Bayesian inference is widely used in many different fields to test hypotheses against observations. In most such applications, an assumption is made of precise input values to produce a precise output value. However, this is unrealistic for real-world applications. Often the best available information from subject matter experts (SMEs) in a given field is interval range estimates of the input probabilities involved in Bayes Theorem. This paper provides two key contributions to extend Bayes Theorem to an interval type-2 (IT2) version. First, we develop an IT2 version of Bayes Theorem that uses a novel and conservative method to avoid potential inconsistencies in the input IT2 MFs that otherwise might produce invalid output results. We then describe a novel and flexible algorithm for encoding SME-provided intervals into IT2 fuzzy membership functions (MFs), which we can use to specify the input probabilities in Bayes Theorem. Our algorithm generalizes and extends previous work on this problem that primarily addressed the encoding of intervals into word MFs for Computing with Words applications.

Modern neural networks (NNs) often achieve high predictive accuracy but are poorly calibrated, producing overconfident predictions even when wrong. This miscalibration poses serious challenges in applications where reliable uncertainty estimates are critical. In this work, we investigate how human perceptual uncertainty compares to uncertainty estimated by NNs. Using three vision benchmarks annotated with both human disagreement and crowdsourced confidence, we assess the correlation between model-predicted uncertainty and human-perceived uncertainty. Our results show that current methods only weakly align with human intuition, with correlations varying significantly across tasks and uncertainty metrics. Notably, we find that incorporating human-derived soft labels into the training process can improve calibration without compromising accuracy. These findings reveal a persistent gap between model and human uncertainty and highlight the potential of leveraging human insights to guide the development of more trustworthy AI systems.

We propose a method for inferring entropy production (EP) in high-dimensional stochastic systems, including many-body systems and non-Markovian systems with long memory. Standard techniques for estimating EP become intractable in such systems due to computational and statistical limitations. We infer trajectory-level EP and lower bounds on average EP by exploiting a nonequilibrium analogue of the Maximum Entropy principle, along with convex duality. Our approach uses only samples of trajectory observables, such as spatiotemporal correlations. It does not require reconstruction of high-dimensional probability distributions or rate matrices, nor impose any special assumptions such as discrete states or multipartite dynamics. In addition, it may be used to compute a hierarchical decomposition of EP, reflecting contributions from different interaction orders, and it has an intuitive physical interpretation as a "thermodynamic uncertainty relation." We demonstrate its numerical performance on a disordered nonequilibrium spin model with 1000 spins and a large neural spike-train dataset.

The increasing availability of personal data has enabled significant advances in fields such as machine learning, healthcare, and cybersecurity. However, this data abundance also raises serious privacy concerns, especially in light of powerful re-identification attacks and growing legal and ethical demands for responsible data use. Differential privacy (DP) has emerged as a principled, mathematically grounded framework for mitigating these risks. This review provides a comprehensive survey of DP, covering its theoretical foundations, practical mechanisms, and real-world applications. It explores key algorithmic tools and domain-specific challenges - particularly in privacy-preserving machine learning and synthetic data generation. The report also highlights usability issues and the need for improved communication and transparency in DP systems. Overall, the goal is to support informed adoption of DP by researchers and practitioners navigating the evolving landscape of data privacy.

We present a novel recursive Bayesian estimation framework using B-splines for continuous-time 6-DoF dynamic motion estimation. The state vector consists of a recurrent set of position control points and orientation control point increments, enabling efficient estimation via a modified iterated extended Kalman filter without involving error-state formulations. The resulting recursive spline estimator (RESPLE) is further leveraged to develop a versatile suite of direct LiDAR-based odometry solutions, supporting the integration of one or multiple LiDARs and an IMU. We conduct extensive real-world evaluations using public datasets and our own experiments, covering diverse sensor setups, platforms, and environments. Compared to existing systems, RESPLE achieves comparable or superior estimation accuracy and robustness, while attaining real-time efficiency. Our results and analysis demonstrate RESPLE's strength in handling highly dynamic motions and complex scenes within a lightweight and flexible design, showing strong potential as a universal framework for multi-sensor motion estimation. We release the source code and experimental datasets at https://github.com/ASIG-X/RESPLE .

The Bayesian paradigm offers principled tools for sequential decision-making under uncertainty, but its reliance on a probabilistic model for all parameters can hinder the incorporation of complex structural constraints. We introduce a minimalist Bayesian framework that places a prior only on the component of interest, such as the location of the optimum. Nuisance parameters are eliminated via profile likelihood, which naturally handles constraints. As a direct instantiation, we develop a MINimalist Thompson Sampling (MINTS) algorithm. Our framework accommodates structured problems, including continuum-armed Lipschitz bandits and dynamic pricing. It also provides a probabilistic lens on classical convex optimization algorithms such as the center of gravity and ellipsoid methods. We further analyze MINTS for multi-armed bandits and establish near-optimal regret guarantees.

Uncertainty Quantification (UQ) is essential in probabilistic machine learning models, particularly for assessing the reliability of predictions. In this paper, we present a systematic framework for estimating both epistemic and aleatoric uncertainty in probabilistic models. We focus on Gaussian Process Latent Variable Models and employ scalable Random Fourier Features-based Gaussian Processes to approximate predictive distributions efficiently. We derive a theoretical formulation for UQ, propose a Monte Carlo sampling-based estimation method, and conduct experiments to evaluate the impact of uncertainty estimation. Our results provide insights into the sources of predictive uncertainty and illustrate the effectiveness of our approach in quantifying the confidence in the predictions.

We introduce a comprehensive framework for the detection and demodulation of covert electromagnetic signals using solid-state spin sensors. Our approach, named RAPID, is a two-stage hybrid strategy that leverages nitrogen-vacancy (NV) centers to operate below the classical noise floor employing a robust adaptive policy via imitation and distillation. We first formulate the joint detection and estimation task as a unified stochastic optimal control problem, optimizing a composite Bayesian risk objective under realistic physical constraints. The RAPID algorithm solves this by first computing a robust, non-adaptive baseline protocol grounded in the quantum Fisher information matrix (QFIM), and then using this baseline to warm-start an online, adaptive policy learned via deep reinforcement learning (Soft Actor-Critic). This method dynamically optimizes control pulses, interrogation times, and measurement bases to maximize information gain while actively suppressing non-Markovian noise and decoherence. Numerical simulations demonstrate that the protocol achieves a significant sensitivity gain over static methods, maintains high estimation precision in correlated noise environments, and, when applied to sensor arrays, enables coherent quantum beamforming that achieves Heisenberg-like scaling in precision. This work establishes a theoretically rigorous and practically viable pathway for deploying quantum sensors in security-critical applications such as electronic warfare and covert surveillance.

We consider two-player zero-sum concurrent stochastic games (CSGs) played on graphs with reachability and safety objectives. These include degenerate classes such as Markov decision processes or turn-based stochastic games, which can be solved by linear or quadratic programming; however, in practice, value iteration (VI) outperforms the other approaches and is the most implemented method. Similarly, for CSGs, this practical performance makes VI an attractive alternative to the standard theoretical solution via the existential theory of reals. VI starts with an under-approximation of the sought values for each state and iteratively updates them, traditionally terminating once two consecutive approximations are $ε$-close. However, this stopping criterion lacks guarantees on the precision of the approximation, which is the goal of this work. We provide bounded (a.k.a. interval) VI for CSGs: it complements standard VI with a converging sequence of over-approximations and terminates once the over- and under-approximations are $ε$-close.

This paper presents a feature-based Partially Observable Markov Decision Process (POMDP) framework for quantum network routing, combining belief-state planning with Graph Neural Networks (GNNs) to address partial observability, decoherence, and scalability challenges in dynamic quantum systems. Our approach encodes complex quantum network dynamics, including entanglement degradation and time-varying channel noise, into a low-dimensional feature space, enabling efficient belief updates and scalable policy learning. The core of our framework is a hybrid GNN-POMDP architecture that processes graph-structured representations of entangled links to learn routing policies, coupled with a noise-adaptive mechanism that fuses POMDP belief updates with GNN outputs for robust decision making. We provide a theoretical analysis establishing guarantees for belief convergence, policy improvement, and robustness to noise. Experiments on simulated quantum networks with up to 100 nodes demonstrate significant improvements in routing fidelity and entanglement delivery rates compared to state-of-the-art baselines, particularly under high decoherence and nonstationary conditions.