Edge detection is crucial in image processing, but existing methods often produce overly detailed edge maps, affecting clarity. Fixed-window statistical testing faces issues like scale mismatch and computational redundancy. To address these, we propose a novel Multi-scale Adaptive Independence Testing-based Edge Detection and Denoising (EDD-MAIT), a Multi-scale Adaptive Statistical Testing-based edge detection and denoising method that integrates a channel attention mechanism with independence testing. A gradient-driven adaptive window strategy adjusts window sizes dynamically, improving detail preservation and noise suppression. EDD-MAIT achieves better robustness, accuracy, and efficiency, outperforming traditional and learning-based methods on BSDS500 and BIPED datasets, with improvements in F-score, MSE, PSNR, and reduced runtime. It also shows robustness against Gaussian noise, generating accurate and clean edge maps in noisy environments.
Post-nonlinear (PNL) causal models stand out as a versatile and adaptable framework for modeling intricate causal relationships. However, accurately capturing the invertibility constraint required in PNL models remains challenging in existing studies. To address this problem, we introduce CAF-PoNo (Causal discovery via Normalizing Flows for Post-Nonlinear models), harnessing the power of the normalizing flows architecture to enforce the crucial invertibility constraint in PNL models. Through normalizing flows, our method precisely reconstructs the hidden noise, which plays a vital role in cause-effect identification through statistical independence testing. Furthermore, the proposed approach exhibits remarkable extensibility, as it can be seamlessly expanded to facilitate multivariate causal discovery via causal order identification, empowering us to efficiently unravel complex causal relationships. Extensive experimental evaluations on both simulated and real datasets consistently demonstrate that the proposed method outperforms several state-of-the-art approaches in both bivariate and multivariate causal discovery tasks.
We present a novel framework for learning system design with neural feature extractors. First, we introduce the feature geometry, which unifies statistical dependence and feature representations in a function space equipped with inner products. This connection defines function-space concepts on statistical dependence, such as norms, orthogonal projection, and spectral decomposition, exhibiting clear operational meanings. In particular, we associate each learning setting with a dependence component and formulate learning tasks as finding corresponding feature approximations. We propose a nesting technique, which provides systematic algorithm designs for learning the optimal features from data samples with off-the-shelf network architectures and optimizers. We further demonstrate multivariate learning applications, including conditional inference and multimodal learning, where we present the optimal features and reveal their connections to classical approaches.
Conditional independence (CI) tests underlie many approaches to model testing and structure learning in causal inference. Most existing CI tests for categorical and ordinal data stratify the sample by the conditioning variables, perform simple independence tests in each stratum, and combine the results. Unfortunately, the statistical power of this approach degrades rapidly as the number of conditioning variables increases. Here we propose a simple unified CI test for ordinal and categorical data that maintains reasonable calibration and power in high dimensions. We show that our test outperforms existing baselines in model testing and structure learning for dense directed graphical models while being comparable for sparse models. Our approach could be attractive for causal model testing because it is easy to implement, can be used with non-parametric or parametric probability models, has the symmetry property, and has reasonable computational requirements.
Statistical independence and conditional independence are two fundamental concepts in statistics and machine learning. Copula Entropy is a mathematical concept defined by Ma and Sun for multivariate statistical independence measuring and testing, and also proved to be closely related to conditional independence (or transfer entropy). As the unified framework for measuring both independence and causality, CE has been applied to solve several related statistical or machine learning problems, including association discovery, structure learning, variable selection, and causal discovery. The nonparametric methods for estimating copula entropy and transfer entropy were also proposed previously. This paper introduces copent, the R package which implements these proposed methods for estimating copula entropy and transfer entropy. The implementation detail of the package is introduced. Three examples with simulated data and real-world data on variable selection and causal discovery are also presented to demonstrate the usage of this package. The examples on variable selection and causal discovery show the strong ability of copent on testing (conditional) independence compared with the related packages. The copent package is available on the Comprehensive R Archive Network (CRAN) and also on GitHub at https://github.com/majianthu/copent.