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Deep learning is a topic of considerable current interest. The availability of massive data collections and powerful software resources has led to an impressive amount of results in many application areas that reveal essential but hidden properties of the observations. System identification learns mathematical descriptions of dynamic systems from input-output data and can thus benefit from the advances of deep neural networks to enrich the possible range of models to choose from. For this reason, we provide a survey of deep learning from a system identification perspective. We cover a wide spectrum of topics to enable researchers to understand the methods, providing rigorous practical and theoretical insights into the benefits and challenges of using them. The main aim of the identified model is to predict new data from previous observations. This can be achieved with different deep learning-based modelling techniques and we discuss architectures commonly adopted in the literature, like feedforward, convolutional, and recurrent networks. Their parameters have to be estimated from past data to optimize the prediction performance. For this purpose, we discuss a specific set of first-order optimization tools that have emerged as efficient. The survey then draws connections to the well-studied area of kernel-based methods. They control the data fit by regularization terms that penalize models not in line with prior assumptions. We illustrate how to cast them in deep architectures to obtain deep kernel-based methods. The success of deep learning also resulted in surprising empirical observations, like the counter-intuitive behaviour of models with many parameters. We discuss the role of overparameterized models, including their connection to kernels, as well as implicit regularization mechanisms which affect generalization, specifically the interesting phenomena of benign overfitting and double-descent. Finally, we highlight numerical, computational and software aspects in the area with the help of applied examples.

Imbalances in electrolyte concentrations can have severe consequences, but accurate and accessible measurements could improve patient outcomes. The current measurement method based on blood tests is accurate but invasive and time-consuming and is often unavailable for example in remote locations or an ambulance setting. In this paper, we explore the use of deep neural networks (DNNs) for regression tasks to accurately predict continuous electrolyte concentrations from electrocardiograms (ECGs), a quick and widely adopted tool. We analyze our DNN models on a novel dataset of over 290,000 ECGs across four major electrolytes and compare their performance with traditional machine learning models. For improved understanding, we also study the full spectrum from continuous predictions to a binary classification of extreme concentration levels. Finally, we investigate probabilistic regression approaches and explore uncertainty estimates for enhanced clinical usefulness. Our results show that DNNs outperform traditional models but model performance varies significantly across different electrolytes. While discretization leads to good classification performance, it does not address the original problem of continuous concentration level prediction. Probabilistic regression has practical potential, but our uncertainty estimates are not perfectly calibrated. Our study is therefore a first step towards developing an accurate and reliable ECG-based method for electrolyte concentration level prediction—a method with high potential impact within multiple clinical scenarios.

In science and engineering, we are often concerned with creating mathematical models from data. These models are abstractions of observed real-world processes where the goal is often to understand these processes or to use the models to predict future instances of the observed process. Natural processes often exhibit low-dimensional structures which we can embed into the model. In mechanistic models, we directly include this structure into the model through mathematical equations often inspired by physical constraints. In contrast, within machine learning and particularly in deep learning we often deal with high-dimensional data such as images and learn a model without imposing a low-dimensional structure. Instead, we learn some kind of representations that are useful for the task at hand. While representation learning arguably enables the power of deep neural networks, it is less clear how to understand real-world processes from these models or whether we can benefit from including a low-dimensional structure in the model.

Learning from data with intrinsic low-dimensional structure and how to replicate this structure in machine learning models is studied within this dissertation. While we put specific emphasis on deep neural networks, we also consider kernel machines in the context of Gaussian processes, as well as linear models, for example by studying the generalisation of models with an explicit low-dimensional structure. First, we argue that many real-world observations have an intrinsic low-dimensional structure. We can find evidence of this structure for example through low-rank approximations of many real-world data sets. Then, we face two open-ended research questions. First, we study the behaviour of machine learning models when they are trained on data with low-dimensional structures. Here we investigate fundamental aspects of learning low-dimensional representations and how well models with explicit low-dimensional structures perform. Second, we focus on applications in the modelling of dynamical systems and the medical domain. We investigate how we can benefit from low-dimensional representations for these applications and explore the potential of low-dimensional model structures for predictive tasks. Finally, we give a brief outlook on how we go beyond learning low-dimensional structures and identify the underlying mechanisms that generate the data to better model and understand these processes.

This dissertation provides an overview of learning low-dimensional structures in machine learning models. It covers a wide range of topics from representation learning over the study of generalisation in overparameterized models to applications with time series and medical applications. However, each contribution opens up a range of questions to study in the future. Therefore this dissertation serves as a starting point to further explore learning of low-dimensional structure and representations.

In conventional regression analysis, predictions are typically represented as point estimates derived from covariates. The Gaussian Process (GP) offer a kernel-based framework that predicts and additionally quantifies associated uncertainties. However, kernel-based methods often underperform ensemble-based decision tree approaches in regression tasks involving tabular and categorical data. Recently, Recursive Feature Machines (RFMs) were proposed as a novel feature-learning kernel which strengthens the capabilities of kernel machines. In this study, we harness the power RFMs in a probabilistic GP-based approach to enhance uncertainty estimation through feature extraction within kernel methods. We employ this learned kernel for in-depth uncertainty analysis. On tabular datasets, our RFM-based method surpasses other leading uncertainty estimation techniques, including NGBoost and CatBoost-ensemble. Additionally, when assessing out-of-distribution performance, we found that boosting-based methods are surpassed by our RFM-based approach.

In conventional regression analysis, predictions are typically represented as point estimates derived from covariates. The Gaussian Process (GP) offer a kernel-based framework that predicts and quantifies associated uncertainties. However, kernelbased methods often underperform ensemble-based decision tree approaches in regression tasks involving tabular and categorical data. Recently, Recursive Feature Machines (RFMs) were proposed as a novel feature-learning kernel which strengthens the capabilities of kernel machines. In this study, we harness the power of these RFMs in a probabilistic GP-based approach to enhance uncertainty estimation through feature extraction within kernel methods. We employ this learned kernel for in-depth uncertainty analysis. On tabular datasets, our RFM-based method surpasses other leading uncertainty estimation techniques, including NGBoost and CatBoost-ensemble. Additionally, when assessing out-of-distribution performance, we found that boosting-based methods are surpassed by our RFM-based approach.

Background: Atrial fibrillation (AF) is one of the most common cardiac arrhythmias that affects millions of people each year worldwide and it is closely linked to increased risk of cardiovas-cular diseases such as stroke and heart failure. Machine learning methods have shown promising results in evaluating the risk of developing atrial fibrillation from the electrocardiogram. We aim to develop and evaluate one such algorithm on a large CODE dataset collected in Brazil.

Methods: We used the CODE cohort to develop and test a model for AF risk prediction for individual patients from the raw ECG recordings without the use of additional digital biomarkers. The cohort is a collection of ECG recordings and annotations by the Telehealth Network of Minas Gerais, in Brazil. A convolutional neural network based on a residual network architecture was implemented to produce class probabilities for the classification of AF. The probabilities were used to develop a Cox proportional hazards model and a Kaplan-Meier model to carry out survival analysis. Hence, our model is able to perform risk prediction for the development of AF in patients without the condition.

Results: The deep neural network model identified patients without indication of AF in the presented ECG but who will develop AF in the future with an AUC score of 0.845. From our survival model, we obtain that patients in the high-risk group (i.e. with the probability of a future AF case being >0.7) are 50% more likely to develop AF within 40 weeks, while patients belonging to the minimal-risk group (i.e. with the probability of a future AF case being less than or equal to 0.1) have >85% chance of remaining AF free up until after seven years.

Conclusion: We developed and validated a model for AF risk prediction. If applied in clinical practice, the model possesses the potential of providing valuable and useful information in decision- making and patient management processes.

Kernel principal component analysis (kPCA) is a widely studied method to construct a low-dimensional data representation after a nonlinear transformation. The prevailing method to reconstruct the original input signal from kPCA-an important task for denoising-requires us to solve a supervised learning problem. In this paper, we present an alternative method where the reconstruction follows naturally from the compression step. We first approximate the kernel with random Fourier features. Then, we exploit the fact that the nonlinear transformation is invertible in a certain subdomain. Hence, the name invertible kernel PCA (ikPCA). We experiment with different data modalities and show that ikPCA performs similarly to kPCA with supervised reconstruction on denoising tasks, making it a strong alternative.

Chagas disease (ChD) is a neglected tropical disease, and the diagnosis relies on blood testing of patients from endemic areas. However, there is no clear recommendation on how to select patients for testing in endemic regions. Since most cases of Chronic ChD are asymptomatic, the diagnostic rates are low, preventing patients from receiving adequate treatment.

The Electrocardiogram (ECG) is a widely available, low-cost exam, often available in primary care settings. We present an Artificial intelligence (AI) model for automatically detecting ChD from the ECG. AI algorithms have allowed the detection of hidden conditions on the ECG and, to the best of our knowledge, this is the first study that does it for ChD. We utilize large cohorts of patients from the relevant population of all-comers in affected regions in Brazil to develop a model for ChD detection that is then validated on datasets with ground truth labels obtained directly from the patients’ serological status.

Our findings demonstrate a promising AI-ECG-based model for discriminating patients with chronic Chagas cardiomyopathy (CCC). The capacity of detecting ChD patients without CCC is still limited. But we believe this can be improved with the addition of epidemiological questions, and that such models can become useful tools for pre-selecting patients for further testing.

Background: Worldwide, it is estimated that over 6 million people are infected with Chagas disease (ChD). It is a neglected disease that can lead to severe heart conditions in its chronic phase. While early treatment can avoid complications, the early-stage detection rate is low. We explore the use of deep neural networks to detect ChD from electrocardiograms (ECGs) to aid in the early detection of the disease.

Methods: We employ a convolutional neural network model that uses 12-lead ECG data to compute the probability of a ChD diagnosis. Our model is developed using two datasets which jointly comprise over two million entries from Brazilian patients: The SaMi-Trop study focusing on ChD patients, enriched with data from the CODE study from the general population. The model’s performance is evaluated on two external datasets: the REDS-II, a study focused on ChD with 631 patients, and the ELSA-Brasil study, with 13,739 civil servant patients.

Findings: Evaluating our model, we obtain an AUC-ROC of 0.80 (CI 95% 0.79-0.82) for the validation set (samples from CODE and SaMi-Trop), and in external validation datasets: 0.68 (CI 95% 0.63-0.71) for REDS-II and 0.59 (CI 95% 0.56-0.63) for ELSA-Brasil. In the latter, we report a sensitivity of 0.52 (CI 95% 0.47-0.57) and 0.36 (CI 95% 0.30-0.42) and a specificity of 0.77 (CI 95% 0.72-0.81) and 0.76 (CI 95% 0.75-0.77), respectively. Additionally, when considering only patients with Chagas cardiomyopathy as positive, the model achieved an AUC-ROC of 0.82 (CI 95% 0.77-0.86) for REDS-II and 0.77 (CI 95% 0.68-0.85) for ELSA-Brasil.

Interpretation: The neural network detects chronic Chagas cardiomyopathy (CCC) from ECG—with weaker performance for early-stage cases. Future work should focus on curating large higher-quality datasets. The CODE dataset, our largest development dataset includes self-reported and therefore less reliable labels, limiting performance for non-CCC patients. Our findings can improve ChD detection and treatment, particularly in high-prevalence areas.

Myocardial infarction diagnosis is a common challenge in the emergency department. In managed settings, deep learning-based models and especially convolutional deep models have shown promise in electrocardiogram (ECG) classification, but there is a lack of high-performing models for the diagnosis of myocardial infarction in real-world scenarios. We aimed to train and validate a deep learning model using ECGs to predict myocardial infarction in real-world emergency department patients. We studied emergency department patients in the Stockholm region between 2007 and 2016 that had an ECG obtained because of their presenting complaint. We developed a deep neural network based on convolutional layers similar to a residual network. Inputs to the model were ECG tracing, age, and sex; and outputs were the probabilities of three mutually exclusive classes: non-ST-elevation myocardial infarction (NSTEMI), ST-elevation myocardial infarction (STEMI), and control status, as registered in the SWEDEHEART and other registries. We used an ensemble of five models. Among 492,226 ECGs in 214,250 patients, 5,416 were recorded with an NSTEMI, 1,818 a STEMI, and 485,207 without a myocardial infarction. In a random test set, our model could discriminate STEMIs/NSTEMIs from controls with a C-statistic of 0.991/0.832 and had a Brier score of 0.001/0.008. The model obtained a similar performance in a temporally separated test set of the study sample, and achieved a C-statistic of 0.985 and a Brier score of 0.002 in discriminating STEMIs from controls in an external test set. We developed and validated a deep learning model with excellent performance in discriminating between control, STEMI, and NSTEMI on the presenting ECG of a real-world sample of the important population of all-comers to the emergency department. Hence, deep learning models for ECG decision support could be valuable in the emergency department.