Purdue University is a public research university in West Lafayette, Indiana, and the flagship campus of the Purdue University system. The university was founded in 1869 after Lafayette businessman John Purdue donated land and money to establish a college of science, technology, and agriculture in his name. The first classes were held on September 16, 1874, with six instructors and 39 students.The main campus in West Lafayette offers more than 200 majors for undergraduates, over 69 masters and doctoral programs, and professional degrees in pharmacy and veterinary medicine. In addition, Purdue has 18 intercollegiate sports teams and more than 900 student organizations. Purdue is a member of the Big Ten Conference and enrolls the second largest student body of any university in Indiana, as well as the fourth largest foreign student population of any university in the United States.Purdue University is a member of the Association of American Universities and is classified among "R1: Doctoral Universities – Very high research activity". Purdue has 25 American astronauts as alumni and as of April 2019, the university has been associated with 13 Nobel Prizes.
Motivated by applications in tissue-wide association studies (TWAS), we develop a flexible and theoretically grounded empirical Bayes approach for integrating
Deep learning has revolutionized modern data science. However, how to accurately quantify the uncertainty of predictions from large-scale deep neural networks (DNNs) remains an unresolved issue. To address this issue, we introduce a novel post-processing approach. This approach feeds the output from the last hidden layer of a pre-trained large-scale DNN model into a stochastic neural network (StoNet), then trains the StoNet with a sparse penalty on a validation dataset and constructs prediction intervals for future observations. We establish a theoretical guarantee for the validity of this approach; in particular, the parameter estimation consistency for the sparse StoNet is essential for the success of this approach. Comprehensive experiments demonstrate that the proposed approach can construct honest confidence intervals with shorter interval lengths compared to conformal methods and achieves better calibration compared to other post-hoc calibration techniques. Additionally, we show that the StoNet formulation provides us with a platform to adapt sparse learning theory and methods from linear models to DNNs.
Traffic state estimation from sparse fixed sensors is challenging because physics-informed neural networks (PINNs) tend to over-smooth sharp transitions admitted by the Lighthill-Whitham-Richards (LWR) model. This study proposes Two-Stage Domain Decomposition Physics Informed Neural Networks (TSDD-PINN), an observation-aligned framework for LWR-based fline speed-field reconstruction. The framework supports spatial, temporal, and space-time refinement. Matched direction analysis shows that spatial refinement has the lowest mean error and less than half the training time of space-time refinement in the tested setting, while temporal finement is faster. A global parent PINN is first trained. In the controlled spatial implementation, its residual profile guides a deterministic partition for warm-started child networks. An optional operational safeguard retains Stage 1 when the prespecified screen does not activate. The primary I-24 MOTION evaluation spans six methods, five days, five sensor configurations, and ten seeds per configuration, yielding 1,500 runs. Controlled TSDD-PINN attains the lowest relative L2 error in 18 of 25 configurations and 14 of 15 sparse-sensing cases, while training 2.4 times faster than the extended PINN (XPINN) baseline under the evaluated implementations and training budgets. Non-neural comparisons show that the advantage over interpolation is concentrated under sparse sensing, whereas dense sensing often favors interpolation. A separate 250-run operational evaluation finds infrequent activation and motivates the Stage-1-preserving safeguard. The residual treated as an indicator of model difficulty rather than a validated shock detector. The evidence supports a sensing-density-dependent operating range rather than uniform improvement.
The paper considers the construction of two new orthogonal multiwavelets with supercompact support by using the Fast Bauer's method for matrix spectral factorization on the matrix product filter of the orthogonal CL multiwavelet filter. The new multiwavelets possess orthogonality, symmetry/antisymmetry, and one of them provides better coding and smoothness than other supercompact multiwavelets. The performance of the new multiwavelet filters in subband-based edge detection, grayscale and color image compression and 1D and 2D signal denoising is compared with the GHM, SA4, CL, Integer Haar and Alpert multifilters. The comparative analysis shows that new multiwavelets can provides better human visual measures, SSIM and MS-SSIM in image compression and denoising applications.
Large spatial datasets with non-Gaussian responses are increasingly common in environmental monitoring, ecology, and remote sensing, yet scalable Bayesian inference for such data remains challenging. Markov chain Monte Carlo (MCMC) methods are often prohibitive for large datasets, and existing variational Bayes methods rely on conjugacy or strong approximations that limit their applicability and can underestimate posterior variances. A scalable variational framework that incorporates semi-implicit variational inference (SIVI) with basis representations of spatial generalized linear mixed models (SGLMMs), which may not have conjugacy, is proposed. The proposed framework accommodates gamma, negative binomial, Poisson, Bernoulli, and Gaussian responses on continuous spatial domains. Across 20 simulation scenarios with 50,000 locations, SIVI achieves predictive accuracy and posterior distributions comparable to Metropolis-Hastings and Hamiltonian Monte Carlo while providing notable computational speedups. Applications to MODIS land surface temperature and Blue Jay abundance further demonstrate the utility of the approach for large non-Gaussian spatial datasets.
