The proliferation and ubiquity of temporal data across many disciplines has sparked interest for similarity, classification and clustering methods specifically designed to handle time series data. A core issue when dealing with time series is determining their pairwise similarity, i.e., the degree to which a given time series resembles another. Traditional distance measures such as the Euclidean are not well-suited due to the time-dependent nature of the data. Elastic metrics such as dynamic time warping (DTW) offer a promising approach, but are limited by their computational complexity, non-differentiability and sensitivity to noise and outliers. This thesis proposes novel elastic alignment methods that use parametric \& diffeomorphic warping transformations as a means of overcoming the shortcomings of DTW-based metrics. The proposed method is differentiable \& invertible, well-suited for deep learning architectures, robust to noise and outliers, computationally efficient, and is expressive and flexible enough to capture complex patterns. Furthermore, a closed-form solution was developed for the gradient of these diffeomorphic transformations, which allows an efficient search in the parameter space, leading to better solutions at convergence. Leveraging the benefits of these closed-form diffeomorphic transformations, this thesis proposes a suite of advancements that include: (a) an enhanced temporal transformer network for time series alignment and averaging, (b) a deep-learning based time series classification model to simultaneously align and classify signals with high accuracy, (c) an incremental time series clustering algorithm that is warping-invariant, scalable and can operate under limited computational and time resources, and finally, (d) a normalizing flow model that enhances the flexibility of affine transformations in coupling and autoregressive layers.

Set-membership estimation is commonly used in adaptive/learning-based control algorithms that require robustness over the model uncertainty sets, e.g., online robustly stabilizing control and robust adaptive model predictive control. Despite having broad applications, non-asymptotic estimation error bounds in the stochastic setting are limited. This paper provides such a non-asymptotic bound on the diameter of the uncertainty sets generated by set membership estimation on linear dynamical systems under bounded, i.i.d. disturbances. Further, this result is applied to robust adaptive model predictive control with uncertainty sets updated by set membership. We numerically demonstrate the performance of the robust adaptive controller, which rapidly approaches the performance of the offline optimal model predictive controller, in comparison with the control design based on least square estimation's confidence regions.

Feature selection is one of the most relevant processes in any methodology for creating a statistical learning model. Usually, existing algorithms establish some criterion to select the most influential variables, discarding those that do not contribute to the model with any relevant information. This methodology makes sense in a static situation where the joint distribution of the data does not vary over time. However, when dealing with real data, it is common to encounter the problem of the dataset shift and, specifically, changes in the relationships between variables (concept shift). In this case, the influence of a variable cannot be the only indicator of its quality as a regressor of the model, since the relationship learned in the training phase may not correspond to the current situation. In tackling this problem, our approach establishes a direct relationship between the Shapley values and prediction errors, operating at a more local level to effectively detect the individual biases introduced by each variable. The proposed methodology is evaluated through various examples, including synthetic scenarios mimicking sudden and incremental shift situations, as well as two real-world cases characterized by concept shifts. Additionally, we perform three analyses of standard situations to assess the algorithm's robustness in the absence of shifts. The results demonstrate that our proposed algorithm significantly outperforms state-of-the-art feature selection methods in concept shift scenarios, while matching the performance of existing methodologies in static situations.

This research aims to evaluate the performance of the rotors and study the behavior of the human driver in interacting with the rotors. In recent years, rotors have been increasingly used between countries due to their safety, capacity, and environmental advantages, and because they provide safe and fluid flows of vehicles for transit and integration. It turns out that roundabouts can significantly reduce speed at twisting intersections, entry speed and the resulting effect on speed depends on the rating of road users. In our research, (bus, car, truck) drivers were given special attention and their behavior was categorized into (conservative, normal, aggressive). Anticipating and recognizing driver behavior is an important challenge. Therefore, the aim of this research is to study the effect of roundabouts on these classifiers and to develop a method for predicting the behavior of road users at roundabout intersections. Safety is primarily due to two inherent features of the rotor. First, by comparing the data collected and processed in order to classify and evaluate drivers' behavior, and comparing the speeds of the drivers (bus, car and truck), the speed of motorists at crossing the roundabout was more fit than that of buses and trucks. We looked because the car is smaller and all parts of the rotor are visible to it. So drivers coming from all directions have to slow down, giving them more time to react and mitigating the consequences in the event of an accident. Second, with fewer conflicting flows (and points of conflict), drivers only need to look to their left (in right-hand traffic) for other vehicles, making their job of crossing the roundabout easier as there is less need to split attention between different directions.

Controller Area Network bus systems within vehicular networks are not equipped with the tools necessary to ward off and protect themselves from modern cyber-security threats. Work has been done on using machine learning methods to detect and report these attacks, but common methods are not robust towards unknown attacks. These methods usually rely on there being a sufficient representation of attack data, which may not be available due to there either not being enough data present to adequately represent its distribution or the distribution itself is too diverse in nature for there to be a sufficient representation of it. With the use of one-class classification methods, this issue can be mitigated as only normal data is required to train a model for the detection of anomalous instances. Research has been done on the efficacy of these methods, most notably One-Class Support Vector Machine and Support Vector Data Description, but many new extensions of these works have been proposed and have yet to be tested for injection attacks in vehicular networks. In this paper, we investigate the performance of various state-of-the-art one-class classification methods for detecting injection attacks on Controller Area Network bus traffic. We investigate the effectiveness of these techniques on attacks launched on Controller Area Network buses from two different vehicles during normal operation and while being attacked. We observe that the Subspace Support Vector Data Description method outperformed all other tested methods with a Gmean of about 85%.

An accurate estimation of the state of health (SOH) of batteries is critical to ensuring the safe and reliable operation of electric vehicles (EVs). Feature-based machine learning methods have exhibited enormous potential for rapidly and precisely monitoring battery health status. However, simultaneously using various health indicators (HIs) may weaken estimation performance due to feature redundancy. Furthermore, ignoring real-world driving behaviors can lead to inaccurate estimation results as some features are rarely accessible in practical scenarios. To address these issues, we proposed a feature-based machine learning pipeline for reliable battery health monitoring, enabled by evaluating the acquisition probability of features under real-world driving conditions. We first summarized and analyzed various individual HIs with mechanism-related interpretations, which provide insightful guidance on how these features relate to battery degradation modes. Moreover, all features were carefully evaluated and screened based on estimation accuracy and correlation analysis on three public battery degradation datasets. Finally, the scenario-based feature fusion and acquisition probability-based practicality evaluation method construct a useful tool for feature extraction with consideration of driving behaviors. This work highlights the importance of balancing the performance and practicality of HIs during the development of feature-based battery health monitoring algorithms.

Traditional approaches to variational inference rely on parametric families of variational distributions, with the choice of family playing a critical role in determining the accuracy of the resulting posterior approximation. Simple mean-field families often lead to poor approximations, while rich families of distributions like normalizing flows can be difficult to optimize and usually do not incorporate the known structure of the target distribution due to their black-box nature. To expand the space of flexible variational families, we revisit Variational Rejection Sampling (VRS) [Grover et al., 2018], which combines a parametric proposal distribution with rejection sampling to define a rich non-parametric family of distributions that explicitly utilizes the known target distribution. By introducing a low-variance reparameterized gradient estimator for the parameters of the proposal distribution, we make VRS an attractive inference strategy for models with continuous latent variables. We argue theoretically and demonstrate empirically that the resulting method--Reparameterized Variational Rejection Sampling (RVRS)--offers an attractive trade-off between computational cost and inference fidelity. In experiments we show that our method performs well in practice and that it is well-suited for black-box inference, especially for models with local latent variables.

The increased attention to regulating the outputs of deep generative models, driven by growing concerns about privacy and regulatory compliance, has highlighted the need for effective control over these models. This necessity arises from instances where generative models produce outputs containing undesirable, offensive, or potentially harmful content. To tackle this challenge, the concept of machine unlearning has emerged, aiming to forget specific learned information or to erase the influence of undesired data subsets from a trained model. The objective of this work is to prevent the generation of outputs containing undesired features from a pre-trained GAN where the underlying training data set is inaccessible. Our approach is inspired by a crucial observation: the parameter space of GANs exhibits meaningful directions that can be leveraged to suppress specific undesired features. However, such directions usually result in the degradation of the quality of generated samples. Our proposed method, known as 'Adapt-then-Unlearn,' excels at unlearning such undesirable features while also maintaining the quality of generated samples. This method unfolds in two stages: in the initial stage, we adapt the pre-trained GAN using negative samples provided by the user, while in the subsequent stage, we focus on unlearning the undesired feature. During the latter phase, we train the pre-trained GAN using positive samples, incorporating a repulsion regularizer. This regularizer encourages the model's parameters to be away from the parameters associated with the adapted model from the first stage while also maintaining the quality of generated samples. To the best of our knowledge, our approach stands as first method addressing unlearning in GANs. We validate the effectiveness of our method through comprehensive experiments.

Recent research efforts on semantic communication have mostly considered accuracy as a main problem for optimizing goal-oriented communication systems. However, these approaches introduce a paradox: the accuracy of artificial intelligence (AI) tasks should naturally emerge through training rather than being dictated by network constraints. Acknowledging this dilemma, this work introduces an innovative approach that leverages the rate-distortion theory to analyze distortions induced by communication and semantic compression, thereby analyzing the learning process. Specifically, we examine the distribution shift between the original data and the distorted data, thus assessing its impact on the AI model's performance. Founding upon this analysis, we can preemptively estimate the empirical accuracy of AI tasks, making the goal-oriented semantic communication problem feasible. To achieve this objective, we present the theoretical foundation of our approach, accompanied by simulations and experiments that demonstrate its effectiveness. The experimental results indicate that our proposed method enables accurate AI task performance while adhering to network constraints, establishing it as a valuable contribution to the field of signal processing. Furthermore, this work advances research in goal-oriented semantic communication and highlights the significance of data-driven approaches in optimizing the performance of intelligent systems.

To date, endovascular surgeries are performed using the golden standard of Fluoroscopy, which uses ionising radiation to visualise catheters and vasculature. Prolonged Fluoroscopic exposure is harmful for the patient and the clinician, and may lead to severe post-operative sequlae such as the development of cancer. Meanwhile, the use of interventional Ultrasound has gained popularity, due to its well-known benefits of small spatial footprint, fast data acquisition, and higher tissue contrast images. However, ultrasound images are hard to interpret, and it is difficult to localise vessels, catheters, and guidewires within them. This work proposes a solution using an adaptation of a state-of-the-art machine learning transformer architecture to detect and segment catheters in axial interventional Ultrasound image sequences. The network architecture was inspired by the Attention in Attention mechanism, temporal tracking networks, and introduced a novel 3D segmentation head that performs 3D deconvolution across time. In order to facilitate training of such deep learning networks, we introduce a new data synthesis pipeline that used physics-based catheter insertion simulations, along with a convolutional ray-casting ultrasound simulator to produce synthetic ultrasound images of endovascular interventions. The proposed method is validated on a hold-out validation dataset, thus demonstrated robustness to ultrasound noise and a wide range of scanning angles. It was also tested on data collected from silicon-based aorta phantoms, thus demonstrated its potential for translation from sim-to-real. This work represents a significant step towards safer and more efficient endovascular surgery using interventional ultrasound.