Kernel techniques are among the most influential approaches in data science and statistics. Under mild conditions, the reproducing kernel Hilbert space associated to a kernel is capable of encoding the independence of $M\ge2$ random variables. Probably the most widespread independence measure relying on kernels is the so-called Hilbert-Schmidt independence criterion (HSIC; also referred to as distance covariance in the statistics literature). Despite various existing HSIC estimators designed since its introduction close to two decades ago, the fundamental question of the rate at which HSIC can be estimated is still open. In this work, we prove that the minimax optimal rate of HSIC estimation on $\mathbb{R}^d$ for Borel measures containing the Gaussians with continuous bounded translation-invariant characteristic kernels is $\mathcal{O}\left(n^{-1/2}\right)$. Specifically, our result implies the optimality in the minimax sense of many of the most-frequently used estimators (including the U-statistic, the V-statistic, and the Nyström-based one) on $\mathbb{R}^d$.

This paper presents a new efficient black-box attribution method built on Hilbert-Schmidt Independence Criterion (HSIC). Based on Reproducing Kernel Hilbert Spaces (RKHS), HSIC measures the dependence between regions of an input image and the output of a model using the kernel embedding of their distributions. It thus provides explanations enriched by RKHS representation capabilities. HSIC can be estimated very efficiently, significantly reducing the computational cost compared to other black-box attribution methods.Our experiments show that HSIC is up to 8 times faster than the previous best black-box attribution methods while being as faithful.Indeed, we improve or match the state-of-the-art of both black-box and white-box attribution methods for several fidelity metrics on Imagenet with various recent model architectures.Importantly, we show that these advances can be transposed to efficiently and faithfully explain object detection models such as YOLOv4. Finally, we extend the traditional attribution methods by proposing a new kernel enabling an ANOVA-like orthogonal decomposition of importance scores based on HSIC, allowing us to evaluate not only the importance of each image patch but also the importance of their pairwise interactions.

As a representative optic degenerative condition, glaucoma has been a threat to millions due to its irreversibility and severe impact on human vision fields. Mainly characterized by dimmed and blurred visions, or peripheral vision loss, glaucoma is well known to occur due to damages in the optic nerve from increased intraocular pressure (IOP) or neovascularization within the retina. Traditionally, most glaucoma related works and clinical diagnosis focused on detecting these damages in the optic nerve by using patient data from perimetry tests, optic papilla inspections and tonometer-based IOP measurements. Recently, with advancements in computer vision AI models, such as VGG16 or Vision Transformers (ViT), AI-automatized glaucoma detection and optic cup segmentation based on retinal fundus images or OCT recently exhibited significant performance in aiding conventional diagnosis with high performance. However, current AI-driven glaucoma detection approaches still have significant room for improvement in terms of reliability, excessive parameter usage, possibility of spurious correlation within detection, and limitations in applications to intervention analysis or clinical simulations. Thus, this research introduced a novel causal representation driven glaucoma detection model: LightHCG, an extremely lightweight Convolutional VAE-based latent glaucoma representation model that can consider the true causality among glaucoma-related physical factors within the optic nerve region. Using HSIC-based latent space disentanglement and Graph Autoencoder based unsupervised causal representation learning, LightHCG not only exhibits higher performance in classifying glaucoma with 93~99% less weights, but also enhances the possibility of AI-driven intervention analysis, compared to existing advanced vision models such as InceptionV3, MobileNetV2 or VGG16.

Time series forecasting relies on predicting future values from historical data, yet most state-of-the-art approaches-including transformer and multilayer perceptron-based models-optimize using Mean Squared Error (MSE), which has two fundamental weaknesses: its point-wise error computation fails to capture temporal relationships, and it does not account for inherent noise in the data. To overcome these limitations, we introduce the Residual-Informed Loss (RI-Loss), a novel objective function based on the Hilbert-Schmidt Independence Criterion (HSIC). RI-Loss explicitly models noise structure by enforcing dependence between the residual sequence and a random time series, enabling more robust, noise-aware representations. Theoretically, we derive the first non-asymptotic HSIC bound with explicit double-sample complexity terms, achieving optimal convergence rates through Bernstein-type concentration inequalities and Rademacher complexity analysis. This provides rigorous guarantees for RI-Loss optimization while precisely quantifying kernel space interactions. Empirically, experiments across eight real-world benchmarks and five leading forecasting models demonstrate improvements in predictive performance, validating the effectiveness of our approach. The code is publicly available at: https://github.com/shang-xl/RI-Loss.

Parameterizing the approximate posterior of a generative model with neural networks has become a common theme in recent machine learning research.

A prime example is single-cell RNA sequencing (scRNA-seq) data (Figure 1).

To address these challenges, a multitude of works grounded on these measures have emerged.

We appreciate the praise for the "Extremely good and unique empirical Lasso or Markov Blanket (MB) requires causal sufficiency, let alone curse of dimensionality. In sparse large graphs FS gives more FP . BE performs worse in small sparse graphs. BE and FS computations took significantly long. Indeed, an empirical example of this was given in section A2, Figure 1 of suppl.