Conditional independence (CI) testing is a fundamental task in modern statistics and machine learning. The conditional randomization test (CRT) was recently introduced to test whether two random variables, X and Y, are conditionally independent given a potentially high-dimensional set of random variables, Z. The CRT operates exceptionally well under the assumption that the conditional distribution X|Z is known. However, since this distribution is typically unknown in practice, accurately approximating it becomes crucial. In this paper, we propose using conditional diffusion models (CDMs) to learn the distribution of X|Z. Theoretically and empirically, it is shown that CDMs closely approximate the true conditional distribution. Furthermore, CDMs offer a more accurate approximation of X|Z compared to GANs, potentially leading to a CRT that performs better than those based on GANs. To accommodate complex dependency structures, we utilize a computationally efficient classifier-based conditional mutual information (CMI) estimator as our test statistic. The proposed testing procedure performs effectively without requiring assumptions about specific distribution forms or feature dependencies, and is capable of handling mixed-type conditioning sets that include both continuous and discrete variables. Theoretical analysis shows that our proposed test achieves a valid control of the type I error. A series of experiments on synthetic data demonstrates that our new test effectively controls both type-I and type-II errors, even in high dimensional scenarios.

In this paper, we propose a novel framework, the Sampling-guided Heterogeneous Graph Neural Network (HT-GNN), to effectively tackle the challenge of missing data imputation in longitudinal studies. Unlike traditional methods, which often require extensive preprocessing to handle irregular or inconsistent missing data, our approach accommodates arbitrary missing data patterns while maintaining computational efficiency. HT-GNN models both observations and covariates as distinct node types, connecting observation nodes at successive time points through subject-specific longitudinal subnetworks, while covariate-observation interactions are represented by attributed edges within bipartite graphs. By leveraging subject-wise mini-batch sampling and a multi-layer temporal smoothing mechanism, HT-GNN efficiently scales to large datasets, while effectively learning node representations and imputing missing data. Extensive experiments on both synthetic and real-world datasets, including the Alzheimer's Disease Neuroimaging Initiative (DNI) dataset, demonstrate that HT-GNN significantly outperforms existing imputation methods, even with high missing data rates (e.g., 80%). The empirical results highlight HT-GNN's robust imputation capabilities and superior performance, particularly in the context of complex, large-scale longitudinal data.

The conditional randomization test (CRT) was recently proposed to test whether two random variables X and Y are conditionally independent given random variables Z. The CRT assumes that the conditional distribution of X given Z is known under the null hypothesis and then it is compared to the distribution of the observed samples of the original data. The aim of this paper is to develop a novel alternative of CRT by using nearest-neighbor sampling without assuming the exact form of the distribution of X given Z. Specifically, we utilize the computationally efficient 1-nearest-neighbor to approximate the conditional distribution that encodes the null hypothesis. Then, theoretically, we show that the distribution of the generated samples is very close to the true conditional distribution in terms of total variation distance. Furthermore, we take the classifier-based conditional mutual information estimator as our test statistic. The test statistic as an empirical fundamental information theoretic quantity is able to well capture the conditional-dependence feature. We show that our proposed test is computationally very fast, while controlling type I and II errors quite well. Finally, we demonstrate the efficiency of our proposed test in both synthetic and real data analyses.

Conditional independence (CI) testing is a fundamental task in statistics and machine learning, but its effectiveness is hindered by the challenges posed by high-dimensional conditioning variables and limited data samples. This article introduces a novel testing approach to address these challenges and enhance control of the type I error while achieving high power under alternative hypotheses. The proposed approach incorporates a computationally efficient classifier-based conditional mutual information (CMI) estimator, capable of capturing intricate dependence structures among variables. To approximate a distribution encoding the null hypothesis, a $k$-nearest-neighbor local sampling strategy is employed. An important advantage of this approach is its ability to operate without assumptions about distribution forms or feature dependencies. Furthermore, it eliminates the need to derive asymptotic null distributions for the estimated CMI and avoids dataset splitting, making it particularly suitable for small datasets. The method presented in this article demonstrates asymptotic control of the type I error and consistency against all alternative hypotheses. Extensive analyses using both synthetic and real data highlight the computational efficiency of the proposed test. Moreover, it outperforms existing state-of-the-art methods in terms of type I and II errors, even in scenarios with high-dimensional conditioning sets. Additionally, the proposed approach exhibits robustness in the presence of heavy-tailed data.

Deep neural networks (DNNs) have achieved great success in image classification, but can be very vulnerable to adversarial attacks with small perturbations to images. To improve adversarial image generation for DNNs, we develop a novel method, called mFI-PSO, which utilizes a Manifold-based First-order Influence measure for vulnerable image and pixel selection and the Particle Swarm Optimization for various objective functions. Our mFI-PSO can thus effectively design adversarial images with flexible, customized options on the number of perturbed pixels, the misclassification probability, and the targeted incorrect class. Experiments demonstrate the flexibility and effectiveness of our mFI-PSO in adversarial attacks and its appealing advantages over some popular methods.