The discovery began, as many breakthroughs do, with an observation that didn't quite make sense. In 1948, two French researchers, Paul Mandel and Pierre Métais, published a little-noticed paper in a scientific journal. Working in a laboratory in Strasbourg, they had been cataloguing the chemical contents of blood plasma--that river of life teeming with proteins, sugars, waste, nutrients, and cellular debris. Amid this familiar inventory, they'd spotted an unexpected presence: fragments of DNA drifting freely. The finding defied biological orthodoxy. DNA was thought to remain locked inside the nuclei of cells, and not float around on its own.

Clinical communication skills are critical in medical education, and practicing and assessing clinical communication skills on a scale is challenging. Although LLM-powered clinical scenario simulations have shown promise in enhancing medical students' clinical practice, providing automated and scalable clinical evaluation that follows nuanced physician judgment is difficult. This paper combines fuzzy logic and Large Language Model (LLM) and proposes LLM-as-a-Fuzzy-Judge to address the challenge of aligning the automated evaluation of medical students' clinical skills with subjective physicians' preferences. LLM-as-a-Fuzzy-Judge is an approach that LLM is fine-tuned to evaluate medical students' utterances within student-AI patient conversation scripts based on human annotations from four fuzzy sets, including Professionalism, Medical Relevance, Ethical Behavior, and Contextual Distraction. The methodology of this paper started from data collection from the LLM-powered medical education system, data annotation based on multidimensional fuzzy sets, followed by prompt engineering and the supervised fine-tuning (SFT) of the pre-trained LLMs using these human annotations. The results show that the LLM-as-a-Fuzzy-Judge achieves over 80\% accuracy, with major criteria items over 90\%, effectively leveraging fuzzy logic and LLM as a solution to deliver interpretable, human-aligned assessment. This work suggests the viability of leveraging fuzzy logic and LLM to align with human preferences, advances automated evaluation in medical education, and supports more robust assessment and judgment practices. The GitHub repository of this work is available at https://github.com/2sigmaEdTech/LLMAsAJudge

Opinion dynamics models such as the bounded confidence models (BCMs) describe how a population can reach consensus, fragmentation, or polarization, depending on a few parameters. Connecting such models to real-world data could help understanding such phenomena, testing model assumptions. To this end, estimation of model parameters is a key aspect, and maximum likelihood estimation provides a principled way to tackle it. Here, our goal is to outline the properties of statistical estimators of the two key BCM parameters: the confidence bound and the convergence rate. We find that their maximum likelihood estimators present different characteristics: the one for the confidence bound presents a small-sample bias but is consistent, while the estimator of the convergence rate shows a persistent bias. Moreover, the joint parameter estimation is affected by identifiability issues for specific regions of the parameter space, as several local maxima are present in the likelihood function. Our results show how the analysis of the likelihood function is a fruitful approach for better understanding the pitfalls and possibilities of estimating the parameters of opinion dynamics models, and more in general, agent-based models, and for offering formal guarantees for their calibration.

Machine learning models should not reveal particular information that is not otherwise accessible. Differential privacy provides a formal framework to mitigate privacy risks by ensuring that the inclusion or exclusion of any single data point does not significantly alter the output of an algorithm, thus limiting the exposure of private information. This survey paper explores the foundational definitions of differential privacy, reviews its original formulations and tracing its evolution through key research contributions. It then provides an in-depth examination of how DP has been integrated into machine learning models, analyzing existing proposals and methods to preserve privacy when training ML models. Finally, it describes how DP-based ML techniques can be evaluated in practice. %Finally, it discusses the broader implications of DP, highlighting its potential for public benefit, its real-world applications, and the challenges it faces, including vulnerabilities to adversarial attacks. By offering a comprehensive overview of differential privacy in machine learning, this work aims to contribute to the ongoing development of secure and responsible AI systems.

--Research on lane change prediction has gained a lot of momentum in the last couple of years. However, most research is confined to simulation or results obtained from datasets, leaving a gap between algorithmic advances and on-road deployment. This work closes that gap by demonstrating, on real hardware, a lane-change prediction system based on Knowledge Graph Embeddings (KGEs) and Bayesian inference. Moreover, the ego-vehicle employs a longitudinal braking action to ensure the safety of both itself and the surrounding vehicles. Our architecture consists of two modules: (i) a perception module that senses the environment, derives input numerical features, and converts them into linguistic categories; and communicates them to the prediction module; (ii) a pretrained prediction module that executes a KGE and Bayesian inference model to anticipate the target vehicle's maneuver and transforms the prediction into longitudinal braking action. Real-world hardware experimental validation demonstrates that our prediction system anticipates the target vehicle's lane change three to four seconds in advance, providing the ego vehicle sufficient time to react and allowing the target vehicle to make the lane change safely. Traffic accidents are one of the leading causes of death worldwide. As road networks become more complex and the number of vehicles increases, the ability to anticipate the lane change maneuvers of surrounding vehicles becomes not only beneficial but also essential for enhancing road safety. That's why research on lane change prediction has gained significant momentum in recent years.

This is a course project report with complete methodology, experiments, references and mathematical derivations. Matrix factorization [1] is a widely used technique in recommendation systems. Probabilistic Matrix Factorization (PMF) [2] extends traditional matrix factorization by incorporating probability distributions over latent factors, allowing for uncertainty quantification. However, computing the posterior distribution is intractable due to the high-dimensional integral. To address this, we employ two Bayesian inference methods: Markov Chain Monte Carlo (MCMC) [3, 4] and Variational Inference (VI) [5, 6] to approximate the posterior. We evaluate their performance on MovieLens dataset [7] and compare their convergence speed, predictive accuracy, and computational efficiency. Experimental results demonstrate that VI offers faster convergence, while MCMC provides more accurate posterior estimates.

We introduce scalable algorithms for online learning and generalized Bayesian inference of neural network parameters, designed for sequential decision making tasks. Our methods combine the strengths of frequentist and Bayesian filtering, which include fast low-rank updates via a block-diagonal approximation of the parameter error covariance, and a well-defined posterior predictive distribution that we use for decision making. More precisely, our main method updates a low-rank error covariance for the hidden layers parameters, and a full-rank error covariance for the final layer parameters. Although this characterizes an improper posterior, we show that the resulting posterior predictive distribution is well-defined. Our methods update all network parameters online, with no need for replay buffers or offline retraining. We show, empirically, that our methods achieve a competitive tradeoff between speed and accuracy on (non-stationary) contextual bandit problems and Bayesian optimization problems.

Solving inverse problems in cardiovascular modeling is particularly challenging due to the high computational cost of running high-fidelity simulations. In this work, we focus on Bayesian parameter estimation and explore different methods to reduce the computational cost of sampling from the posterior distribution by leveraging low-fidelity approximations. A common approach is to construct a surrogate model for the high-fidelity simulation itself. Another is to build a surrogate for the discrepancy between high- and low-fidelity models. This discrepancy, which is often easier to approximate, is modeled with either a fully connected neural network or a nonlinear dimensionality reduction technique that enables surrogate construction in a lower-dimensional space. A third possible approach is to treat the discrepancy between the high-fidelity and surrogate models as random noise and estimate its distribution using normalizing flows. This allows us to incorporate the approximation error into the Bayesian inverse problem by modifying the likelihood function. We validate five different methods which are variations of the above on analytical test cases by comparing them to posterior distributions derived solely from high-fidelity models, assessing both accuracy and computational cost. Finally, we demonstrate our approaches on two cardiovascular examples of increasing complexity: a lumped-parameter Windkessel model and a patient-specific three-dimensional anatomy.

--Accurate prediction of traffic flow parameters and real-time identification of congestion states are essential for the efficient operation of intelligent transportation systems. This paper proposes a Periodic Pattern-Transformer Network (PPTNet) for traffic flow prediction, integrating periodic pattern extraction with the Transformer architecture, coupled with a fuzzy inference method for real-time congestion identification. Firstly, a high-precision traffic flow dataset (Traffic Flow Dataset for China's Congested Highways & Expressways, TF4CHE) suitable for congested highway scenarios in China is constructed based on drone aerial imagery data. Subsequently, the proposed PPTNet employs Fast Fourier Transform to capture multi-scale periodic patterns and utilizes two-dimensional Inception convolutions to efficiently extract intra and inter periodic features. Finally, congestion probabilities are calculated in real-time using the predicted outcomes via a Mamdani fuzzy inference-based congestion identification module. Experimental results demonstrate that the proposed PPTNet significantly outperforms mainstream traffic prediction methods in prediction accuracy, and the congestion identification module effectively identifies real-time road congestion states, verifying the superiority and practicality of the proposed method in real-world traffic scenarios. ITH the rapid advancement of Intelligent Transportation Systems (ITS), traffic flow prediction has become a core technology to optimize traffic management and improve operational efficiency [1]. As a critical component of national transportation infrastructure, expressways are particularly susceptible to traffic congestion, which not only directly reduces throughput but also indirectly contributes to a higher incidence of traffic accidents.

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.