Causal reasoning is often challenging with spatial data, particularly when handling high-dimensional inputs. To address this, we propose a neural network (NN) based framework integrated with an approximate Gaussian process to manage spatial interference and unobserved confounding. Additionally, we adopt a generalized propensity-score-based approach to address partially observed outcomes when estimating causal effects with continuous treatments. We evaluate our framework using synthetic, semi-synthetic, and real-world data inferred from satellite imagery. Our results demonstrate that NN-based models significantly outperform linear spatial regression models in estimating causal effects. Furthermore, in real-world case studies, NN-based models offer more reasonable predictions of causal effects, facilitating decision-making in relevant applications.

It is challenging to guide neural network (NN) learning with prior knowledge. In contrast, many known properties, such as spatial smoothness or seasonality, are straightforward to model by choosing an appropriate kernel in a Gaussian process (GP). Many deep learning applications could be enhanced by modeling such known properties. For example, convolutional neural networks (CNNs) are frequently used in remote sensing, which is subject to strong seasonal effects. We propose to blend the strengths of deep learning and the clear modeling capabilities of GPs by using a composite kernel that combines a kernel implicitly defined by a neural network with a second kernel function chosen to model known properties (e.g., seasonality). We implement this idea by combining a deep network and an efficient mapping based on the Nystrom approximation, which we call Implicit Composite Kernel (ICK). We then adopt a sample-then-optimize approach to approximate the full GP posterior distribution. We demonstrate that ICK has superior performance and flexibility on both synthetic and real-world data sets. We believe that ICK framework can be used to include prior information into neural networks in many applications.

Causal mediation analysis (CMA) is a powerful method to dissect the total effect of a treatment into direct and mediated effects within the potential outcome framework. This is important in many scientific applications to identify the underlying mechanisms of a treatment effect. However, in many scientific applications the mediator is unobserved, but there may exist related measurements. For example, we may want to identify how changes in brain activity or structure mediate an antidepressant's effect on behavior, but we may only have access to electrophysiological or imaging brain measurements. To date, most CMA methods assume that the mediator is one-dimensional and observable, which oversimplifies such real-world scenarios. To overcome this limitation, we introduce a CMA framework that can handle complex and indirectly observed mediators based on the identifiable variational autoencoder (iVAE) architecture. We prove that the true joint distribution over observed and latent variables is identifiable with the proposed method. Additionally, our framework captures a disentangled representation of the indirectly observed mediator and yields accurate estimation of the direct and mediated effects in synthetic and semi-synthetic experiments, providing evidence of its potential utility in real-world applications.

A number of methods have been proposed for causal effect estimation, yet few have demonstrated efficacy in handling data with complex structures, such as images. To fill this gap, we propose Causal Multi-task Deep Ensemble (CMDE), a novel framework that learns both shared and group-specific information from the study population. We provide proofs demonstrating equivalency of CDME to a multi-task Gaussian process (GP) with a coregionalization kernel a priori. Compared to multi-task GP, CMDE efficiently handles high-dimensional and multi-modal covariates and provides pointwise uncertainty estimates of causal effects. We evaluate our method across various types of datasets and tasks and find that CMDE outperforms state-of-the-art methods on a majority of these tasks.

Unsupervised domain adaptation (UDA) is a technique used to transfer knowledge from a labeled source domain to a different but related unlabeled target domain. While many UDA methods have shown success in the past, they often assume that the source and target domains must have identical class label distributions, which can limit their effectiveness in real-world scenarios. To address this limitation, we propose a novel generalization bound that reweights source classification error by aligning source and target sub-domains. We prove that our proposed generalization bound is at least as strong as existing bounds under realistic assumptions, and we empirically show that it is much stronger on real-world data. We then propose an algorithm to minimize this novel generalization bound. We demonstrate by numerical experiments that this approach improves performance in shifted class distribution scenarios compared to state-of-the-art methods.

To improve the compressive sensing MRI (CS - MRI) approaches in terms of fine structure loss under high acceleration factors, we have propose d an iterative feature refinement model (IFR - CS), equipped with fixed transforms, to restore the meaningful structure s and details. Nevertheless, the proposed IFR - CS still has some limitations, such as the selection of hyper - parameters, a lengthy reconstruction time, and the fixed sparsifying transform . To alleviate these issues, we unroll the iterative feature refinement procedure s in IFR - CS to a supervised model - driven network, dubbed IFR - Net. Equipped with training data pairs, both Additionally, inspired by the powerful representation capability of convolutional neural network (CNN), CNN - based inversion blocks are explored in the sparsity - promoting denoising module to generalize the sparsity - enforcing operator . Extensive experiments on both simulated and in v ivo MR datasets have shown that the proposed network possesses a strong capability to capture image details and preserve well the structural information with fast reconstruction speed. Index terms -- Compressed Sensing; Undersampled image reconstruction; IFR - CS; Deep learning; Model - driven network. Magnetic resonance imaging (MRI) is a non - invasive and widely used imaging technique that can provide both functional and anatomical information for clinic al diagnosis. However, the slow imaging speed may result in patient discomfort and motion artifacts. Therefore, increasing MR imaging speed is an important and worthwhile research goal. During the past decades, compressed sensing (CS) has become a popular and successful strategy for fast MR imaging reconstruction [1] - [6] . Zhang and Q. Yang are with the Department of Electronic Information Engineering, Nanchang Universi ty, Nanchang 330031, China. Liu did the work during her internship at Paul C. Lauterbur Research Center for Biomedical Imaging, Chinese Academy of Sciences, Shenzhen, China. S. Wang and D. Liang are with Paul C. Lauterbur Research Center for Biomedical Imaging and the Medical AI Research Center, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China ( sophiasswang@hotmail.com, dong.liang@siat.ac.cn).