We appreciate the opportunity to further clarify our findings in response to the insightful comments from Shota Yamamoto and colleagues and Luis Felipe Reyes and Ignacio Martin-Loeches regarding our recent community-acquired pneumonia (CAP) study. [...]

Federated learning is an upcoming machine learning paradigm which allows data from multiple sources to be used for training of classifiers without the data leaving the source it originally resides. This can be highly valuable for use cases such as medical research, where gathering data at a central location can be quite complicated due to privacy and legal concerns of the data. In such cases, federated learning has the potential to vastly speed up the research cycle. Although federated and central learning have been compared from a theoretical perspective, an extensive experimental comparison of performances and learning behavior still lacks. We have performed a comprehensive experimental comparison between federated and centralized learning. We evaluated various classifiers on various datasets exploring influences of different sample distributions as well as different class distributions across the clients. The results show similar performances under a wide variety of settings between the federated and central learning strategies. Federated learning is able to deal with various imbalances in the data distributions. It is sensitive to batch effects between different datasets when they coincide with location, similar to central learning, but this setting might go unobserved more easily. Federated learning seems to be robust to various challenges such as skewed data distributions, high data dimensionality, multiclass problems, and complex models. Taken together, the insights from our comparison gives much promise for applying federated learning as an alternative to sharing data. Code for reproducing the results in this work can be found at: https://github.com/swiergarst/FLComparison.

Federated learning is a technique that enables the use of distributed datasets for machine learning purposes without requiring data to be pooled, thereby better preserving privacy and ownership of the data. While supervised FL research has grown substantially over the last years, unsupervised FL methods remain scarce. This work introduces an algorithm which implements K-means clustering in a federated manner, addressing the challenges of varying number of clusters between centers, as well as convergence on less separable datasets.

Introduction
The field of forensic DNA analysis has undergone rapid advancements in recent decades. The integration of massively parallel sequencing (MPS) has notably expanded the forensic toolkit, moving beyond identity matching to predicting phenotypic traits and biogeographical ancestry. This shift is of particular significance in cases where conventional DNA profiling fails to identify a single suspect. Supplementing forensic analyses with estimated biological age may be valuable but involves a complex and time-consuming DNA methylation analysis. This study explores and validates the performance of a comprehensive forensic third-generation sequencing assay utilizing Oxford Nanopore Technologies (ONT) in an adaptive and direct sequencing approach. We incorporated the most widely used forensic markers, i.e., STRs, SNPs, InDels, mitochondrial DNA (mtDNA), and two methylation-based clock classifiers, thereby combining forensic genetic and epigenetic analysis in one single workflow.

Methods and results
In our investigation, DNA from six anonymous individuals was sequenced using the ONT standard adaptive direct sequencing approach, reaching a mean percentage of on-target reads ranging from 6.6 % to 7.7 % per sample. ONT data was compared to standard MPS data and Illumina EPIC DNA methylation profiles. Basecalling employed recommended ONT software packages. TREAT was used for ONT-based analysis of autosomal and Y-chromosome STRs, achieving 90–92 % correct calls depending on allelic read depth thresholds. InDel analyses for two lower-quality samples proved challenging due to inadequate read depth, while the remaining four samples significantly contributed to the observed percentage markers (60.9 %) and correct calls (97.8 %). SNP analysis achieved a 98 % call rate, with only two mismatches and two missed alleles. ONT-generated DNA methylation data demonstrated Pearson’s correlation coefficients with EPIC data ranging from 0.67 to 0.97 for Horvath’s clock. Additional age-associated markers exhibited Pearson’s correlation coefficients with chronological age between 0.14 (ELOVL2) and 0.96 (FHL2) at read depths of <30 and <20, respectively. Despite excluding mtDNA from our targeted sequencing approach, adaptive proof-reading fragments covered the complete mtDNA with an average read depth of 21–72, showing 100 % concordance with reference data.

Discussion
Our exploratory study using ONT adaptive sequencing for conventional forensic and age associated DNA methylation markers showed high sequencing accuracy for a significant number of markers, showcasing ONT as a promising (epi)genetic forensic method. Future studies must address three critical aspects: determining clear quantity and quality measures and detection thresholds for accuracy, optimizing input DNA quantity for forensic casework expectations, and addressing ethical considerations associated with phenotype and ancestry analysis to prevent ethnic biases.

While deep learning (DL) is used in patients’ outcome predictions, the insufficiency of patient samples limits the accuracy. In this study, we investigated how transfer learning (TL) alleviates the small sample size problem. A 2-step TL framework was constructed for a difficult task: predicting the response of the drug temozolomide (TMZ) in glioblastoma (GBM) cell cultures. The GBM is aggressive, and most patients do not benefit from the only approved chemotherapeutic agent TMZ. O6-methylguanine-DNA methyltransferase (MGMT) promoter methylation status is the only biomarker for TMZ responsiveness but has shown limited predictive power. The 2-step TL framework was built on 3 datasets: (1) the subset of the Genomics of Drug Sensitivity in Cancer (GDSC) dataset, including miscellaneous cell cultures treated by TMZ, cyclophosphamide, bortezomib, and oxaliplatin, as the source dataset; (2) the Human Glioblastoma Cell Culture (HGCC) dataset, for fine-tuning; and (3) a small target dataset GSE232173, for validation. The latter two included specifically TMZ-treated GBM cell cultures. The DL models were pretrained on the cell cultures treated by each of the 4 drugs from GDSC, respectively. Then, the DL models were refined on HGCC, where the best source drug was identified. Finally, the DL model was validated on GSE232173. Using 2-step TL with pretraining on oxaliplatin was not only superior to those without TL and with 1-step TL but also better than 3 benchmark methods, including MGMT. The oxaliplatin-based TL improved the performance probably by increasing the weights of cell cycle-related genes, which relates to the TMZ response processes. Our findings support the potential of oxaliplatin being an alternative therapy for patients with GBM and TL facilitating drug repurposing research. We recommend that following our methodology, using mixed cancers and a related drug as the source and then fine-tuning the model with the target cancer and the target drug will enhance drug response prediction.

Smartwatches enable longitudinal and continuous data acquisition. This has the potential to remotely monitor (changes) of the health of users. However, differences among subjects (inter-subject variability) limit a model to generalize to unseen subjects. This study focused on binary classification tasks using heart rate and step counter from smartwatches, including night/day and inactive/active classification, as well as sleep and SpO2-related (oxygen saturation) tasks. To address inter-subject variability, we explored different transforming and normalization regimes for time series including per-subject and population-based strategies. We propose a modified factorized autoencoder, which separates the data into two latent spaces capturing class-specific and subject-specific information. Our proposed generalized factorized autoencoder and triplet factorized autoencoder improved classification accuracy over the baseline from 74.8 (± 10.5) to 83.1 (± 5.1) and 83.4 (± 5.3), respectively, for night/day classification, gains for inactive/active classification were modest, improving from 84.3 (± 9.4) to 86.9 (± 4.4) and 86.6 (± 4.3), respectively. Our study highlights challenges of handling inter-subject variability in smartwatch data and how factorization models can be used to enable more robust and personalized health monitoring solutions for diverse populations.

Background
Switching from controlled to assisted ventilation is crucial in the trajectory of intensive care unit (ICU) stay, but no guidelines exist. We described current practices, analyzed patient characteristics associated with switch success or failure, and explored the feasibility to predict switch failure.

Methods
In this retrospective study, we obtained highly granular longitudinal ICU data sets from three medical centers, covering demographics, severity scores, vital signs, ventilation, and laboratory parameters. The primary endpoint was switch success, considering a switch attempt to be successful if a patient did not return to controlled ventilation for the next 72 h while alive, and to be failed otherwise. We compared the characteristics of patients with successful vs. failed first switch attempts at ICU admission, immediately before, and 3 h after the attempt. We trained LASSO logistic regression models to predict switch failure.

Results
In 4524/6715 (67%) patients attempting a switch, the first attempt failed. The first switch attempt, regardless of success or failure, was generally made at normalized PaCO2 and pH levels, with PEEP < 10 cmH2O and PaO2/FiO2 indicating mild injury. Despite very similar baseline disease severity, switch failure was associated with significantly worse outcomes, including a 28-day mortality of 27% vs. 16% and median ventilator-free days of 16 vs. 22 (p < 0.001). Failed attempts were initiated significantly earlier than successful ones (median 1.8 vs. 1.3 days, p < 0.001). Before the switch, PaO2/FiO2, if measured at PEEP > 10 cmH2O, and respiratory system compliance was lower in patients with switch failure (median 185 vs. 205 mmHg, p < 0.001; 39 vs. 41 mL/cmH2O, P = 0.001), and post-switch, patients with switch failure experienced greater deterioration in gas exchange and minimal improvement in ventilatory parameters post-switch. Contrary to our hypotheses, patient characteristics for failed vs. successful switches were surprisingly similar, resulting in prediction models with limited discriminative performance.

Conclusions
Approximately two-thirds of attempts to switch patients to assisted ventilation fail, which are associated with significantly worse clinical outcomes, despite similar baseline disease severity. Contrary to our hypotheses, patients with successful and failed attempts showed similar characteristics, making switch failure difficult to predict. These findings underscore the importance of preventing switch failures and, given the retrospective nature of this study, highlight the need for prospective studies to better understand the reasons for switch failure and when spontaneous breathing can be safely initiated.

Plants respond to stresses like drought and heat through complex gene regulatory networks (GRNs). To improve resilience, understanding these is crucial, but large-scale GRNs (>100 genes) are difficult to model using ordinary differential equations (ODEs) due to the high number of parameters that have to be estimated. Here we solve this problem by introducing BADDADAN, which uses machine learning to identify gene modules—groups of co-expressed and/or co-regulated genes—and constructs an ODE model that predicts gene module dynamics under stress. By integrating time-series gene expression data with prior co-expression data it finds modules that are both coherent and interpretable. We demonstrate BADDADAN on heat and drought datasets of A. thaliana, modelling over 1,000 genes, recovering known mechanistic insights, and proposing new hypotheses. By combining machine learning with mechanistic modelling, BADDADAN deepens our understanding of stress-related GRNs in plants and potentially other organisms.

Background: Despite several randomised controlled trials (RCTs) on the use of adjuvant treatment with corticosteroids in patients with community-acquired pneumonia (CAP), the effect of this intervention on mortality remains controversial. We aimed to evaluate heterogeneity of treatment effect (HTE) of adjuvant treatment with corticosteroids on 30-day mortality in patients with CAP. Methods: In this individual patient data meta-analysis, we included RCTs published before July 1, 2024, comparing adjuvant treatment with corticosteroids versus placebo in patients hospitalised with CAP. The primary endpoint was 30-day all-cause mortality, collected across all trials, and analyses followed the intention-to-treat principle. We analysed HTE using risk and effect modelling. For risk modelling, patients were classified as having less severe or severe CAP based on the pneumonia severity index (PSI), comparing PSI class I–III versus class IV–V. For effect modelling, we trained a corticosteroid-effect model on six trials and externally validated it using data from two trials, received after model preregistration. This model classified patients into two groups: no predicted benefit and predicted benefit from adjuvant treatment with corticosteroids. The literature search was registered on PROSPERO, CRD42022380746. Findings: We included eight RCTs with 3224 patients. Across all eight trials, 246 (7·6%) patients died within 30 days (106 [6·6%] of 1618 in the corticosteroid group vs 140 [8·7%] of 1606 in the placebo group; odds ratio [OR] 0·72 [95% CI 0·56–0·94], p=0·017). The corticosteroid-effect model, which selected C-reactive protein (CRP), showed significant HTE during external validation in the two most recent trials. In these trials, 154 (11·4%) of 1355 patients died within 30 days (88 [13·1%] of 671 in the placebo group vs 66 [9·6%] of 684 in the corticosteroid group; OR 0·71 [95% CI 0·50–0·99], p=0·044). Among patients predicted to have no benefit (CRP ≤204 mg/L, n=725), no significant effect was observed (OR 0·98 [95% CI 0·63–1·50]), whereas for those with predicted benefit (CRP >204 mg/L, n=630), 39 (13·0%) of 301 patients died in the placebo group compared with 20 (6·1%) of 329 in the corticosteroid group (0·43 [0·25–0·76], p_interaction=0·026). No significant HTE was found between less severe CAP (PSI class I–III, n=229) and severe CAP (PSI class IV–V, n=1126). Corticosteroid therapy significantly increased hyperglycaemia risk (44 [12·8%] of 344 in the placebo group vs 84 [24·8%] of 339 in the corticosteroid group; OR 2·50 [95% CI 1·63–3·83], p<0·0001) and hospital re-admission risk (30 [3·7%] of 814 in the placebo group vs 57 [7·0%] of 819 in the corticosteroid group; 1·95 [1·24–3·07], p=0·0038). Interpretation: Overall, adjuvant therapy with corticosteroids significantly reduces 30-day mortality in patients hospitalised with CAP. The treatment effect varied significantly among subgroups based on CRP concentrations, with a substantial mortality reduction observed only in patients with high baseline CRP. Funding: None.

A polygenic score (PGS) for Alzheimer’s disease (AD) was derived recently from data on genome-wide significant loci in European ancestry populations. We applied this PGS to populations in 17 European countries and observed a consistent association with the AD risk, age at onset and cerebrospinal fluid levels of AD biomarkers, independently of apolipoprotein E locus (APOE). This PGS was also associated with the AD risk in many other populations of diverse ancestries. A cross-ancestry polygenic risk score improved the association with the AD risk in most of the multiancestry populations tested when the APOE region was included. Finally, we found that the PGS/polygenic risk score captured AD-specific information because the association weakened as the diagnosis was broadened. In conclusion, a simple PGS captures the AD-specific genetic information that is common to populations of different ancestries, although studies of more diverse populations are still needed to better characterize the genetics of AD.

Background and ObjectivesIdentifying genetic causes of dementia in patients visiting memory clinics is important for patient care and family planning. Traditional clinical selection criteria for genetic testing may miss carriers of pathogenic variants in dementia-related genes. This study aimed identify how many carriers we are missing and to optimize criteria for selecting patients for genetic counseling in memory clinics.MethodsIn this clinical cohort study, we retrospectively genetically tested patients during 2.5 years (2010-2012) visiting the Alzheimer Center Amsterdam, a specialized memory clinic. Genetic tests consisted of a 54-gene dementia panel, focusing on Class IV/V variants per American College of Medical Genetics and Genomics guidelines, including APP duplications and the C9ORF72 repeat expansion. We determined the prevalence of pathogenic variants and propose new eligibility criteria for genetic testing in memory clinics. The eligibility criteria were prospectively applied for 1 year (2021-2022), and results were compared with the retrospective cohort.ResultsGenetic tests were retrospectively performed in in 1,022 of 1,138 patients (90%) who consecutively visited the memory clinic. Among these, 1,022 patients analyzed (mean age 62.1 ± 8.9 years; 40.4% were female), 34 pathogenic variant carriers were identified (3.3%), with 24 being symptomatic. Previous clinical criteria would have identified only 15 carriers (44% of all carriers, 65% of symptomatic carriers). The proposed criteria increased identification to 22 carriers (62.5% of all carriers, 91% of symptomatic carriers). In the prospective cohort, 148 (28.7%) of 515 patients were eligible for testing under the new criteria. Of the 90 eligible patients who consented to testing, 13 pathogenic carriers were identified, representing a 73% increase compared with the previous criteria.DiscussionWe found that patients who visit a memory clinic and carry a pathogenic genetic variant are often not eligible for genetic testing. The proposed new criteria improve the identification of patients with a genetic cause for their cognitive complaints. In systems without practical or financial barriers to genetic testing, the new criteria can enhance personalized care. In other countries where the health care systems differs and in other genetic ancestry groups, the performance of the criteria may be different.

Multi-omic analyses are necessary to understand the complex biological processes taking place at the tissue and cell level, but also to make reliable predictions about, for example, disease outcome. Several linear methods exist that create a joint embedding using paired information per sample, but recently there has been a rise in the popularity of neural architectures that embed paired -omics into the same non-linear manifold. This work describes a head-to-head comparison of linear and non-linear joint embedding methods using both bulk and single-cell multi-modal datasets. We found that non-linear methods have a clear advantage with respect to linear ones for missing modality imputation. Performance comparisons in the downstream tasks of survival analysis for bulk tumor data and cell type classification for single-cell data lead to the following insights: First, concatenating the principal components of each modality is a competitive baseline and hard to beat if all modalities are available at test time. However, if we only have one modality available at test time, training a predictive model on the joint space of that modality can lead to performance improvements with respect to just using the unimodal principal components. Second, -omic profiles imputed by neural joint embedding methods are realistic enough to be used by a classifier trained on real data with limited performance drops. Taken together, our comparisons give hints to which joint embedding to use for which downstream task. Overall, product-of-experts performed well in most tasks and was reasonably fast, while early integration (concatenation) of modalities did quite poorly.

Photoplethysmography (PPG) signals, typically acquired from wearable devices, hold significant potential for continuous fitness-health monitoring. In particular, heart conditions that manifest in rare and subtle deviating heart patterns may be interesting. However, robust and reliable anomaly detection within these data remains a challenge due to the scarcity of labeled data and high inter-subject variability. This paper introduces a two-stage framework leveraging representation learning and personalization to improve anomaly detection performance in PPG data. The proposed framework first employs representation learning to transform the original PPG signals into a more discriminative and compact representation. We then apply three different unsupervised anomaly detection methods for movement detection and biometric identification. We validate our approach using two different datasets in both generalized and personalized scenarios. Our results demonstrate significant improvements: for movement detection, in the generalized scenario, AUCs improved from barely 0.5 to above 0.9 with representation learning. Importantly, inter-subject variability was substantially reduced, from around 0.4 to below 0.1. In the personalized scenario, AUCs became close to 1.0, with variability further reduced to below 0.05, indicating the effectiveness of both representation learning and personalization for anomaly detection in PPG data. Similar enhancements were observed in biometric identification, emphasizing how our approach can minimize inter-subject variability and enhance PPG-based health monitoring systems.

Evaluating anomaly detection algorithms in time series data is critical as inaccuracies can lead to flawed decision-making in various domains where real-time analytics and data-driven strategies are essential. Traditional performance metrics assume iid data and fail to capture the complex temporal dynamics and specific characteristics of time series anomalies, such as early and delayed detections. We introduce Proximity-Aware Time series anomaly Evaluation (PATE), a novel evaluation metric that incorporates the temporal relationship between prediction and anomaly intervals. PATE uses proximity-based weighting considering buffer zones around anomaly intervals, enabling a more detailed and informed assessment of a detection. Using these weights, PATE computes a weighted version of the area under the Precision and Recall curve. Our experiments with synthetic and real-world datasets show the superiority of PATE in providing more sensible and accurate evaluations than other evaluation metrics. We also tested several state-of-the-art anomaly detectors across various benchmark datasets using the PATE evaluation scheme. The results show that a common metric like Point-Adjusted F1 Score fails to characterize the detection performances well, and that PATE is able to provide a more fair model comparison. By introducing PATE, we redefine the understanding of model efficacy that steers future studies toward developing more effective and accurate detection models.

Molecular effects of lifestyle interventions are typically studied in a single tissue. Here, we perform a secondary analysis on the sex-specific effects of the Growing Old TOgether trial (GOTO, trial registration number GOT NL3301 (https://onderzoekmetmensen.nl/nl/trial/27183), NL-OMON27183, primary outcomes have been previously reported in ref. 1), a moderate 13-week combined lifestyle intervention on the transcriptomes of postprandial blood, subcutaneous adipose tissue (SAT) and muscle tissue in healthy older adults, the overlap in effect between tissues and their relation to whole-body parameters of metabolic health. The GOTO intervention has virtually no effect on the postprandial blood transcriptome, while the SAT and muscle transcriptomes respond significantly. In SAT, pathways involved in HDL remodeling, O2/CO2 exchange and signaling are overrepresented, while in muscle, collagen and extracellular matrix pathways are significantly overexpressed. Additionally, we find that the effects of the SAT transcriptome closest associates with gains in metabolic health. Lastly, in males, we identify a shared variation between the transcriptomes of the three tissues. We conclude that the GOTO intervention has a significant effect on metabolic and muscle fibre pathways in the SAT and muscle transcriptome, respectively. Aligning the response in the three tissues revealed a blood transcriptome component which may act as an integrated health marker for metabolic intervention effects across tissues.

Background
Genome-Wide Association Studies (GWAS) have identified 86 SNPs associated with Alzheimer’s disease (AD). GWAS-SNPs are markers of genetic variation in linkage disequilibrium (LD), which may drive the association with AD. One major class of genetic variation are Structural Variants (SVs), which can regulate transcription and translation of nearby genes. Here, we explored the interplay between large SVs (>50 bp) and AD-associated SNPs.

Method
We performed long-read whole-genome sequencing of 214 individuals representing the extreme ends of the cognitive spectrum: N = 93 AD patients (age 67.2∓8.5), and N = 121 cognitively healthy centenarians (age 101.2∓1.8). We identified SVs using sniffles2 genome-wide, further characterised them through (local) de novo assembly, and annotated tandem repeats (TR) and transposable elements (TE). Next, we estimated LD between SVs and 86 AD-associated GWAS-SNPs, Finally, we compared SNP frequencies and SV sizes between AD cases and centenarians using logistic regression models.

Result
Across all 214 individuals, we found >27,404 SVs (>50 bp), with a Minor Allele Frequency (MAF) ≥ 5%. Most SVs were TRs (63%), followed by TEs (37%). We found that 37 AD GWAS-SNPs paired with 90 SVs in low to strong LD (R2 > 0.1), 56 of which involved SNP-TR pairs (62%) and 34 involved SNP-TE pairs (38%). In six AD loci, the SVs associated more strongly with AD risk than the leading GWAS-SNP (p < 0.05). This includes ADAM10, CTSH, SLC2A4RG, CD2AP, SPI1, and IDUA, which were encompassed by complex haplotypes harbouring multiple TRs and TEs.

Conclusion
Our findings provide the first support for SVs as candidate-drivers of the association between respective GWAS loci with AD risk. Hence, SVs may lead to increased effect sizes.

Tandem repeats (TRs) play important roles in genomic variation and disease risk in humans. Long-read sequencing allows for the accurate characterization of TRs; however, the underlying bioinformatics perspectives remain challenging. We present otter and TREAT: otter is a fast targeted local assembler, cross-compatible across different sequencing platforms. It is integrated in TREAT, an end-to-end workflow for TR characterization, visualization, and analysis across multiple genomes. In a comparison with existing tools based on long-read sequencing data from both Oxford Nanopore Technology (ONT, Simplex and Duplex) and Pacific Bioscience (PacBio, Sequel II and Revio), otter and TREAT achieve state-of-the-art genotyping and motif characterization accuracy. Applied to clinically relevant TRs, TREAT/otter significantly identify individuals with pathogenic TR expansions. When applied to a case-control setting, we replicate previously reported associations of TRs with Alzheimer's disease, including those near or within APOC1 (P = 2.63 × 10−9), SPI1 (P = 6.5 × 10−3), and ABCA7 (P = 0.04) genes. Finally, we use TREAT/otter to systematically evaluate potential biases when genotyping TRs using diverse ONT and PacBio long-read sequencing data sets. We show that, in rare cases (0.06%), long-read sequencing from coverage drops in TRs, including the disease-associated TRs in ABCA7 and RFC1 genes. Such coverage drops can lead to TR misgenotyping, hampering the accurate characterization of TR alleles. Taken together, our tools can accurately genotype TRs across different sequencing technologies and with minimal requirements, allowing end-to-end analysis and comparisons of TRs in human genomes, with broad applications in research and clinical fields.

Cardiovascular disease (CVD) is the most important cause of morbidity and mortality worldwide. Early detection, prevention or even prediction is of pivotal importance to reduce the burden of cardiovascular disease and its associated costs. Low cost, consumer-grade smartwatches have the potential to revolutionize cardiovascular medicine by enabling continuous monitoring of heart rate and activity. When combined with machine learning(ML), the resulting large amounts of time series data hold the potential of detection, or exclusion of CVD. However, analyzing such large datasets is challenging due to the sparse presence of informative segments. Efficient selection of these segments is essential for developing predictive models for clinical deployment. The objective of this paper was to investigate the potential of an acceleration-deceleration curvebased ML model as a novel clinical indicator for the detection of cardiovascular diseases. We used data from the ME-TIME study; 42 participants from which 21 have a cardiovascular disease and 21 are health controls. Data from each subject was normalized to decrease inter-subject variability. A neural network model aggregated predictions per week. We showed that per-subject normalization by the peak value of curves during inactivity, aggregation of model predictions over a week, and using a contrastive loss, resulted in a predictive model with 99 % ± 3 % specificity and 40 % ± 49 % sensitivity on the development set, and 100 % specificity with 67 % ± 47 % sensitivity on the test set. Acceleration-deceleration curves are effective patterns for ruling out the presence of cardiovascular disease, but caution must be taken to properly pre-process the curves and carefully choosing a model that reduces the variability in the extracted curves.

Anomaly detection in time series data is crucial across various domains. The scarcity of labeled data for such tasks has increased the attention towards unsupervised learning methods. These approaches, often relying solely on reconstruction error, typically fail to detect subtle anomalies in complex datasets. To address this, we introduce RESTAD, an adaptation of the Transformer model by incorporating a layer of Radial Basis Function (RBF) neurons within its architecture. This layer fits a non-parametric density in the latent representation, such that a high RBF output indicates similarity with predominantly normal training data. RESTAD integrates the RBF similarity scores with the reconstruction errors to increase sensitivity to anomalies. Our empirical evaluations demonstrate that RESTAD outperforms various established baselines across multiple benchmark datasets.