Scientific machine learning increasingly uses spectral methods to understand physical systems. Current spectral learning approaches provide only point estimates without uncertainty quantification, limiting their use in safety-critical applications where prediction confidence is essential. Parametric matrix models have emerged as powerful tools for scientific machine learning, achieving exceptional performance by learning governing equations. However, their deterministic nature limits deployment in uncertainty quantification applications. We introduce Bayesian parametric matrix models (B-PMMs), a principled framework that extends PMMs to provide uncertainty estimates while preserving their spectral structure and computational efficiency. B-PMM addresses the fundamental challenge of quantifying uncertainty in matrix eigenvalue problems where standard Bayesian methods fail due to the geometric constraints of spectral decomposition. The theoretical contributions include: (i) adaptive spectral decomposition with regularized matrix perturbation bounds that characterize eigenvalue uncertainty propagation, (ii) structured variational inference algorithms using manifold-aware matrix-variate Gaussian posteriors that respect Hermitian constraints, and (iii) finite-sample calibration guarantees with explicit dependence on spectral gaps and problem conditioning. Experimental validation across matrix dimensions from 5x5 to 500x500 with perfect convergence rates demonstrates that B-PMMs achieve exceptional uncertainty calibration (ECE < 0.05) while maintaining favorable scaling. The framework exhibits graceful degradation under spectral ill-conditioning and provides reliable uncertainty estimates even in near-degenerate regimes. The proposed framework supports robust spectral learning in uncertainty-critical domains and lays the groundwork for broader Bayesian spectral machine learning.

We investigate individual fairness in generative probabilistic classifiers by analysing the robustness of posterior inferences to perturbations in private features. Building on established results in robustness analysis, we hypothesise a correlation between robustness and predictive accuracy, specifically, instances exhibiting greater robustness are more likely to be classified accurately. We empirically assess this hypothesis using a benchmark of fourteen datasets with fairness concerns, employing Bayesian networks as the underlying generative models. To address the computational complexity associated with robustness analysis over multiple private features with Bayesian networks, we reformulate the problem as a most probable explanation task in an auxiliary Markov random field. Our experiments confirm the hypothesis about the correlation, suggesting novel directions to mitigate the traditional trade-off between fairness and accuracy.

Machine learning models and libraries can train datasets of different sizes and perform prediction and classification operations, but machine learning models and libraries cause slow and long training times on large datasets. This article introduces EmbeddedML, a training-time-optimized and mathematically enhanced machine learning library. The speed was increased by approximately times compared to scikit-learn without any loss in terms of accuracy in regression models such as Multiple Linear Regression. Logistic Regression and Support Vector Machines (SVM) algorithms have been mathematically rewritten to reduce training time and increase accuracy in classification models. With the applied mathematical improvements, training time has been reduced by approximately 2 times for SVM on small datasets and by around 800 times on large datasets, and by approximately 4 times for Logistic Regression, compared to the scikit-learn implementation. In summary, the EmbeddedML library offers regression, classification, clustering, and dimensionality reduction algorithms that are mathematically rewritten and optimized to reduce training time.

Robots operating in daily life environments must understand object ownership to carry out instructions naturally given by users, such as "Bring me my cup." Without ownership knowledge, a robot cannot determine which object is being referred to when multiple similar objects exist. This problem is especially evident in kitchens, offices, or laboratories, where objects with similar appearances may belong to different individuals. Relying solely on perceptual features such as location or appearance is insufficient because ownership is inherently context-dependent and often determined by social conventions. Therefore, enabling robots to acquire ownership knowledge is a crucial step toward socially appropriate human-robot interaction. To enable robots to learn object ownership in daily life environments, it is essential to implement a question-generation mechanism that efficiently acquires necessary information. However, in real-world environments with large numbers of objects, this is impractical and imposes a heavy burden on users. Although robots can explore the environment to collect visual features of objects, it remains difficult to obtain ownership knowledge because it depends on users and context. Therefore, allowing robots to ask questions based on the current situation enables them to acquire ownership knowl-Saki Hashimoto is the presenter of this paper.

In this paper, we present a maximum likelihood estimation approach to determine the value vector in transformer models. We model the sequence of value vectors, key vectors, and the query vector as a sequence of Gaussian distributions. The variance in each Gaussian distribution depends on the time step, the corresponding key vector, and the query vector. The mean value in each Gaussian distribution depends on the time step, and the corresponding value vector. This analysis may offer a new explanation of the scaled-dot-product function or softmax function used in transformer architectures [1]. Another explanation, inspired by [4], is based on the maximum entropy approach in natural language processing [5]. In this approach, a query vector and key vectors are used to derive the feature functions for the maximum entropy model.

This paper investigates the strategic concealment of environment representations used by players in competitive games. We consider a defense scenario in which one player (the Defender) seeks to infer and exploit the representation used by the other player (the Attacker). The interaction between the two players is modeled as a Bayesian game: the Defender infers the Attacker's representation from its trajectory and places barriers to obstruct the Attacker's path towards its goal, while the Attacker obfuscates its representation type to mislead the Defender. We solve for the Perfect Bayesian Nash Equilibrium via a bilinear program that integrates Bayesian inference, strategic planning, and belief manipulation. Simulations show that purposeful concealment naturally emerges: the Attacker randomizes its trajectory to manipulate the Defender's belief, inducing suboptimal barrier selections and thereby gaining a strategic advantage.

Evaluating tabular generators remains a challenging problem, as the unique causal structural prior of heterogeneous tabular data does not lend itself to intuitive human inspection. Recent work has introduced structural fidelity as a tabular-specific evaluation dimension to assess whether synthetic data complies with the causal structures of real data. However, existing benchmarks often neglect the interplay between structural fidelity and conventional evaluation dimensions, thus failing to provide a holistic understanding of model performance. Moreover, they are typically limited to toy datasets, as quantifying existing structural fidelity metrics requires access to ground-truth causal structures, which are rarely available for real-world datasets. In this paper, we propose a novel evaluation framework that jointly considers structural fidelity and conventional evaluation dimensions. We introduce a new evaluation metric, $\textbf{global utility}$, which enables the assessment of structural fidelity even in the absence of ground-truth causal structures. In addition, we present $\textbf{TabStruct}$, a comprehensive evaluation benchmark offering large-scale quantitative analysis on 13 tabular generators from nine distinct categories, across 29 datasets. Our results demonstrate that global utility provides a task-independent, domain-agnostic lens for tabular generator performance. We release the TabStruct benchmark suite, including all datasets, evaluation pipelines, and raw results. Code is available at https://github.com/SilenceX12138/TabStruct.

This paper addresses 6-DOF (degree-of-freedom) tactile localization, i.e. the pose estimation of tridimensional objects given tactile measurements. This estimation problem is fundamental for the operation of autonomous robots that are often required to manipulate and grasp objects whose pose is a-priori unknown. The nature of tactile measurements, the strict time requirements for real-time operation and the multimodality of the involved probability distributions pose remarkable challenges and call for advanced nonlinear filtering techniques. Following a Bayesian approach, this paper proposes a novel and effective algorithm, named Memory Unscented Particle Filter (MUPF), which solves the 6-DOF localization problem recursively in real-time by only exploiting contact point measurements. MUPF combines a modified particle filter that incorporates a sliding memory of past measurements to better handle multimodal distributions, along with the unscented Kalman filter that moves the particles towards regions of the search space that are more likely with the measurements. The performance of the proposed MUPF algorithm has been assessed both in simulation and on a real robotic system equipped with tactile sensors (i.e., the iCub humanoid robot). The experiments show that the algorithm provides accurate and reliable localization even with a low number of particles and, hence, is compatible with real-time requirements.

Anomaly detection in dynamic graphs is essential for identifying malicious activities, fraud, and unexpected behaviors in real-world systems such as cybersecurity and power grids. However, existing approaches struggle with scalability, probabilistic interpretability, and adaptability to evolving traffic patterns. In this paper, we propose ADAPTIVE-GRAPHSKETCH, a lightweight and scalable framework for real-time anomaly detection in streaming edge data. Our method integrates temporal multi-tensor sketching with Count-Min Sketch using Conservative Update (CMS-CU) to compactly track edge frequency patterns with bounded memory, while mitigating hash collision issues. We incorporate Bayesian inference for probabilistic anomaly scoring and apply Exponentially Weighted Moving Average (EWMA) for adaptive thresholding tuned to burst intensity. Extensive experiments on four real-world intrusion detection datasets demonstrate that ADAPTIVE-GRAPHSKETCH outperforms state-of-the-art baselines such as ANOEDGE-G/L, MIDAS-R, and F-FADE, achieving up to 6.5% AUC gain on CIC-IDS2018 and up to 15.6% on CIC-DDoS2019, while processing 20 million edges in under 3.4 seconds using only 10 hash functions. Our results show that ADAPTIVE-GRAPHSKETCH is practical and effective for fast, accurate anomaly detection in large-scale streaming graphs. Keywords: Anomaly Detection, Streaming, Real-time, Dynamic Graphs, Edge Streams, Tensor Sketching

Understanding human behavior traits is central to applications in human-computer interaction, computational social science, and personalized AI systems. Such understanding often requires integrating multiple modalities to capture nuanced patterns and relationships. However, existing resources rarely provide datasets that combine behavioral descriptors with complementary modalities such as facial attributes and biographical information. To address this gap, we present PersonaX, a curated collection of multimodal datasets designed to enable comprehensive analysis of public traits across modalities. PersonaX consists of (1) CelebPersona, featuring 9444 public figures from diverse occupations, and (2) AthlePersona, covering 4181 professional athletes across 7 major sports leagues. Each dataset includes behavioral trait assessments inferred by three high-performing large language models, alongside facial imagery and structured biographical features. We analyze PersonaX at two complementary levels. First, we abstract high-level trait scores from text descriptions and apply five statistical independence tests to examine their relationships with other modalities. Second, we introduce a novel causal representation learning (CRL) framework tailored to multimodal and multi-measurement data, providing theoretical identifiability guarantees. Experiments on both synthetic and real-world data demonstrate the effectiveness of our approach. By unifying structured and unstructured analysis, PersonaX establishes a foundation for studying LLM-inferred behavioral traits in conjunction with visual and biographical attributes, advancing multimodal trait analysis and causal reasoning.