, and resulting bias. While no single approach worked best across all tasks, many methodological aspects could be identified that push the performance of medical image registration to new state-of-the-art performance. Furthermore, we demystified the common belief that conventional registration methods have to be much slower than deep-learning-based methods.

Recurrent neural networks (RNNs) are a popular choice for modeling sequential data. Modern RNN architectures assume constant time-intervals between observations. However, in many datasets (e.g. medical records) observation times are irregular and can carry important information. To address this challenge, we propose continuous recurrent units (CRUs) -- a neural architecture that can naturally handle irregular intervals between observations. The CRU assumes a hidden state, which evolves according to a linear stochastic differential equation and is integrated into an encoder-decoder framework. The recursive computations of the CRU can be derived using the continuous-discrete Kalman filter and are in closed form. The resulting recurrent architecture has temporal continuity between hidden states and a gating mechanism that can optimally integrate noisy observations. We derive an efficient parameterization scheme for the CRU that leads to a fast implementation f-CRU. We empirically study the CRU on a number of challenging datasets and find that it can interpolate irregular time series better than methods based on neural ordinary differential equations., Comment: Accepted at ICML 2022, Baltimore, Maryland