Despite several advances in recent years, learning causal structures represented by directed acyclic graphs (DAGs) remains a challenging task in high-dimensional settings when the graphs to be learned are not sparse. In this article, we propose to exploit a low-rank assumption regarding the (weighted) adjacency matrix of a DAG causal model to help address this problem. We utilize existing low-rank techniques to adapt causal structure learning methods to take advantage of this assumption and establish several useful results relating interpretable graphical conditions to the low-rank assumption. Specifically, we show that the maximum rank is highly related to hubs, suggesting that scale-free (SF) networks, which are frequently encountered in practice, tend to be low rank. Our experiments demonstrate the utility of the low-rank adaptations for a variety of data models, especially with relatively large and dense graphs. Moreover, with a validation procedure, the adaptations maintain a superior or comparable performance even when graphs are not restricted to be low rank.

In real-world applications, it is important and desirable to learn a model that performs well on out-of-distribution (OOD) data. Recently, causality has become a powerful tool to tackle the OOD generalization problem, with the idea resting on the causal mechanism that is invariant across domains of interest. To leverage the generally unknown causal mechanism, existing works assume a linear form of causal feature or require sufficiently many and diverse training domains, which are usually restrictive in practice. In this work, we obviate these assumptions and tackle the OOD problem without explicitly recovering the causal feature. Our approach is based on transformations that modify the non-causal feature but leave the causal part unchanged, which can be either obtained from prior knowledge or learned from the training data in the multi-domain scenario. Under the setting of invariant causal mechanism, we theoretically show that if all such transformations are available, then we can learn a minimax optimal model across the domains using only single domain data. Noticing that knowing a complete set of these causal invariant transformations may be impractical, we further show that it suffices to know only a subset of these transformations. Based on the theoretical findings, a regularized training procedure is proposed to improve the OOD generalization capability. Extensive experimental results on both synthetic and real datasets verify the effectiveness of the proposed algorithm, even with only a few causal invariant transformations.

We characterize the asymptotic performance of nonparametric one- and two-sample testing. The exponential decay rate or error exponent of the type-II error probability is used as the asymptotic performance metric, and an optimal test achieves the maximum rate subject to a constant level constraint on the type-I error probability. With Sanov's theorem, we derive a sufficient condition for one-sample tests to achieve the optimal error exponent in the universal setting, i.e., for any distribution defining the alternative hypothesis. We then show that two classes of Maximum Mean Discrepancy (MMD) based tests attain the optimal type-II error exponent on \mathbb R ^d , while the quadratic-time Kernel Stein Discrepancy (KSD) based tests achieve this optimality with an asymptotic level constraint. For general two-sample testing, however, Sanov's theorem is insufficient to obtain a similar sufficient condition. We proceed to establish an extended version of Sanov's theorem and derive an exact error exponent for the quadratic-time MMD based two-sample tests. The obtained error exponent is further shown to be optimal among all two-sample tests satisfying a given level constraint. Our work hence provides an achievability result for optimal nonparametric one- and two-sample testing in the universal setting. Application to off-line change detection and related issues are also discussed.

Existing multiagent exploration works focus on how to explore in the fully cooperative task, which is insufficient in the environment with nonstationarity induced by agent interactions. To tackle this issue, we propose When to Explore (WToE), a simple yet effective variational exploration method to learn WToE under nonstationary environments. WToE employs an interaction-oriented adaptive exploration mechanism to adapt to environmental changes. We first propose a novel graphical model that uses a latent random variable to model the step-level environmental change resulting from interaction effects. Leveraging this graphical model, we employ the supervised variational auto-encoder (VAE) framework to derive a short-term inferred policy from historical trajectories to deal with the nonstationarity. Finally, agents engage in exploration when the short-term inferred policy diverges from the current actor policy. The proposed approach theoretically guarantees the convergence of the $Q$ -value function. In our experiments, we validate our exploration mechanism in grid examples, multiagent particle environments and the battle game of MAgent environments. The results demonstrate the superiority of WToE over multiple baselines and existing exploration methods, such as MAEXQ, NoisyNets, EITI, and PR2.

This paper deals with interactive distributed detection with conditionally independent observations where the fusion center may exchange information with a local sensor. Using a two sensor system, we demonstrate that this two-way interaction provides improvement in detection performance compared with the classical tandem detection system where only one-way communication is allowed. An important observation is that, contrary to that of the tandem network, the fusion rule is no longer a simple likelihood ratio test due to the correlation introduced in the initial feedback from the fusion center to the sensor.

The decrease of feature size and the growing complexity of the fabrication process lead to more failures in manufacturing semiconductor devices. Therefore, identifying the root cause layout patterns of failures becomes increasingly crucial for yield improvement. In this paper, a novel layoutaware diagnosis-based layout pattern analysis framework is proposed to identify the root cause efficiently. At the first stage of the framework, an encoder network trained using contrastive learning is used to extract representations of layout snippets that are invariant to trivial transformations including shift, rotation, and mirroring, which are then clustered to form layout patterns. At the second stage, we model the causal relationship between any potential root cause layout patterns and the systematic defects by a structural causal model, which is then used to estimate the Average Causal Effect (ACE) of candidate layout patterns on the systematic defect to identify the true root cause. Experimental results on real industrial cases demonstrate that our framework outperforms a commercial tool with higher accuracies and around ×8.4 speedup on average.