Related papers: Structure Learning with Continuous Optimization: A…
Despite the tremendous success of graph-based learning systems in handling structural data, it has been widely investigated that they are fragile to adversarial attacks on homophilic graph data, where adversaries maliciously modify the…
Deep learning research has recently witnessed an impressively fast-paced progress in a wide range of tasks including computer vision, natural language processing, and reinforcement learning. The extraordinary performance of these systems…
Performing analytical tasks over graph data has become increasingly interesting due to the ubiquity and large availability of relational information. However, unlike images or sentences, there is no notion of sequence in networks. Nodes…
Recursive linear structural equation models and the associated directed acyclic graphs (DAGs) play an important role in causal discovery. The classic identifiability result for this class of models states that when only observational data…
Consider the execution of a sequential algorithm that requires the program to converge to an optimal state, and then terminate/stutter. To design such an algorithm, we need to ensure that the state space that it traverses forms a directed…
Inferring causal relationships from observational data is crucial when experiments are costly or infeasible. Additive noise models (ANMs) enable unique directed acyclic graph (DAG) identification, but existing sample-efficient ANM methods…
We consider the problem of inferring the causal structure from observational data, especially when the structure is sparse. This type of problem is usually formulated as an inference of a directed acyclic graph (DAG) model. The linear…
While the expressive power and computational capabilities of graph neural networks (GNNs) have been theoretically studied, their optimization and learning dynamics, in general, remain largely unexplored. Our study undertakes the Graph…
Causal structure learning has been a challenging task in the past decades and several mainstream approaches such as constraint- and score-based methods have been studied with theoretical guarantees. Recently, a new approach has transformed…
Learning causal relations from observational data is challenging because the graph search space grows super-exponentially with the number of variables. Ordering-based methods reduce this space by first identifying the topological ordering,…
While visual comparison of directed acyclic graphs (DAGs) is commonly encountered in various disciplines (e.g., finance, biology), knowledge about humans' perception of graph similarity is currently quite limited. By graph similarity…
Adaptive gradient methods such as Adam have gained increasing popularity in deep learning optimization. However, it has been observed that compared with (stochastic) gradient descent, Adam can converge to a different solution with a…
The combinatorial search space presents a significant challenge to learning causality from data. Recently, the problem has been formulated into a continuous optimization framework with an acyclicity constraint, allowing for the exploration…
This paper re-examines a continuous optimization framework dubbed NOTEARS for learning Bayesian networks. We first generalize existing algebraic characterizations of acyclicity to a class of matrix polynomials. Next, focusing on a…
We consider the problem of structure learning for linear causal models based on observational data. We treat models given by possibly cyclic mixed graphs, which allow for feedback loops and effects of latent confounders. Generalizing…
Precise knowledge of causal directed acyclic graphs (DAGs) is assumed for standard approaches towards valid adjustment set selection for unbiased estimation, but in practice, the DAG is often inferred from data or expert knowledge,…
A Bayesian network is a probabilistic graphical model that consists of a directed acyclic graph (DAG), where each node is a random variable and attached to each node is a conditional probability distribution (CPD). A Bayesian network can be…
We establish finite-sample guarantees for a polynomial-time algorithm for learning a nonlinear, nonparametric directed acyclic graphical (DAG) model from data. The analysis is model-free and does not assume linearity, additivity,…
Graph neural networks (GNNs) are an emerging model for learning graph embeddings and making predictions on graph structured data. However, robustness of graph neural networks is not yet well-understood. In this work, we focus on node…
Despite the growing popularity of graph attention mechanisms, their theoretical understanding remains limited. This paper aims to explore the conditions under which these mechanisms are effective in node classification tasks through the…