AISTATS 2025 论文列表

Understanding causal relationships in multivariate time series is essential for predicting and controlling dynamic systems in fields like economics, neuroscience, and climate science. However, existing causal discovery methods often assume stationarity, limiting their effectiveness when time series consist of sequential regimes, consecutive temporal segments with unknown boundaries and changing causal structures. In this work, we firstly introduce a framework to describe and model such time series. Then, we present CASTOR, a novel method that concurrently learns the Directed Acyclic Graph (DAG) for each regime while determining the number of regimes and their sequential arrangement. CASTOR optimizes the data log-likelihood using an expectation-maximization algorithm, alternating between assigning regime indices (expectation step) and inferring causal relationships in each regime (maximization step). We establish the identifiability of the regimes and DAGs within our framework. Extensive experiments show that CASTOR consistently outperforms existing causal discovery models in detecting different regimes and learning their DAGs across various settings, including linear and nonlinear causal relationships, on both synthetic and real world datasets.

When dealing with right-censored data, where some outcomes are missing due to a limited observation period, survival analysis —known as *time-to-event analysis*— focuses on predicting the time until an event of interest occurs. Multiple classes of outcomes lead to a classification variant: predicting the most likely event, a less explored area known as *competing risks*. Classic competing risks models couple architecture and loss, limiting scalability. To address these issues, we design a strictly proper censoring-adjusted separable scoring rule, allowing optimization on a subset of the data as each observation is evaluated independently. The loss estimates outcome probabilities and enables stochastic optimization for competing risks, which we use for efficient gradient boosting trees. **SurvivalBoost** not only outperforms 12 state-of-the-art models across several metrics on 4 real-life datasets, both in competing risks and survival settings, but also provides great calibration, the ability to predict across any time horizon, and computation times faster than existing methods.

Research in adversarial machine learning (AML) has shown that statistical models are vulnerable to maliciously altered data. However, despite advances in Bayesian machine learning models, most AML research remains concentrated on classical techniques. Therefore, we focus on extending the white-box model poisoning paradigm to attack generic Bayesian inference, highlighting its vulnerability in adversarial contexts. A suite of attacks are developed that allow an attacker to steer the Bayesian posterior toward a target distribution through the strategic deletion and replication of true observations, even when only sampling access to the posterior is available. Analytic properties of these algorithms are proven and their performance is empirically examined in both synthetic and real-world scenarios. With relatively little effort, the attacker is able to substantively alter the Bayesian's beliefs and, by accepting more risk, they can mold these beliefs to their will. By carefully constructing the adversarial posterior, surgical poisoning is achieved such that only targeted inferences are corrupted and others are minimally disturbed.

In recent years, studies such as Carmon et al., (2019); Gowal et al., (2021) demonstrate that incorporating additional real or generated data with pseudo-labels can enhance adversarial training through a two-stage training framework. In this paper, we perform a theoretical analysis of the asymptotic behavior of this method in high-dimensional regression problem when using two-layer neural networks. We first derive the asymptotics of the two-stage training framework using linear regression as a preliminary. Then, we analyze the convergence of two-layer neural networks in the two-stage framework. The analysis considers two different regimes: in the first stage of the framework, it is a high-dimensional regime, and in the second stage, the sample size is much larger than the data dimension. To analyze adversarial training, we track the change of the adversarial attack, and reveal that training with two-layer neural networks gives a prediction performance similar to training a linear model with some particular $\mathcal{L}_2$ regularization corresponding to different regimes. To highlight our technical contribution, we are the first to investigate adversarial training in two-layer neural networks under moderate attack strength, which is different from most existing literature in vanishing attack strength.

Bilevel reinforcement learning (RL), which features intertwined two-level problems, has attracted growing interest recently. The inherent non-convexity of the lower-level RL problem is, however, to be an impediment to developing bilevel optimization methods. By employing the fixed point equation associated with the regularized RL, we characterize the hyper-gradient via fully first-order information, thus circumventing the assumption of lower-level convexity. This, remarkably, distinguishes our development of hyper-gradient from the general AID-based bilevel frameworks since we take advantage of the specific structure of RL problems. Moreover, we design both model-based and model-free bilevel reinforcement learning algorithms, facilitated by access to the fully first-order hyper-gradient. Both algorithms enjoy the convergence rate $\mathcal{O}\left(\epsilon^{-1}\right)$. To extend the applicability, a stochastic version of the model-free algorithm is proposed, along with results on its convergence rate and sampling complexity. In addition, numerical experiments demonstrate that the hyper-gradient indeed serves as an integration of exploitation and exploration.

Stochastic multi-armed bandits (MABs) provide a fundamental reinforcement learning model to study sequential decision making in uncertain environments. The upper confidence bounds (UCB) algorithm gave birth to the renaissance of bandit algorithms, as it achieves near-optimal regret rates under various moment assumptions. Up until recently most UCB methods relied on concentration inequalities leading to confidence bounds which depend on moment parameters, such as the variance proxy, that are usually unknown in practice. In this paper, we propose a new distribution-free, data-driven UCB algorithm for symmetric reward distributions, which needs no moment information. The key idea is to combine a refined, one-sided version of the recently developed resampled median-of-means (RMM) method with UCB. We prove a near-optimal regret bound for the proposed anytime, parameter-free RMM-UCB method, even for heavy-tailed distributions.

The operator learning has received significant attention in recent years, with the aim of learning a mapping between function spaces. Prior works have proposed deep neural networks (DNNs) for learning such a mapping, enabling the learning of solution operators of partial differential equations (PDEs). However, these works still struggle to learn dynamics that obeys the laws of physics. This paper proposes Energy-consistent Neural Operators (ENOs), a general framework for learning solution operators of PDEs that follows the energy conservation or dissipation law from observed solution trajectories. We introduce a novel penalty function inspired by the energy-based theory of physics for training, in which the functional derivative is calculated making full use of automatic differentiation, allowing one to bias the outputs of the DNN-based solution operators to obey appropriate energetic behavior without explicit PDEs. Experiments on multiple systems show that ENO outperforms existing DNN models in predicting solutions from data, especially in super-resolution settings.

Estimating causal effects under interference is pertinent to many real-world settings. Recent work with low-order potential outcomes models uses a rollout design to obtain unbiased estimators that require no interference network information. However, the required extrapolation can lead to prohibitively high variance. To address this, we propose a two-stage experiment that selects a sub-population in the first stage and restricts treatment rollout to this sub-population in the second stage. We explore the role of clustering in the first stage by analyzing the bias and variance of a polynomial interpolation-style estimator under this experimental design. Bias increases with the number of edges cut in the clustering of the interference network, but variance depends on qualities of the clustering that relate to homophily and covariate balance. There is a tension between clustering objectives that minimize the number of cut edges versus those that maximize covariate balance across clusters. Through simulations, we explore {a bias-variance} trade-off and compare the performance of the estimator under different clustering strategies.

Incentive design is a popular framework for guiding agents' learning dynamics towards desired outcomes by providing additional payments beyond intrinsic rewards. However, most existing works focus on a finite, small set of agents or assume complete knowledge of the game, limiting their applicability to real-world scenarios involving large populations and model uncertainty. To address this gap, we study the design of steering rewards in Mean-Field Games (MFGs) with density-independent transitions, where both the transition dynamics and intrinsic reward functions are unknown. This setting presents non-trivial challenges, as the mediator must incentivize the agents to explore for its model learning under uncertainty, while simultaneously steer them to converge to desired behaviors without incurring excessive incentive payments. Assuming agents exhibit no(-adaptive) regret behaviors, we contribute novel optimistic exploration algorithms. Theoretically, we establish sub-linear regret guarantees for the cumulative gaps between the agents' behaviors and the desired ones. In terms of the steering cost, we demonstrate that our total incentive payments incur only sub-linear excess, competing with a baseline steering strategy that stabilizes the target policy as an equilibrium. Our work presents an effective framework for steering agents behaviors in large-population systems under uncertainty.

Many applications require minimizing a family of optimization problems indexed by some hyperparameter $\lambda \in \Lambda$ to obtain an entire solution path. Traditional approaches proceed by discretizing $\Lambda$ and solving a series of optimization problems. We propose an alternative approach that parameterizes the solution path with a set of basis functions and solves a \emph{single} stochastic optimization problem to learn the entire solution path. Our method offers substantial complexity improvements over discretization. When using constant-step size SGD, the uniform error of our learned solution path relative to the true path exhibits linear convergence to a constant related to the expressiveness of the basis. When the true solution path lies in the span of the basis, this constant is zero. We also prove stronger results for special cases common in machine learning: When $\lambda \in [-1, 1]$ and the solution path is $\nu$-times differentiable, constant step-size SGD learns a path with $\epsilon$ uniform error after at most $O(\epsilon^{\frac{1}{1-\nu}} \log(1/\epsilon))$ iterations, and when the solution path is analytic, it only requires $O\left(\log^2(1/\epsilon)\log\log(1/\epsilon)\right)$. By comparison, the best-known discretization schemes in these settings require at least $O(\epsilon^{-1/2})$ discretization points (and even more gradient calls). Finally, we propose an adaptive variant of our method that sequentially adds basis functions and demonstrate strong numerical performance through experiments.

A probabilistic graphical model is proposed, modeling the joint model parameter and multiplier evolution, with a hypervolume based likelihood, promoting multi-objective descent in structural risk minimization. We address multi-objective model parameter optimization via a surrogate single objective penalty loss with time-varying multipliers, equivalent to online scheduling of loss landscape. The multi-objective descent goal is dispatched hierarchically into a series of constraint optimization sub-problems with shrinking bounds according to Pareto dominance. The bound serves as setpoint for the low-level multiplier controller to schedule loss landscapes via output feedback of each loss term. Our method forms closed loop of model parameter dynamic, circumvents excessive memory requirements and extra computational burden of existing multi-objective deep learning methods, and is robust against controller hyperparameter variation, demonstrated on domain generalization tasks.

Causal discovery is a structured prediction task that aims to predict causal relations among variables based on their data samples. Supervised Causal Learning (SCL) is an emerging paradigm in this field. Existing Deep Neural Network (DNN)-based methods commonly adopt the “Node-Edge approach”, in which the model first computes an embedding vector for each variable-node, then uses these variable-wise representations to concurrently and independently predict for each directed causal-edge. In this paper, we first show that this architecture has some systematic bias that cannot be mitigated regardless of model size and data size. We then propose SiCL, a DNN-based SCL method that predicts a skeleton matrix together with a v-tensor (a third-order tensor representing the v-structures). According to the Markov Equivalence Class (MEC) theory, both the skeleton and the v-structures are *identifiable* causal structures under the canonical MEC setting, so predictions about skeleton and v-structures do not suffer from the identifiability limit in causal discovery, thus SiCL can avoid the systematic bias in Node-Edge architecture, and enable consistent estimators for causal discovery. Moreover, SiCL is also equipped with a specially designed pairwise encoder module with a unidirectional attention layer to model both internal and external relationships of pairs of nodes. Experimental results on both synthetic and real-world benchmarks show that SiCL significantly outperforms other DNN-based SCL approaches.

Graph classification in medical imaging and drug discovery requires accuracy and robust uncertainty quantification. To address this need, we introduce Conditional Prediction ROC (CP-ROC) bands, offering uncertainty quantification for ROC curves and robustness to distributional shifts in test data. Although developed for Tensorized Graph Neural Networks (TGNNs), CP-ROC is adaptable to general Graph Neural Networks (GNNs) and other machine learning models. We establish statistically guaranteed coverage for CP-ROC under a local exchangeability condition. This addresses uncertainty challenges for ROC curves under non-iid setting, ensuring reliability when test graph distributions differ from training data. Empirically, to establish local exchangeability for TGNNs, we introduce a data-driven approach to construct local calibration sets for graphs. Comprehensive evaluations show that CP-ROC significantly improves prediction reliability across diverse tasks. This method enhances uncertainty quantification efficiency and reliability for ROC curves, proving valuable for real-world applications with non-iid objects.

Mixup is a widely adopted data augmentation technique known for enhancing the generalization of machine learning models by interpolating between data points. Despite its success and popularity, limited attention has been given to understanding the statistical properties of the synthetic data it generates. In this paper, we delve into the theoretical underpinnings of mixup, specifically its effects on the statistical structure of synthesized data. We demonstrate that while mixup improves model performance, it can distort key statistical properties such as variance, potentially leading to unintended consequences in data synthesis. To address this, we propose a novel mixup method that incorporates a generalized and flexible weighting scheme, better preserving the original data’s structure. Through theoretical developments, we provide conditions under which our proposed method maintains the (co)variance and distributional properties of the original dataset. Numerical experiments confirm that the new approach not only preserves the statistical characteristics of the original data but also sustains model performance across repeated synthesis, alleviating concerns of model collapse identified in previous research.

We initiate the study of a new notion of adversarial loss which we call distributional adversarial loss. In this notion, we assume for each original example, the allowed adversarial perturbation set is a family of distributions, and the adversarial loss over each example is the maximum loss over all the associated distributions. The goal is to minimize the overall adversarial loss. We show sample complexity bounds in the PAC-learning setting for our notion of adversarial loss. Our notion of adversarial loss contrasts the prior work on robust learning that considers a set of points, not distributions, as the perturbation set of each clean example. As an application of our approach, we show how to unify the two lines of work on randomized smoothing and robust learning in the PAC-learning setting and derive sample complexity bounds for randomized smoothing methods. Furthermore, we investigate the role of randomness in achieving robustness against adversarial attacks. We show a general derandomization technique that preserves the extent of a randomized classifier's robustness against adversarial attacks and show its effectiveness empirically.

In voxel-based neuroimaging disease prediction, it was recently found that in addition to lesion features, there exists another type of feature called "Procedural Bias", which is introduced during preprocessing and can further improve the prediction power. However, traditional sparse learning methods fail to simultaneously capture both types of features due to their heterogeneity in sparsity types. Specifically, the lesion features are spatially coherent and suffer from volumetric degeneration, while the procedural bias refers to enlarged voxels that are dispersedly distributed. In this paper, we propose a new method based on differential inclusion, which generates a sparse regularized solution path on multiple parameters that are enforced with heterogeneous sparsity to capture lesion features and the procedural bias separately. Specifically, we employ Total Variation with a non-negative constraint for the parameter associated with degenerated and spatially coherent lesions; on the other hand, we impose $\ell_1$ sparsity with a non-positive constraint on the parameter related to enlarged and scatterly distributed procedural bias. We theoretically show that our method enjoys model selection consistency and $\ell_2$ consistency in estimation. The utility of our method is demonstrated by improved prediction power and interpretability in the early prediction of Alzheimer's Disease.

We study first-order algorithms that are uniformly stable for empirical risk minimization (ERM) problems that are convex and smooth with respect to $p$-norms, $p \geq 1$. We propose a black-box reduction method that, by employing properties of uniformly convex regularizers, turns an optimization algorithm for Hölder smooth convex losses into a uniformly stable learning algorithm with optimal statistical risk bounds on the excess risk, up to a constant factor depending on $p$. Achieving a black-box reduction for uniform stability was posed as an open question by Attia and Koren (2022), which had solved the Euclidean case $p=2$. We explore applications that leverage non-Euclidean geometry in addressing binary classification problems.

Stochastic simulation models are generative models that mimic complex systems to help with decision-making. The reliability of these models heavily depends on well-calibrated input model parameters. However, in many practical scenarios, only output-level data are available to learn the input model parameters, which is challenging due to the often intractable likelihood of the stochastic simulation model. Moreover, stochastic simulation models are frequently inexact, with discrepancies between the model and the target system. No existing methods can effectively learn and quantify the uncertainties of input parameters using only output-level data. In this paper, we propose to learn differentiable input parameters of stochastic simulation models using output-level data via kernel score minimization with stochastic gradient descent. We quantify the uncertainties of the learned input parameters using a frequentist confidence set procedure based on a new asymptotic normality result that accounts for model inexactness. The proposed method is evaluated on exact and inexact G/G/1 queueing models as well as a stochastic volatility model.

Motivated by applications to deep learning which often fail standard Lipschitz smoothness requirements, we examine the problem of sampling from distributions that are not log-concave and are only weakly dissipative, with log-gradients allowed to grow superlinearly at infinity. In terms of structure, we only assume that the target distribution satisfies either a Log-Sobolev or a Poincare inequality and a local Lipschitz smoothness assumption with modulus growing possibly polynomially at infinity. This set of assumptions greatly exceeds the operational limits of the "vanilla" ULA, making sampling from such distributions a highly involved affair. To account for this, we introduce a taming scheme which is tailored to the growth and decay properties of the target distribution, and we provide explicit non-asymptotic guarantees for the proposed sampler in terms of the KL divergence, total variation, and Wasserstein distance to the target distribution.