UAI 2022 论文列表

Graph sparsification aims to reduce the number of edges of a graph while maintaining its structural properties. In this paper, we propose the first general and effective information-theoretic formulation of graph sparsification, by taking inspiration from the Principle of Relevant Information (PRI). To this end, we extend the PRI from a standard scalar random variable setting to structured data (i.e., graphs). Our Graph-PRI objective is achieved by operating on the graph Laplacian, made possible by expressing the graph Laplacian of a subgraph in terms of a sparse edge selection vector w. We provide both theoretical and empirical justifications on the validity of our Graph-PRI approach. We also analyze its analytical solutions in a few special cases. We finally present three representative real-world applications, namely graph sparsification, graph regularized multi-task learning, and medical imaging-derived brain network classification, to demonstrate the effectiveness, the versatility and the enhanced interpretability of our approach over prevalent sparsification techniques. Code of Graph-PRI is available at https://github.com/SJYuCNEL/PRI-Graphs.

Recent developments have shown that modeling in the spectral domain improves the accuracy in time series forecasting. However, state-of-the-art neural spectral forecasters do not generally yield trustworthy predictions. In particular, they lack the means to gauge predictive likelihoods and provide uncertainty estimates. We propose predictive Whittle networks to bridge this gap, which exploit both the advances of neural forecasting in the spectral domain and leverage tractable likelihoods of probabilistic circuits. For this purpose, we propose a novel Whittle forecasting loss that makes use of these predictive likelihoods to guide the training of the neural forecasting component. We demonstrate how predictive Whittle networks improve real-world forecasting accuracy, while also allowing a transformation back into the time domain, in order to provide the necessary feedback of when the model’s prediction may become erratic.

Direct numerical simulation (DNS) of turbulent flows is computationally expensive and cannot be applied to flows with large Reynolds numbers. Low-resolution large eddy simulation (LES) is a popular alternative, but it is unable to capture all of the scales of turbulent transport accurately. Reconstructing DNS from low-resolution LES is critical for large-scale simulation in many scientific and engineering disciplines, but it poses many challenges to existing super-resolution methods due to the complexity of turbulent flows and computational cost of generating frequent LES data. We propose a physics-guided neural network for reconstructing frequent DNS from sparse LES data by enhancing its spatial resolution and temporal frequency. Our proposed method consists of a partial differential equation (PDE)-based recurrent unit for capturing underlying temporal processes and a physics-guided super-resolution model that incorporates additional physical constraints. We demonstrate the effectiveness of both components in reconstructing the Taylor-Green Vortex using sparse LES data. Moreover, we show that the proposed recurrent unit can preserve the physical characteristics of turbulent flows by leveraging the physical relationships in the Navier-Stokes equation.

Recent works in adversarial robustness have proposed defenses to improve the robustness of a single model against the union of multiple perturbation types. However, these methods still suffer significant trade-offs compared to the ones specifically trained to be robust against a single perturbation type. In this work, we introduce the problem of categorizing adversarial examples based on their perturbation types. We first theoretically show on a toy task that adversarial examples of different perturbation types constitute different distributions—making it possible to distinguish them. We support these arguments with experimental validation on multiple l_p attacks and common corruptions. Instead of training a single classifier, we propose PROTECTOR, a two-stage pipeline that first categorizes the perturbation type of the input, and then makes the final prediction using the classifier specifically trained against the predicted perturbation type. We theoretically show that at test time the adversary faces a natural trade-off between fooling the perturbation classifier and the succeeding classifier optimized with perturbation-specific adversarial training. This makes it challenging for an adversary to plant strong attacks against the whole pipeline. Experiments on MNIST and CIFAR-10 show that PROTECTOR outperforms prior adversarial training-based defenses by over 5% when tested against the union of l_1, l_2, l_inf attacks. Additionally, our method extends to a more diverse attack suite, also showing large robustness gains against multiple l_p, spatial and recolor attacks.

Sampling from a Boltzmann distribution to calculate important macro statistics is one of the central tasks in the study of large atomic and molecular systems. Recently, a one-shot configuration sampler, the Boltzmann generator [Noé et al., 2019], is introduced. Though a Boltzmann generator can directly generate independent metastable states, it lacks the ability to find transition pathways and describe the whole transition process. In this paper, we propose PathFlow that can function as a one-shot generator as well as a transition pathfinder. More specifically, a normalizing flow model is constructed to map the base distribution and linear interpolated path in the latent space to the Boltzmann distribution and a minimum (free) energy path in the configuration space simultaneously. PathFlow can be trained by standard gradient-based optimizers using the proposed gradient estimator with a theoretical guarantee. PathFlow, validated with the extensively studied examples including a synthetic Müller potential and Alanine dipeptide, shows a remarkable performance.

This paper assumes that cause-effect relationships among variables can be described with a linear structural equation model. Then, a situation is considered where a set of observed covariates satisfies the back-door criterion but the ordinary least squares method cannot be applied to estimate linear causal effects because of multicollinearity/high-dimensional data problems. In this situation, we propose a novel regression approach, the “partially adaptive L$_p$-regularized multiple regression analysis” (PAL$_p$MA) method for estimating the total effects. Different from standard regularized regression analysis, PAL$_p$MA provides a consistent or less-biased estimator of the linear causal effect. PAL$_p$MA is also applicable to evaluating direct effects through the single-door criterion. Given space constraints, the proofs, some numerical experiments, and an industrial case study on setting up painting conditions of car bodies are provided in the Supplementary Material.

We consider the problem of deciding how best to target and prioritize existing vaccines that may offer protection against new variants of an infectious disease. Sequential experiments are a promising approach; however, challenges due to delayed feedback and the overall ebb and flow of disease prevalence make available methods inapplicable for this task. We present a method, partial likelihood Thompson sampling, that can handle these challenges. Our method involves running Thompson sampling with belief updates determined by partial likelihood each time we observe an event. To test our approach, we ran a semi-synthetic experiment based on 200 days of COVID-19 infection data in the US.

Many modern machine learning applications, such as multi-task learning, require finding optimal model parameters to trade-off multiple objective functions that may conflict with each other. The notion of the Pareto set allows us to focus on the set of (often infinite number of) models that cannot be strictly improved. But it does not provide an actionable procedure for picking one or a few special models to return to practical users. In this paper, we consider optimization in Pareto set (OPT-in-Pareto), the problem of finding Pareto models that optimize an extra reference criterion function within the Pareto set. This function can either encode a specific preference from the users, or represent a generic diversity measure for obtaining a set of diversified Pareto models that are representative of the whole Pareto set. Unfortunately, despite being a highly useful framework, efficient algorithms for OPT-in-Pareto have been largely missing, especially for large-scale, non-convex, and non-linear objectives in deep learning. A naive approach is to apply Riemannian manifold gradient descent on the Pareto set, which yields a high computational cost due to the need for eigen-calculation of Hessian matrices. We propose a first-order algorithm that approximately solves OPT-in-Pareto using only gradient information, with both high practical efficiency and theoretically guaranteed convergence property. Empirically, we demonstrate that our method works efficiently for a variety of challenging multi-task-related problems.

Accurate absolute pose regression is one of the key challenges in robotics and computer vision. Existing direct regression methods suffer from two limitations. First, some noisy scenarios such as poor illumination conditions are likely to result in the uncertainty of pose estimation. Second, the output n-dimensional feature vector in the Euclidean space $\mathbb{R}^n$ cannot be well mapped to $SE(3)$ manifold. In this work, we propose a deep dual quaternion network that performs the absolute pose regression on $SE(3)$. We first develop an antipodally symmetric probability distribution over the unit dual quaternion on $SE(3)$ to model uncertainties and then propose an intermediary differential representation space to replace the final output pose, which avoids the mapping problem from $\mathbb{R}^n$ to $SE(3)$. In addition, we introduce a backpropagation method that considers the continuousness and differentiability of the proposed intermediary space. Extensive experiments on the camera re-localization task on the Cambridge Landmarks and 7-Scenes datasets demonstrate that our method greatly improves the accuracy of the pose as well as the robustness in dealing with uncertainty and ambiguity, compared to the state-of-the-art.

Multiclass neural networks are a common tool in modern unsupervised domain adaptation, yet an appropriate theoretical description for their non-uniform sample complexity is lacking in the adaptation literature. To fill this gap, we propose the first PAC-Bayesian adaptation bounds for multiclass learners. We facilitate practical use of our bounds by also proposing the first approximation techniques for the multiclass distribution divergences we consider. For divergences dependent on a Gibbs predictor, we propose additional PAC-Bayesian adaptation bounds which remove the need for inefficient Monte-Carlo estimation. Empirically, we test the efficacy of our proposed approximation techniques as well as some novel design-concepts which we include in our bounds. Finally, we apply our bounds to analyze a common adaptation algorithm that uses neural networks.

Comparing structured data from possibly different metric-measure spaces is a fundamental task in machine learning, with applications in, e.g., graph classification. The Gromov-Wasserstein (GW) discrepancy formulates a coupling between the structured data based on optimal transportation, tackling the incomparability between different structures by aligning the intra-relational geometries. Although efficient local solvers such as conditional gradient and Sinkhorn are available, the inherent non-convexity still prevents a tractable evaluation, and the existing lower bounds are not tight enough for practical use. To address this issue, we take inspirations from the connection with the quadratic assignment problem, and propose the orthogonal Gromov-Wasserstein (OGW) discrepancy as a surrogate of GW. It admits an efficient and closed-form lower bound with O(n^3) complexity, and directly extends to the fused Gromov-Wasserstein distance, incorporating node features into the coupling. Extensive experiments on both the synthetic and real-world datasets show the tightness of our lower bounds, and both OGW and its lower bounds efficiently deliver accurate predictions and satisfactory barycenters for graph sets.

Causal discovery for purely observational, categorical data is a long-standing challenging problem. Unlike continuous data, the vast majority of existing methods for categorical data focus on inferring the Markov equivalence class only, which leaves the direction of some causal relationships undetermined. This paper proposes an identifiable ordinal causal discovery method that exploits the ordinal information contained in many real-world applications to uniquely identify the causal structure. The proposed method is applicable beyond ordinal data via data discretization. Through real-world and synthetic experiments, we demonstrate that the proposed ordinal causal discovery method combined with simple score-and-search algorithms has favorable and robust performance compared to state-of-the-art alternative methods in both ordinal categorical and non-categorical data. An accompanied R package OCD is freely available at the first author’s website.

Autonomous agents often operate in environments where the state is partially observed. In addition to maximizing their cumulative reward, agents must execute complex tasks with rich temporal and logical structures. These tasks can be expressed using temporal logic languages like finite linear temporal logic. This paper, for the first time, provides a structured framework for designing agent policies that maximize the reward while ensuring that the probability of satisfying the temporal logic specification is sufficiently high. We reformulate the problem as a constrained partially observable Markov decision process (POMDP) and provide a novel approach that can leverage off-the-shelf unconstrained POMDP solvers for solving it. Our approach guarantees approximate optimality and constraint satisfaction with high probability. We demonstrate its effectiveness by implementing it on several models of interest.

We consider the problem of efficient patrolling strategy adaptation in a changing environment where the topology of Defender’s moves and the importance of guarded targets change unpredictably. The Defender must instantly switch to a new strategy optimized for the new environment, not disrupting the ongoing patrolling task, and the new strategy must be computed promptly under all circumstances. Since strategy switching may cause unintended security risks compromising the achieved protection, our solution includes mechanisms for detecting and mitigating this problem. The efficiency of our framework is evaluated experimentally.

Learning functions over Boolean variables is a fundamental problem in machine learning. But not much is known about learning such functions using neural networks. Here we focus on learning read-once disjunctive normal forms (DNFs) under the uniform distribution with a convex neural network and gradient methods. We first observe empirically that gradient methods converge to compact solutions with neurons that are aligned with the terms of the DNF. This is despite the fact that there are many zero training error networks that do not have this property. Thus, the learning process has a clear inductive bias towards such logical formulas. Following recent results which connect the inductive bias of gradient flow (GF) to Karush-Kuhn-Tucker (KKT) points of minimum norm problems, we study these KKT points in our setting. We prove that zero training error solutions that memorize training points are not KKT points and therefore GF cannot converge to them. On the other hand, we prove that globally optimal KKT points correspond exactly to networks that are aligned with the DNF terms. These results suggest a strong connection between the inductive bias of GF and solutions that align with the DNF. We conclude with extensive experiments which verify our findings.

The literature on robustness towards common corruptions shows no consensus on whether adversarial training can improve the performance in this setting. First, we show that, when used with an appropriately selected perturbation radius, Lp adversarial training can serve as a strong baseline against common corruptions improving both accuracy and calibration. Then we explain why adversarial training performs better than data augmentation with simple Gaussian noise which has been observed to be a meaningful baseline on common corruptions. Related to this, we identify the sigma-overfitting phenomenon when Gaussian augmentation overfits to a particular standard deviation used for training which has a significant detrimental effect on common corruption accuracy. We discuss how to alleviate this problem and then how to further enhance Lp adversarial training by introducing an efficient relaxation of adversarial training with learned perceptual image patch similarity as the distance metric. Through experiments on CIFAR-10 and ImageNet-100, we show that our approach does not only improve the Lp adversarial training baseline but also has cumulative gains with data augmentation methods such as AugMix, DeepAugment, ANT, and SIN, leading to state-of-the-art performance on common corruptions.

Causal treewidth is a recently introduced notion allowing one to speed up Bayesian network inference and to bound its complexity in the presence of functional dependencies (causal mechanisms) whose identities are unknown. Causal treewidth is no greater than treewidth and can be bounded even when treewidth is unbounded. The utility of causal treewidth has been illustrated recently in the context of causal inference and model-based supervised learning. However, the current definition of causal treewidth is descriptive rather than perspective, therefore limiting its full exploitation in a practical setting. We provide an extensive study of causal treewidth in this paper which moves us closer to realizing the full computational potential of this notion both theoretically and practically.

The front-door criterion can be used to identify and compute causal effects despite the existence of unmeasured confounders between a treatment and outcome. However, the key assumptions – (i) the existence of a variable (or set of variables) that fully mediates the effect of the treatment on the outcome, and (ii) which simultaneously does not suffer from similar issues of confounding as the treatment-outcome pair – are often deemed implausible. This paper explores the testability of these assumptions. We show that under mild conditions involving an auxiliary variable, the assumptions encoded in the front-door model (and simple extensions of it) may be tested via generalized equality constraints a.k.a Verma constraints. We propose two goodness-of-fit tests based on this observation, and evaluate the efficacy of our proposal on real and synthetic data. We also provide theoretical and empirical comparisons to instrumental variable approaches to handling unmeasured confounding.

Bayesian optimization (BO) has become popular for sequential optimization of black-box functions. When BO is used to optimize a target function, we often have access to previous evaluations of potentially related functions. This begs the question as to whether we can leverage these previous experiences to accelerate the current BO task through meta-learning (meta-BO), while ensuring robustness against potentially harmful dissimilar tasks that could sabotage the convergence of BO. This paper introduces two scalable and provably robust meta-BO algorithms: robust meta-Gaussian process-upper confidence bound (RM-GP-UCB) and RM-GP-Thompson sampling (RM-GP-TS). We prove that both algorithms are asymptotically no-regret even when some or all previous tasks are dissimilar to the current task, and show that RM-GP-UCB enjoys a better theoretical robustness than RM-GP-TS. We also exploit the theoretical guarantees to optimize the weights assigned to individual previous tasks through regret minimization via online learning, which diminishes the impact of dissimilar tasks and hence further enhances the robustness. Empirical evaluations show that (a) RM-GP-UCB performs effectively and consistently across various applications, and (b) RM-GP-TS, despite being less robust than RM-GP-UCB both in theory and in practice, performs competitively in some scenarios with less dissimilar tasks and is more computationally efficient.