Post-hoc explanation techniques on graph neural networks (GNNs) provide economical solutions for opening the black-box graph models without model retraining. Many GNN explanation variants have achieved state-of-the-art explaining results on a diverse set of benchmarks, while they rarely provide theoretical analysis for their inherent properties and explanatory capability.

Graph neural networks, a popular class of models effective in a wide range of graph-based learning tasks, have been shown to be vulnerable to adversarial attacks. While the majority of the literature focuses on such vulnerability in node-level classification tasks, little effort has been dedicated to analysing adversarial attacks on graph-level classification, an important problem with numerous real-life applications such as biochemistry and social network analysis. The few existing methods often require unrealistic setups, such as access to internal information of the victim models, or an impractically-large number of queries. We present a novel Bayesian optimisation-based attack method for graph classification models. Our method is black-box, query-efficient and parsimonious with respect to the perturbation applied. We empirically validate the effectiveness and flexibility of the proposed method on a wide range of graph classification tasks involving varying graph properties, constraints and modes of attack. Finally, we analyse common interpretable patterns behind the adversarial samples produced, which may shed further light on the adversarial robustness of graph classification models.

We consider the problem of building a reinforcement learning (RL) agent that can both accomplish non-trivial tasks, like winning a real-time strategy game, and strictly follow high-level language commands from humans, like "attack", even if a command is sub-optimal. We call this novel yet important problem, Grounded Reinforcement Learning (GRL). Compared with other language grounding tasks, GRL is particularly non-trivial and cannot be simply solved by pure RL or behavior cloning (BC). From the RL perspective, it is extremely challenging to derive a precise reward function for human preferences since the commands are abstract and the valid behaviors are highly complicated and multi-modal. From the BC perspective, it is impossible to obtain perfect demonstrations since human strategies in complex games are typically sub-optimal. We tackle GRL via a simple, tractable, and practical constrained RL objective and develop an iterative RL algorithm, REinforced demonstration Distillation (RED), to obtain a strong GRL policy. We evaluate the policies derived by RED, BC and pure RL methods on a simplified real-time strategy game, MiniRTS. Experiment results and human studies show that the RED policy is able to consistently follow human commands and achieve a higher win rate than the baselines. We release our code and present more examples at https://sites.google.com/view/grounded-rl.

Recent advances in neuroscience data acquisition allow for the simultaneous recording of large populations of neurons across multiple brain areas while subjects perform complex cognitive tasks. Interpreting these data requires us to index how task-relevant information is shared across brain regions, but this is often confounded by the mixing of different task parameters at the single neuron level. Here, inspired by a method developed for a single brain area, we introduce a new technique for demixing variables across multiple brain areas, called demixed shared component analysis (dSCA).

Due to the drastic gap in complexity between sequential and batch statistical learning, recent work has studied a smoothed sequential learning setting, where Nature is constrained to select contexts with density bounded by $1/\sigma$ with respect to a known measure $\mu$. Unfortunately, for some function classes, there is an exponential gap between the statistically optimal regret and that which can be achieved efficiently. In this paper, we give a computationally efficient algorithm that is the first to enjoy the statistically optimal $\log(T/\sigma)$ regret for realizable $K$-wise linear classification. We extend our results to settings where the true classifier is linear in an over-parameterized polynomial featurization of the contexts, as well as to a realizable piecewise-regression setting assuming access to an appropriate ERM oracle. Somewhat surprisingly, standard disagreement-based analyses are insufficient to achieve regret logarithmic in $1/\sigma$. Instead, we develop a novel characterization of the geometry of the disagreement region induced by generalized linear classifiers. Along the way, we develop numerous technical tools of independent interest, including a general anti-concentration bound for the determinant of certain matrix averages.

This paper considers doing quantile regression on censored data using neural networks (NNs). This adds to the survival analysis toolkit by allowing direct prediction of the target variable, along with a distribution-free characterisation of uncertainty, using a flexible function approximator. We begin by showing how an algorithm popular in linear models can be applied to NNs. However, the resulting procedure is inefficient, requiring sequential optimisation of an individual NN at each desired quantile. Our major contribution is a novel algorithm that simultaneously optimises a grid of quantiles output by a single NN. To offer theoretical insight into our algorithm, we show firstly that it can be interpreted as a form of expectation-maximisation, and secondly that it exhibits a desirable `self-correcting' property. Experimentally, the algorithm produces quantiles that are better calibrated than existing methods on 10 out of 12 real datasets.

Analyzing causality in multivariate systems involves establishing how information is generated, distributed and combined, and thus requires tools that capture interactions beyond pairwise relations. Higher-order information theory provides such tools. In particular, Partial Information Decomposition (PID) allows the decomposition of the information that a set of sources provides about a target into redundant, unique, and synergistic components. Yet the mathematical connection between such higher-order information-theoretic measures and causal structure remains undeveloped. Here we establish the first theoretical correspondence between PID components and causal structure in both Bayesian networks and hypergraphs. We first show that in Bayesian networks unique information precisely characterizes direct causal neighbors, while synergy identifies collider relationships. This establishes a localist causal discovery paradigm in which the structure surrounding each variable can be recovered from its immediate informational footprint, eliminating the need for global search over graph space. Extending these results to higher-order systems, we prove that PID signatures in Bayesian hypergraphs differentiate parents, children, co-heads, and co-tails, revealing a higher-order collider effect unique to multi-tail hyperedges. We also present procedures by which our results can be used to characterize systematically the causal structure of Bayesian networks and hypergraphs. Our results position PID as a rigorous, model-agnostic foundation for inferring both pairwise and higher-order causal structure, and introduce a fundamentally local information-theoretic viewpoint on causal discovery.

Survival analysis relies fundamentally on the semi-parametric Cox Proportional Hazards (CoxPH) model and the parametric Accelerated Failure Time (AFT) model. CoxPH assumes constant hazard ratios, often failing to capture real-world dynamics, while traditional AFT models are limited by rigid distributional assumptions. Although deep learning models like DeepAFT address these constraints by improving predictive accuracy and handling censoring, they inherit the significant challenge of black-box interpretability. The recent introduction of CoxKAN demonstrated the successful integration of Kolmogorov-Arnold Networks (KANs), a novel architecture that yields highly accurate and interpretable symbolic representations, within the CoxPH framework. Motivated by the interpretability gains of CoxKAN, we introduce KAN-AFT (Kolmogorov Arnold Network-based AFT), the first framework to apply KANs to the AFT model. Our primary contributions include: (i) a principled AFT-KAN formulation, (ii) robust optimization strategies for right-censored observations (e.g., Buckley-James and IPCW), and (iii) an interpretability pipeline that converts the learned spline functions into closed-form symbolic equations for survival time. Empirical results on multiple datasets confirm that KAN-AFT achieves performance comparable to or better than DeepAFT, while uniquely providing transparent, symbolic models of the survival process.

We introduce two nonlinear sufficient dimension reduction methods for regressions with tensor-valued predictors. Our goal is two-fold: the first is to preserve the tensor structure when performing dimension reduction, particularly the meaning of the tensor modes, for improved interpretation; the second is to substantially reduce the number of parameters in dimension reduction, thereby achieving model parsimony and enhancing estimation accuracy. Our two tensor dimension reduction methods echo the two commonly used tensor decomposition mechanisms: one is the Tucker decomposition, which reduces a larger tensor to a smaller one; the other is the CP-decomposition, which represents an arbitrary tensor as a sequence of rank-one tensors. We developed the Fisher consistency of our methods at the population level and established their consistency and convergence rates. Both methods are easy to implement numerically: the Tucker-form can be implemented through a sequence of least-squares steps, and the CP-form can be implemented through a sequence of singular value decompositions. We investigated the finite-sample performance of our methods and showed substantial improvement in accuracy over existing methods in simulations and two data applications.

Collecting operationally realistic data to inform machine learning models can be costly. Before collecting new data, it is helpful to understand where a model is deficient. For example, object detectors trained on images of rare objects may not be good at identification in poorly represented conditions. We offer a way of informing subsequent data acquisition to maximize model performance by leveraging the toolkit of computer experiments and metadata describing the circumstances under which the training data was collected (e.g., season, time of day, location). We do this by evaluating the learner as the training data is varied according to its metadata. A Gaussian process (GP) surrogate fit to that response surface can inform new data acquisitions. This meta-learning approach offers improvements to learner performance as compared to data with randomly selected metadata, which we illustrate on both classic learning examples, and on a motivating application involving the collection of aerial images in search of airplanes.