Variations in hidden parameters, such as a robot's mass distribution or friction, pose safety risks during execution. We develop a runtime shielding mechanism for reinforcement learning, building on the formalism of constrained hidden-parameter Markov decision processes. Function encoders enable real-time inference of hidden parameters from observations, allowing the shield and the underlying policy to adapt online. The shield constrains the action space by forecasting future safety risks (such as obstacle proximity) and accounts for uncertainty via conformal prediction. We prove that the proposed mechanism satisfies probabilistic safety guarantees and yields optimal policies among the set of safety-compliant policies. Experiments across diverse environments with varying hidden parameters show that our method significantly reduces safety violations and achieves strong out-of-distribution generalization, while incurring minimal runtime overhead.

Diffusion models have demonstrated remarkable performance in generating unimodal data across various tasks, including image, video, and text generation. On the contrary, the joint generation of multimodal data through diffusion models is still in the early stages of exploration. Existing approaches heavily rely on external preprocessing protocols, such as tokenizers and variational autoencoders, to harmonize varied data representations into a unified, unimodal format. This process heavily demands the high accuracy of encoders and decoders, which can be problematic for applications with limited data. To lift this restriction, we propose a novel framework for building multimodal diffusion models on arbitrary state spaces, enabling native generation of coupled data across different modalities. By introducing an innovative decoupled noise schedule for each modality, we enable both unconditional and modality-conditioned generation within a single model simultaneously. We empirically validate our approach for text-image generation and mixed-type tabular data synthesis, demonstrating that it achieves competitive performance.

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.

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.

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

Open multi-agent systems are increasingly important in modeling real-world applications, such as smart grids, swarm robotics, etc. In this paper, we aim to investigate a recently proposed problem for open multi-agent systems, referred to as n-agent ad hoc teamwork (NAHT), where only a number of agents are controlled. Existing methods tend to be based on heuristic design and consequently lack theoretical rigor and ambiguous credit assignment among agents. To address these limitations, we model and solve NAHT through the lens of cooperative game theory. More specifically, we first model an open multi-agent system, characterized by its value, as an instance situated in a space of cooperative games, generated by a set of basis games. We then extend this space, along with the state space, to accommodate dynamic scenarios, thereby characterizing NAHT. Exploiting the justifiable assumption that basis game values correspond to a sequence of n-step returns with different horizons, we represent the state values for NAHT in a form similar to $λ$-returns. Furthermore, we derive Shapley values to allocate state values to the controlled agents, as credits for their contributions to the ad hoc team. Different from the conventional approach to shaping Shapley values in an explicit form, we shape Shapley values by fulfilling the three axioms uniquely describing them, well defined on the extended game space describing NAHT. To estimate Shapley values in dynamic scenarios, we propose a TD($λ$)-like algorithm. The resulting reinforcement learning (RL) algorithm is referred to as Shapley Machine. To our best knowledge, this is the first time that the concepts from cooperative game theory are directly related to RL concepts. In experiments, we demonstrate the effectiveness of Shapley Machine and verify reasonableness of our theory.

--We introduce PRISM (Predictive Reasoning in Sequential Medicine), a transformer-based architecture designed to model the sequential progression of clinical decision-making processes. Unlike traditional approaches that rely on isolated diagnostic classification, PRISM frames clinical trajectories as tokenized sequences of events -- including diagnostic tests, laboratory results, and diagnoses -- and learns to predict the most probable next steps in the patient diagnostic journey. Leveraging a large custom clinical vocabulary and an autoregressive training objective, PRISM demonstrates the ability to capture complex dependencies across longitudinal patient timelines. Experimental results show substantial improvements over random baselines in next-token prediction tasks, with generated sequences reflecting realistic diagnostic pathways, laboratory result progressions, and clinician ordering behaviors. These findings highlight the feasibility of applying generative language modeling techniques to structured medical event data, enabling applications in clinical decision support, simulation, and education. PRISM establishes a foundation for future advancements in sequence-based healthcare modeling, bridging the gap between machine learning architectures and real-world diagnostic reasoning. Accurate and timely clinical decision-making is fundamental to high-quality patient care.

This paper addresses the problem of learning an undirected graph from data gathered at each nodes. Within the graph signal processing framework, the topology of such graph can be linked to the support of the conditional correlation matrix of the data. The corresponding graph learning problem then scales to the squares of the number of variables (nodes), which is usually problematic at large dimension. To tackle this issue, we propose a graph learning framework that leverages a low-rank factorization of the conditional correlation matrix. In order to solve for the resulting optimization problems, we derive tools required to apply Riemannian optimization techniques for this particular structure. The proposal is then particularized to a low-rank constrained counterpart of the GLasso algorithm, i.e., the penalized maximum likelihood estimation of a Gaussian graphical model. Experiments on synthetic and real data evidence that a very efficient dimension-versus-performance trade-off can be achieved with this approach.

Diffusion models have become an influential tool for generative modeling, offering a flexible framework that performs well across a range of data types including images, audio, and text (Dhariwal and Nichol, 2021; Kong et al., 2021; Li et al., 2022; Ho et al., 2022). Originally formulated in continuous state spaces (Ho et al., 2020; Song et al., 2021), these models simulate a forward noising process--typically modeled by a stochastic differential equation and learn a reverse process to denoise and reconstruct the original data. More recently, the diffusion framework has been extended to discrete state spaces (Campbell et al., 2022; Lou et al., 2023), where the forward process is defined via a continuous-time Markov chain over a finite state space. This has enabled generative modeling for discrete domains such as language modeling, molecule generation, and protein design (Lou et al., 2023; Nie et al.; Huang et al., 2023; Gruver et al., 2023). A key innovation that has enhanced the performance and flexibility of diffusion models is guidance, which introduces an auxiliary parameter to steer the reverse process toward desired outputs. In the continuous setting, classifier guidance (Dhariwal and Nichol, 2021) and classifier-free guidance (Ho and Salimans, 2021; Nichol et al., 2022) are widely used for conditional generation based on class labels or text prompts, significantly improving sample quality and alignment with conditioning signals. This technique has been critical to the success of models such as GLIDE (Nichol et al., 2022) and Imagen (Saharia et al., 2022). Theoretical analyses of guided diffusion models in continuous state spaces have examined how guidance modifies the reverse dynamics, most of which focus on simple settings such as low-dimensional and mixture of Gaussian models (Bradley and Nakkiran, 2024; Wu et al., 2024; Chidambaram et al., 2024). Classifier-free guidance (CFG) has also been recently introduced to discrete diffusion models, for applications such as text generation and controlled molecule design (Huang et al., 2023; Nisonoff et al., 2024).