Inverse problems are concerned with the reconstruction of unknown physical quantities using indirect measurements and are fundamental across diverse fields such as medical imaging, remote sensing, and material sciences. These problems serve as critical tools for visualizing internal structures beyond what is visible to the naked eye, enabling quantification, diagnosis, prediction, and discovery. However, most inverse problems are ill-posed, necessitating robust mathematical treatment to yield meaningful solutions. While classical approaches provide mathematically rigorous and computationally stable solutions, they are constrained by the ability to accurately model solution properties and implement them efficiently. A more recent paradigm considers deriving solutions to inverse problems in a data-driven manner. Instead of relying on classical mathematical modeling, this approach utilizes highly over-parameterized models, typically deep neural networks, which are adapted to specific inverse problems using carefully selected training data. Current approaches that follow this new paradigm distinguish themselves through solution accuracy paired with computational efficiency that was previously inconceivable. These notes offer an introduction to this data-driven paradigm for inverse problems. The first part of these notes will provide an introduction to inverse problems, discuss classical solution strategies, and present some applications. The second part will delve into modern data-driven approaches, with a particular focus on adversarial regularization and provably convergent linear plug-and-play denoisers. Throughout the presentation of these methodologies, their theoretical properties will be discussed, and numerical examples will be provided. The lecture series will conclude with a discussion of open problems and future perspectives in the field.

The primary objective of the AIIB 2023 competition is to evaluate the predictive significance of airway-related imaging biomarkers in determining the survival outcomes of patients with lung fibrosis.This study introduces a comprehensive three-stage approach. Initially, a segmentation network, namely nn-Unet, is employed to delineate the airway's structural boundaries. Subsequently, key features are extracted from the radiomic images centered around the trachea and an enclosing bounding box around the airway. This step is motivated by the potential presence of critical survival-related insights within the tracheal region as well as pertinent information encoded in the structure and dimensions of the airway. Lastly, radiomic features obtained from the segmented areas are integrated into an SVM classifier. We could obtain an overall-score of 0.8601 for the segmentation in Task 1 while 0.7346 for the classification in Task 2.

Amnesic probing is a technique used to examine the influence of specific linguistic information on the behaviour of a model. This involves identifying and removing the relevant information and then assessing whether the model's performance on the main task changes. If the removed information is relevant, the model's performance should decline. The difficulty with this approach lies in removing only the target information while leaving other information unchanged. It has been shown that Iterative Nullspace Projection (INLP), a widely used removal technique, introduces random modifications to representations when eliminating target information. We demonstrate that Mean Projection (MP) and LEACE, two proposed alternatives, remove information in a more targeted manner, thereby enhancing the potential for obtaining behavioural explanations through Amnesic Probing.

Deep neural networks (DNNs) have achieved remarkable success across diverse domains, but their performance can be severely degraded by noisy or corrupted training data. Conventional noise mitigation methods often rely on explicit assumptions about noise distributions or require extensive retraining, which can be impractical for large-scale models. Inspired by the principles of machine unlearning, we propose a novel framework that integrates attribution-guided data partitioning, discriminative neuron pruning, and targeted fine-tuning to mitigate the impact of noisy samples. Our approach employs gradient-based attribution to probabilistically distinguish high-quality examples from potentially corrupted ones without imposing restrictive assumptions on the noise. It then applies regression-based sensitivity analysis to identify and prune neurons that are most vulnerable to noise. Finally, the resulting network is fine-tuned on the high-quality data subset to efficiently recover and enhance its generalization performance. This integrated unlearning-inspired framework provides several advantages over conventional noise-robust learning approaches. Notably, it combines data-level unlearning with model-level adaptation, thereby avoiding the need for full model retraining or explicit noise modeling. We evaluate our method on representative tasks (e.g., CIFAR-10 image classification and speech recognition) under various noise levels and observe substantial gains in both accuracy and efficiency. For example, our framework achieves approximately a 10% absolute accuracy improvement over standard retraining on CIFAR-10 with injected label noise, while reducing retraining time by up to 47% in some settings. These results demonstrate the effectiveness and scalability of the proposed approach for achieving robust generalization in noisy environments.

State estimation or filtering serves as a fundamental task to enable intelligent decision-making in applications such as autonomous vehicles, robotics, healthcare monitoring, smart grids, intelligent transportation, and predictive maintenance. Standard filtering assumes prior knowledge of noise statistics to extract latent system states from noisy sensor data. However, real-world scenarios involve abnormalities like outliers, biases, drifts, and missing observations with unknown or partially known statistics, limiting conventional approaches. This thesis presents novel robust nonlinear filtering methods to mitigate these challenges. Based on insights from our filtering proposals, we extend the formulations to offline estimation/learning setups and propose smoothing extensions. Our methods leverage Bayesian inference frameworks, employing both deterministic and stochastic approximation techniques including Variational Inference (VI) and Particle Filters/Sequential Monte Carlo (SMC). We also study theoretical estimation limits using Bayesian Cramér-Rao bounds (BCRBs) in the context of measurement abnormalities. To validate the performance gains of the proposed methods, we perform simulations and experiments in scenarios including target tracking, indoor localization, 3D point cloud registration, mesh registration, and pose graph optimization. The fundamental nature of the work makes it useful in diverse applications, with possible future extensions toward developing outlier-robust machine learning pipelines, learning system dynamics from anomalous data, and addressing challenges in generative AI where standard diffusion models struggle with outliers, imbalanced datasets, and mode collapse.

In recent years, deep discrete representation learning (DRL) has achieved significant success across various domains. Most DRL frameworks (e.g., the widely used VQ-VAE and its variants) have primarily focused on generative settings, where the quality of a representation is implicitly gauged by the fidelity of its generation. In fact, the goodness of a discrete representation remain ambiguously defined across the literature. In this work, we adopt a practical approach that examines DRL from a task-driven perspective. We propose a unified framework that explores the usefulness of discrete features in relation to downstream tasks, with generation naturally viewed as one possible application. In this context, the properties of discrete representations as well as the way they benefit certain tasks are also relatively understudied. We therefore provide an additional theoretical analysis of the trade-off between representational capacity and sample complexity, shedding light on how discrete representation utilization impacts task performance. Finally, we demonstrate the flexibility and effectiveness of our framework across diverse applications.

Vesicoureteral reflux (VUR) is traditionally assessed using subjective grading systems, which introduces variability in diagnosis. This study investigates the use of machine learning to improve diagnostic consistency by analyzing voiding cystourethrogram (VCUG) images. A total of 113 VCUG images were reviewed, with expert grading of VUR severity. Nine image-based features were selected to train six predictive models: Logistic Regression, Decision Tree, Gradient Boosting, Neural Network, and Stochastic Gradient Descent. The models were evaluated using leave-one-out cross-validation. Analysis identified deformation patterns in the renal calyces as key indicators of high-grade VUR. All models achieved accurate classifications with no false positives or negatives. High sensitivity to subtle image patterns characteristic of different VUR grades was confirmed by substantial Area Under the Curve (AUC) values. The results suggest that machine learning can offer an objective and standardized alternative to current subjective VUR assessments. These findings highlight renal calyceal deformation as a strong predictor of severe cases. Future research should aim to expand the dataset, refine imaging features, and improve model generalizability for broader clinical use.

Diabetes has emerged as a significant global health issue, especially with the increasing number of cases in many countries. This trend Underlines the need for a greater emphasis on early detection and proactive management to avert or mitigate the severe health complications of this disease. Over recent years, machine learning algorithms have shown promising potential in predicting diabetes risk and are beneficial for practitioners. Objective: This study highlights the prediction capabilities of statistical and non-statistical machine learning methods over Diabetes risk classification in 768 samples from the Pima Indians Diabetes Database. It consists of the significant demographic and clinical features of age, body mass index (BMI) and blood glucose levels that greatly depend on the vulnerability against Diabetes. The experimentation assesses the various types of machine learning algorithms in terms of accuracy and effectiveness regarding diabetes prediction. These algorithms include Logistic Regression, Decision Tree, Random Forest, K-Nearest Neighbors, Naive Bayes, Support Vector Machine, Gradient Boosting and Neural Network Models. The results show that the Neural Network algorithm gained the highest predictive accuracy with 78,57 %, and then the Random Forest algorithm had the second position with 76,30 % accuracy. These findings show that machine learning techniques are not just highly effective. Still, they also can potentially act as early screening tools in predicting Diabetes within a data-driven fashion with valuable information on who is more likely to get affected. In addition, this study can help to realize the potential of machine learning for timely intervention over the longer term, which is a step towards reducing health outcomes and disease burden attributable to Diabetes on healthcare systems

Predicting guide RNA (gRNA) activity is critical for effective CRISPR-Cas12 genome editing but remains challenging due to limited data, variation across protospacer adjacent motifs (PAMs-short sequence requirements for Cas binding), and reliance on large-scale training. We investigate whether pre-trained biological foundation model originally trained on transcriptomic data can improve gRNA activity estimation even without domain-specific pre-training. Using embeddings from existing RNA foundation model as input to lightweight regressor, we show substantial gains over traditional baselines. We also integrate chromatin accessibility data to capture regulatory context, improving performance further. Our results highlight the effectiveness of pre-trained foundation models and chromatin accessibility data for gRNA activity prediction.

Offline reinforcement learning (RL) heavily relies on the coverage of pre-collected data over the target policy's distribution. Existing studies aim to improve data-policy coverage to mitigate distributional shifts, but overlook security risks from insufficient coverage, and the single-step analysis is not consistent with the multi-step decision-making nature of offline RL. To address this, we introduce the sequence-level concentrability coefficient to quantify coverage, and reveal its exponential amplification on the upper bound of estimation errors through theoretical analysis. Building on this, we propose the Collapsing Sequence-Level Data-Policy Coverage (CSDPC) poisoning attack. Considering the continuous nature of offline RL data, we convert state-action pairs into decision units, and extract representative decision patterns that capture multi-step behavior. We identify rare patterns likely to cause insufficient coverage, and poison them to reduce coverage and exacerbate distributional shifts. Experiments show that poisoning just 1% of the dataset can degrade agent performance by 90%. This finding provides new perspectives for analyzing and safeguarding the security of offline RL.