Quan Long

Joakim Beck, Ben Mansour Dia, Luis FR Espath et al.

In calculating expected information gain in optimal Bayesian experimental design, the computation of the inner loop in the classical double-loop Monte Carlo requires a large number of samples and suffers from underflow if the number of samples is small. These drawbacks can be avoided by using an importance sampling approach. We present a computationally efficient method for optimal Bayesian experimental design that introduces importance sampling based on the Laplace method to the inner loop. We derive the optimal values for the method parameters in which the average computational cost is minimized according to the desired error tolerance. We use three numerical examples to demonstrate the computational efficiency of our method compared with the classical double-loop Monte Carlo, and a more recent single-loop Monte Carlo method that uses the Laplace method as an approximation of the return value of the inner loop. The first example is a scalar problem that is linear in the uncertain parameter. The second example is a nonlinear scalar problem. The third example deals with the optimal sensor placement for an electrical impedance tomography experiment to recover the fiber orientation in laminate composites.

Quan Long, Mohammad Motamed, Raul Tempone

We develop a fast method for optimally designing experiments in the context of statistical seismic source inversion. In particular, we efficiently compute the optimal number and locations of the receivers or seismographs. The seismic source is modeled by a point moment tensor multiplied by a time-dependent function. The parameters include the source location, moment tensor components, and start time and frequency in the time function. The forward problem is modeled by elastodynamic wave equations. We show that the Hessian of the cost functional, which is usually defined as the square of the weighted L2 norm of the difference between the experimental data and the simulated data, is proportional to the measurement time and the number of receivers. Consequently, the posterior distribution of the parameters, in a Bayesian setting, concentrates around the "true" parameters, and we can employ Laplace approximation and speed up the estimation of the expected Kullback-Leibler divergence (expected information gain), the optimality criterion in the experimental design procedure. Since the source parameters span several magnitudes, we use a scaling matrix for efficient control of the condition number of the original Hessian matrix. We use a second-order accurate finite difference method to compute the Hessian matrix and either sparse quadrature or Monte Carlo sampling to carry out numerical integration. We demonstrate the efficiency, accuracy, and applicability of our method on a two-dimensional seismic source inversion problem.

Quan Long

Most methods in explainable AI (XAI) focus on providing reasons for the prediction of a given set of features. However, we solve an inverse explanation problem, i.e., given the deviation of a label, find the reasons of this deviation. We use a Bayesian framework to recover the ``true'' features, conditioned on the observed label value. We efficiently explain the deviation of a label value from the mode, by identifying and ranking the influential features using the ``distances'' in the ANOVA functional decomposition. We show that the new method is more human-intuitive and robust than methods based on mean values, e.g., SHapley Additive exPlanations (SHAP values). The extra costs of solving a Bayesian inverse problem are dimension-independent.

Karen Ardila, Aashka Mohite, Abdoljalil Addeh et al.

Brain aging trajectories differ between males and females, yet the genetic factors underlying these differences remain underexplored. Using structural MRI and genotyping data from 40,940 UK Biobank participants (aged 45-83), we computed Brain Age Gap Estimates (BrainAGE) for total brain, hippocampal, and ventricular volumes. We conducted sex-stratified genome-wide association studies (GWAS) and Post-GWAS analyses to identify genetic variants associated with accelerated brain aging. Distinct gene sets emerged by sex: in females, neurotransmitter transport and mitochondrial stress response genes were implicated; in males, immune and inflammation-related genes dominated. Shared genes, including GMNC and OSTN, were consistently linked to brain volumes across sexes, suggesting core roles in neurostructural maintenance. Tissue expression analyses revealed sex-specific enrichment in pathways tied to neurodegeneration. These findings highlight the importance of sex-stratified approaches in aging research and suggest genetic targets for personalized interventions against age-related cognitive decline.

Quan Long, Bin Wang, Bing Xue et al.

To address the issue of interpretability in multilayer perceptrons (MLPs), Kolmogorov-Arnold Networks (KANs) are introduced in 2024. However, optimizing KAN structures is labor-intensive, typically requiring manual intervention and parameter tuning. This paper proposes GA-KAN, a genetic algorithm-based approach that automates the optimization of KANs, requiring no human intervention in the design process. To the best of our knowledge, this is the first time that evolutionary computation is explored to optimize KANs automatically. Furthermore, inspired by the use of sparse connectivity in MLPs in effectively reducing the number of parameters, GA-KAN further explores sparse connectivity to tackle the challenge of extensive parameter spaces in KANs. GA-KAN is validated on two toy datasets, achieving optimal results without the manual tuning required by the original KAN. Additionally, GA-KAN demonstrates superior performance across five classification datasets, outperforming traditional methods on all datasets and providing interpretable symbolic formulae for the Wine and Iris datasets, thereby enhancing model transparency. Furthermore, GA-KAN significantly reduces the number of parameters over the standard KAN across all the five datasets. The core contributions of GA-KAN include automated optimization, a new encoding strategy, and a new decoding process, which together improve the accuracy and interpretability, and reduce the number of parameters.

Mingmin Zhen, Jinglu Wang, Lei Zhou et al.

In this paper, we present a joint multi-task learning framework for semantic segmentation and boundary detection. The critical component in the framework is the iterative pyramid context module (PCM), which couples two tasks and stores the shared latent semantics to interact between the two tasks. For semantic boundary detection, we propose the novel spatial gradient fusion to suppress nonsemantic edges. As semantic boundary detection is the dual task of semantic segmentation, we introduce a loss function with boundary consistency constraint to improve the boundary pixel accuracy for semantic segmentation. Our extensive experiments demonstrate superior performance over state-of-the-art works, not only in semantic segmentation but also in semantic boundary detection. In particular, a mean IoU score of 81:8% on Cityscapes test set is achieved without using coarse data or any external data for semantic segmentation. For semantic boundary detection, we improve over previous state-of-the-art works by 9.9% in terms of AP and 6:8% in terms of MF(ODS).