James Martin

Tiangang Cui, James Martin, Youssef M. Marzouk et al.

The intrinsic dimensionality of an inverse problem is affected by prior information, the accuracy and number of observations, and the smoothing properties of the forward operator. From a Bayesian perspective, changes from the prior to the posterior may, in many problems, be confined to a relatively low-dimensional subspace of the parameter space. We present a dimension reduction approach that defines and identifies such a subspace, called the "likelihood-informed subspace" (LIS), by characterizing the relative influences of the prior and the likelihood over the support of the posterior distribution. This identification enables new and more efficient computational methods for Bayesian inference with nonlinear forward models and Gaussian priors. In particular, we approximate the posterior distribution as the product of a lower-dimensional posterior defined on the LIS and the prior distribution marginalized onto the complementary subspace. Markov chain Monte Carlo sampling can then proceed in lower dimensions, with significant gains in computational efficiency. We also introduce a Rao-Blackwellization strategy that de-randomizes Monte Carlo estimates of posterior expectations for additional variance reduction. We demonstrate the efficiency of our methods using two numerical examples: inference of permeability in a groundwater system governed by an elliptic PDE, and an atmospheric remote sensing problem based on Global Ozone Monitoring System (GOMOS) observations.

Chiara Lena, Davide Milesi, Alessandro Casella et al.

Deep learning has the potential to improve colonoscopy by enabling 3D reconstruction of the colon, providing a comprehensive view of mucosal surfaces and lesions, and facilitating the identification of unexplored areas. However, the development of robust methods is limited by the scarcity of large-scale ground truth data. We propose RealSynCol, a highly realistic synthetic dataset designed to replicate the endoscopic environment. Colon geometries extracted from 10 CT scans were imported into a virtual environment that closely mimics intraoperative conditions and rendered with realistic vascular textures. The resulting dataset comprises 28\,130 frames, paired with ground truth depth maps, optical flow, 3D meshes, and camera trajectories. A benchmark study was conducted to evaluate the available synthetic colon datasets for the tasks of depth and pose estimation. Results demonstrate that the high realism and variability of RealSynCol significantly enhance generalization performance on clinical images, proving it to be a powerful tool for developing deep learning algorithms to support endoscopic diagnosis.

Niloufar Mehrabi, Sayed Pedram Haeri Boroujeni, Jenna Hofseth et al.

Unmanned Aerial Vehicles (UAVs) play an increasingly critical role in Intelligence, Surveillance, and Reconnaissance (ISR) missions such as border patrolling and criminal detection, thanks to their ability to access remote areas and transmit real-time imagery to processing servers. However, UAVs are highly constrained by payload size, power limits, and communication bandwidth, necessitating the development of highly selective and efficient data transmission strategies. This has driven the development of various compression and optimal transmission technologies for UAVs. Nevertheless, most methods strive to preserve maximal information in transferred video frames, missing the fact that only certain parts of images/video frames might offer meaningful contributions to the ultimate mission objectives in the ISR scenarios involving moving object detection and tracking (OD/OT). This paper adopts a different perspective, and offers an alternative AI-driven scheduling policy that prioritizes selecting regions of the image that significantly contributes to the mission objective. The key idea is tiling the image into small patches and developing a deep reinforcement learning (DRL) framework that assigns higher transmission probabilities to patches that present higher overlaps with the detected object of interest, while penalizing sharp transitions over consecutive frames to promote smooth scheduling shifts. Although we used Yolov-8 object detection and UDP transmission protocols as a benchmark testing scenario the idea is general and applicable to different transmission protocols and OD/OT methods. To further boost the system's performance and avoid OD errors for cluttered image patches, we integrate it with interframe interpolations.

Jannatun Naim, Jie Cao, Fareen Tasneem et al.

Effective feedback is essential for refining instructional practices in mathematics education, and researchers often turn to advanced natural language processing (NLP) models to analyze classroom dialogues from multiple perspectives. However, utterance-level discourse analysis encounters two primary challenges: (1) multifunctionality, where a single utterance may serve multiple purposes that a single tag cannot capture, and (2) the exclusion of many utterances from domain-specific discourse move classifications, leading to their omission in feedback. To address these challenges, we proposed a multi-perspective discourse analysis that integrates domain-specific talk moves with dialogue act (using the flattened multi-functional SWBD-MASL schema with 43 tags) and discourse relation (applying Segmented Discourse Representation Theory with 16 relations). Our top-down analysis framework enables a comprehensive understanding of utterances that contain talk moves, as well as utterances that do not contain talk moves. This is applied to two mathematics education datasets: TalkMoves (teaching) and SAGA22 (tutoring). Through distributional unigram analysis, sequential talk move analysis, and multi-view deep dive, we discovered meaningful discourse patterns, and revealed the vital role of utterances without talk moves, demonstrating that these utterances, far from being mere fillers, serve crucial functions in guiding, acknowledging, and structuring classroom discourse. These insights underscore the importance of incorporating discourse relations and dialogue acts into AI-assisted education systems to enhance feedback and create more responsive learning environments. Our framework may prove helpful for providing human educator feedback, but also aiding in the development of AI agents that can effectively emulate the roles of both educators and students.

Alessio Spantini, Antti Solonen, Tiangang Cui et al.

In the Bayesian approach to inverse problems, data are often informative, relative to the prior, only on a low-dimensional subspace of the parameter space. Significant computational savings can be achieved by using this subspace to characterize and approximate the posterior distribution of the parameters. We first investigate approximation of the posterior covariance matrix as a low-rank update of the prior covariance matrix. We prove optimality of a particular update, based on the leading eigendirections of the matrix pencil defined by the Hessian of the negative log-likelihood and the prior precision, for a broad class of loss functions. This class includes the Förstner metric for symmetric positive definite matrices, as well as the Kullback-Leibler divergence and the Hellinger distance between the associated distributions. We also propose two fast approximations of the posterior mean and prove their optimality with respect to a weighted Bayes risk under squared-error loss. These approximations are deployed in an offline-online manner, where a more costly but data-independent offline calculation is followed by fast online evaluations. As a result, these approximations are particularly useful when repeated posterior mean evaluations are required for multiple data sets. We demonstrate our theoretical results with several numerical examples, including high-dimensional X-ray tomography and an inverse heat conduction problem. In both of these examples, the intrinsic low-dimensional structure of the inference problem can be exploited while producing results that are essentially indistinguishable from solutions computed in the full space.