We investigate the HSIC (Hilbert-Schmidt independence criterion) bottleneck as a regularizer for learning an adversarially robust deep neural network classifier. In addition to the usual cross-entropy loss, we add regularization terms for every intermediate layer to ensure that the latent representations retain useful information for output prediction while reducing redundant information. We show that the HSIC bottleneck enhances robustness to adversarial attacks both theoretically and experimentally. In particular, we prove that the HSIC bottleneck regularizer reduces the sensitivity of the classifier to adversarial examples. Our experiments on multiple benchmark datasets and architectures demonstrate that incorporating an HSIC bottleneck regularizer attains competitive natural accuracy and improves adversarial robustness, both with and without adversarial examples during training. Our code and adversarially robust models are publicly available.2

Neural Information Processing Systems http://nips.cc/

We propose a few-shot learning method for feature selection that can select relevant features given a small number of labeled instances. Existing methods require many labeled instances for accurate feature selection. However, sufficient instances are often unavailable. We use labeled instances in multiple related tasks to alleviate the lack of labeled instances in a target task. To measure the dependency between each feature and label, we use the Hilbert-Schmidt Independence Criterion, which is a kernel-based independence measure. By modeling the kernel functions with neural networks that take a few labeled instances in a task as input, we can encode the task-specific information to the kernels such that the kernels are appropriate for the task. Feature selection with such kernels is performed by using iterative optimization methods, in which each update step is obtained as a closed-form. This formulation enables us to directly and efficiently minimize the expected test error on features selected by a small number of labeled instances. We experimentally demonstrate that the proposed method outperforms existing feature selection methods.

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.

Human skeleton-based action recognition has long been an indispensable aspect of artificial intelligence. Current state-of-the-art methods tend to consider only the dependencies between connected skeletal joints, limiting their ability to capture non-linear dependencies between physically distant joints. Moreover, most existing approaches distinguish action classes by estimating the probability density of motion representations, yet the high-dimensional nature of human motions invokes inherent difficulties in accomplishing such measurements. In this paper, we seek to tackle these challenges from two directions: (1) We propose a novel dependency refinement approach that explicitly models dependencies between any pair of joints, effectively transcending the limitations imposed by joint distance. (2) We further propose a framework that utilizes the Hilbert-Schmidt Independence Criterion to differentiate action classes without being affected by data dimensionality, and mathematically derive learning objectives guaranteeing precise recognition. Empirically, our approach sets the state-of-the-art performance on NTU RGB+D, NTU RGB+D 120, and Northwestern-UCLA datasets.

We propose a few-shot learning method for feature selection that can select relevant features given a small number of labeled instances. Existing methods require many labeled instances for accurate feature selection. However, sufficient instances are often unavailable. We use labeled instances in multiple related tasks to alleviate the lack of labeled instances in a target task. To measure the dependency between each feature and label, we use the Hilbert-Schmidt Independence Criterion, which is a kernel-based independence measure.

A simple and intuitive method for feature selection consists of choosing the feature subset that maximizes a nonparametric measure of dependence between the response and the features. A popular proposal from the literature uses the Hilbert-Schmidt Independence Criterion (HSIC) as the nonparametric dependence measure. The rationale behind this approach to feature selection is that important features will exhibit a high dependence with the response and their inclusion in the set of selected features will increase the HSIC. Through counterexamples, we demonstrate that this rationale is flawed and that feature selection via HSIC maximization can miss critical features.

State-of-health (SOH) estimation is a key step in ensuring the safe and reliable operation of batteries. Due to issues such as varying data distribution and sequence length in different cycles, most existing methods require health feature extraction technique, which can be time-consuming and labor-intensive. GRU can well solve this problem due to the simple structure and superior performance, receiving widespread attentions. However, redundant information still exists within the network and impacts the accuracy of SOH estimation. To address this issue, a new GRU network based on Hilbert-Schmidt Independence Criterion (GRU-HSIC) is proposed. First, a zero masking network is used to transform all battery data measured with varying lengths every cycle into sequences of the same length, while still retaining information about the original data size in each cycle. Second, the Hilbert-Schmidt Independence Criterion (HSIC) bottleneck, which evolved from Information Bottleneck (IB) theory, is extended to GRU to compress the information from hidden layers. To evaluate the proposed method, we conducted experiments on datasets from the Center for Advanced Life Cycle Engineering (CALCE) of the University of Maryland and NASA Ames Prognostics Center of Excellence. Experimental results demonstrate that our model achieves higher accuracy than other recurrent models.

Independence testing plays a central role in statistical and causal inference from observational data. Standard independence tests assume that the data samples are independent and identically distributed (i.i.d.) but that assumption is violated in many real-world datasets and applications centered on relational systems. This work examines the problem of estimating independence in data drawn from relational systems by defining sufficient representations for the sets of observations influencing individual instances. Specifically, we define marginal and conditional independence tests for relational data by considering the kernel mean embedding as a flexible aggregation function for relational variables. We propose a consistent, non-parametric, scalable kernel test to operationalize the relational independence test for non-i.i.d. observational data under a set of structural assumptions. We empirically evaluate our proposed method on a variety of synthetic and semi-synthetic networks and demonstrate its effectiveness compared to state-of-the-art kernel-based independence tests.

We investigate the use of a non-parametric independence measure, the Hilbert-Schmidt Independence Criterion (HSIC), as a loss-function for learning robust regression and classification models. This loss-function encourages learning models where the distribution of the residuals between the label and the model-prediction is statistically independent of the distribution of the instances themselves. This loss-function was first proposed by Mooij et al. [2009] in the context of learning causal graphs. We adapt it to the task of robust learning for unsupervised covariate shift: learning on a source domain without access to any instances or labels from the unknown target domain. We prove that the proposed loss is expected to generalize to a class of target domains described in terms of the complexity of their density ratio function with respect to the source domain. Experiments on tasks of unsupervised covariate shift demonstrate that models learned with the proposed loss-function outperform several baseline methods.