Probabilistic graphical modeling is a branch of machine learning that uses probability distributions to describe the world, make predictions, and support decision-making under uncertainty. Underlying this modeling framework is an elegant body of theory that bridges two mathematical traditions: probability and graph theory. This framework provides compact yet expressive representations of joint probability distributions, yielding powerful generative models for probabilistic reasoning. This tutorial provides a concise introduction to the formalisms, methods, and applications of this modeling framework. After a review of basic probability and graph theory, we explore three dominant themes: (1) the representation of multivariate distributions in the intuitive visual language of graphs, (2) algorithms for learning model parameters and graphical structures from data, and (3) algorithms for inference, both exact and approximate.

This PhD thesis presents a distributional view of optimization in place of a worst-case perspective. We motivate this view with an investigation of the failure point of classical optimization. Subsequently we consider the optimization of a randomly drawn objective function. This is the setting of Bayesian Optimization. After a review of Bayesian optimization we outline how such a distributional view may explain predictable progress of optimization in high dimension. It further turns out that this distributional view provides insights into optimal step size control of gradient descent. To enable these results, we develop mathematical tools to deal with random input to random functions and a characterization of non-stationary isotropic covariance kernels. Finally, we outline how assumptions about the data, specifically exchangability, can lead to random objective functions in machine learning and analyze their landscape.

Conformal prediction (CP) is an Uncertainty Representation technique that delivers finite-sample calibrated prediction regions for any underlying Machine Learning model. Its status as an Uncertainty Quantification (UQ) tool, though, has remained conceptually opaque: While Conformal Prediction Regions (CPRs) give an ordinal representation of uncertainty (larger regions typically indicate higher uncertainty), they lack the capability to cardinally quantify it (twice as large regions do not imply twice the uncertainty). We adopt a category-theoretic approach to CP -- framing it as a morphism, embedded in a commuting diagram, of two newly-defined categories -- that brings us three joys. First, we show that -- under minimal assumptions -- CP is intrinsically a UQ mechanism, that is, its cardinal UQ capabilities are a structural feature of the method. Second, we demonstrate that CP bridges (and perhaps subsumes) the Bayesian, frequentist, and imprecise probabilistic approaches to predictive statistical reasoning. Finally, we show that a CPR is the image of a covariant functor. This observation is relevant to AI privacy: It implies that privacy noise added locally does not break the global coverage guarantee.

The implementation of Artificial Intelligence (AI) in household environments, especially in the form of proactive autonomous agents, brings about possibilities of comfort and attention as well as it comes with intra or extramural ethical challenges. This article analyzes agentic AI and its applications, focusing on its move from reactive to proactive autonomy, privacy, fairness and user control. We review responsible innovation frameworks, human-centered design principles, and governance practices to distill practical guidance for ethical smart home systems. Vulnerable user groups such as elderly individuals, children, and neurodivergent who face higher risks of surveillance, bias, and privacy risks were studied in detail in context of Agentic AI. Design imperatives are highlighted such as tailored explainability, granular consent mechanisms, and robust override controls, supported by participatory and inclusive methodologies. It was also explored how data-driven insights, including social media analysis via Natural Language Processing(NLP), can inform specific user needs and ethical concerns. This survey aims to provide both a conceptual foundation and suggestions for developing transparent, inclusive, and trustworthy agentic AI in household automation.

In this paper, we consider the distributed optimal control problem for discrete-time linear networked systems. In particular, we are interested in learning distributed optimal controllers using graph recurrent neural networks (GRNNs). Most of the existing approaches result in centralized optimal controllers with offline training processes. However, as the increasing demand of network resilience, the optimal controllers are further expected to be distributed, and are desirable to be trained in an online distributed fashion, which are also the main contributions of our work. To solve this problem, we first propose a GRNN-based distributed optimal control method, and we cast the problem as a self-supervised learning problem. Then, the distributed online training is achieved via distributed gradient computation, and inspired by the (consensus-based) distributed optimization idea, a distributed online training optimizer is designed. Furthermore, the local closed-loop stability of the linear networked system under our proposed GRNN-based controller is provided by assuming that the nonlinear activation function of the GRNN-based controller is both local sector-bounded and slope-restricted. The effectiveness of our proposed method is illustrated by numerical simulations using a specifically developed simulator.

High-fidelity simulations and physical experiments are essential for engineering analysis and design. However, their high cost often limits their applications in two critical tasks: global sensitivity analysis (GSA) and optimization. This limitation motivates the common use of Gaussian processes (GPs) as proxy regression models to provide uncertainty-aware predictions based on a limited number of high-quality observations. GPs naturally enable efficient sampling strategies that support informed decision-making under uncertainty by extracting information from a subset of possible functions for the model of interest. Despite their popularity in machine learning and statistics communities, sampling from GPs has received little attention in the community of engineering optimization. In this paper, we present the formulation and detailed implementation of two notable sampling methods -- random Fourier features and pathwise conditioning -- for generating posterior samples from GPs. Alternative approaches are briefly described. Importantly, we detail how the generated samples can be applied in GSA, single-objective optimization, and multi-objective optimization. We show successful applications of these sampling methods through a series of numerical examples.

--This paper presents Forte, a fully 3D-printable, 6-DoF robotic arm designed to achieve near industrial-grade performance - 0 . As an accessible robot for broad applications across classroom education to AI experiments, Forte pushes forward the performance limitations of existing low-cost educational arms. We introduce a cost-effective mechanical design that combines capstan-based cable drives, timing belts, simple tensioning mechanisms, and lightweight 3D-printed structures, along with topology optimization for structural stiffness. Through careful drivetrain engineering, we minimize backlash and maintain control fidelity without relying on high-power electronics or expensive manufacturing processes. Experimental validation demonstrates that Forte achieves high repeatability and load capacity, offering a compelling robotic platform for both classroom instruction and advanced robotics research. Can we build a 6-degree-of-freedom (DoF) robotic arm with a material cost under $400, while achieving a half-meter workspace, a payload capacity of more than 0.5 kg, and repeatability within 0. 5 mm? We introduce Forte, a fully 3D-printed robotic manipulator, developed to affirmatively answer this question. In light of surging interest in robotics and artificial intelligence, providing accessible, hands-on educational tools has never been more important, as practical experience and experimental validation are essential components of robotics education.

This work evaluates the potential of large language models (LLMs) to power digital assistants capable of complex action execution. These assistants rely on pre-trained programming knowledge to execute multi-step goals by composing objects and functions defined in assistant libraries into action execution programs. To achieve this, we develop ASPERA, a framework comprising an assistant library simulation and a human-assisted LLM data generation engine. Our engine allows developers to guide LLM generation of high-quality tasks consisting of complex user queries, simulation state and corresponding validation programs, tackling data availability and evaluation robustness challenges. Alongside the framework we release Asper-Bench, an evaluation dataset of 250 challenging tasks generated using ASPERA, which we use to show that program generation grounded in custom assistant libraries is a significant challenge to LLMs compared to dependency-free code generation.

Digital textbooks are widely used in various educational contexts, such as university courses and online lectures. Such textbooks yield learning log data that have been used in numerous educational data mining (EDM) studies for student behavior analysis and performance prediction. However, these studies have faced challenges in integrating confidential data, such as academic records and learning logs, across schools due to privacy concerns. Consequently, analyses are often conducted with data limited to a single school, which makes developing high-performing and generalizable models difficult. This study proposes a method that combines federated learning and differential features to address these issues. Federated learning enables model training without centralizing data, thereby preserving student privacy. Differential features, which utilize relative values instead of absolute values, enhance model performance and generalizability. To evaluate the proposed method, a model for predicting at-risk students was trained using data from 1,136 students across 12 courses conducted over 4 years, and validated on hold-out test data from 5 other courses. Experimental results demonstrated that the proposed method addresses privacy concerns while achieving performance comparable to that of models trained via centralized learning in terms of Top-n precision, nDCG, and PR-AUC. Furthermore, using differential features improved prediction performance across all evaluation datasets compared to non-differential approaches. The trained models were also applicable for early prediction, achieving high performance in detecting at-risk students in earlier stages of the semester within the validation datasets.

Diffusion-based generative models have become dominant generators of high-fidelity images and videos but remain limited by their computationally expensive inference procedures. Existing acceleration techniques either require extensive model retraining or compromise significantly on sample quality. This paper explores a general, training-free, and model-agnostic acceleration strategy via multi-core parallelism. Our framework views multi-core diffusion sampling as an ODE solver pipeline, where slower yet accurate solvers progressively rectify faster solvers through a theoretically justified inter-core communication mechanism. This motivates our multi-core training-free diffusion sampling accelerator, CHORDS, which is compatible with various diffusion samplers, model architectures, and modalities. Through extensive experiments, CHORDS significantly accelerates sampling across diverse large-scale image and video diffusion models, yielding up to 2.1x speedup with four cores, improving by 50% over baselines, and 2.9x speedup with eight cores, all without quality degradation. This advancement enables CHORDS to establish a solid foundation for real-time, high-fidelity diffusion generation.