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Discovering causal relations from observational data becomes possible with additional assumptions such as considering the functional relations to be constrained as nonlinear with additive noise (ANM). Even with strong assumptions, causal discovery involves an expensive search problem over the space of directed acyclic graphs (DAGs). \emph{Topological ordering} approaches reduce the optimisation space of causal discovery by searching over a permutation rather than graph space. For ANMs, the \emph{Hessian} of the data log-likelihood can be used for finding leaf nodes in a causal graph, allowing its topological ordering. However, existing computational methods for obtaining the Hessian still do not scale as the number of variables and the number of samples increase. Therefore, inspired by recent innovations in diffusion probabilistic models (DPMs), we propose \emph{DiffAN}\footnote{Implementation is available at \url{//github.com/vios-s/DiffAN} .}, a topological ordering algorithm that leverages DPMs for learning a Hessian function. We introduce theory for updating the learned Hessian without re-training the neural network, and we show that computing with a subset of samples gives an accurate approximation of the ordering, which allows scaling to datasets with more samples and variables. We show empirically that our method scales exceptionally well to datasets with up to $500$ nodes and up to $10^5$ samples while still performing on par over small datasets with state-of-the-art causal discovery methods. Implementation is available at //github.com/vios-s/DiffAN .

The AI community is increasingly focused on merging logic with deep learning to create Neuro-Symbolic (NeSy) paradigms and assist neural approaches with symbolic knowledge. A significant trend in the literature involves integrating axioms and facts in loss functions by grounding logical symbols with neural networks and operators with fuzzy semantics. Logic Tensor Networks (LTN) is one of the main representatives in this category, known for its simplicity, efficiency, and versatility. However, it has been previously shown that not all fuzzy operators perform equally when applied in a differentiable setting. Researchers have proposed several configurations of operators, trading off between effectiveness, numerical stability, and generalization to different formulas. This paper presents a configuration of fuzzy operators for grounding formulas end-to-end in the logarithm space. Our goal is to develop a configuration that is more effective than previous proposals, able to handle any formula, and numerically stable. To achieve this, we propose semantics that are best suited for the logarithm space and introduce novel simplifications and improvements that are crucial for optimization via gradient-descent. We use LTN as the framework for our experiments, but the conclusions of our work apply to any similar NeSy framework. Our findings, both formal and empirical, show that the proposed configuration outperforms the state-of-the-art and that each of our modifications is essential in achieving these results.

Most existing federated learning algorithms are based on the vanilla FedAvg scheme. However, with the increase of data complexity and the number of model parameters, the amount of communication traffic and the number of iteration rounds for training such algorithms increases significantly, especially in non-independently and homogeneously distributed scenarios, where they do not achieve satisfactory performance. In this work, we propose FedND: federated learning with noise distillation. The main idea is to use knowledge distillation to optimize the model training process. In the client, we propose a self-distillation method to train the local model. In the server, we generate noisy samples for each client and use them to distill other clients. Finally, the global model is obtained by the aggregation of local models. Experimental results show that the algorithm achieves the best performance and is more communication-efficient than state-of-the-art methods.

Recent works demonstrate that GNN models are vulnerable to adversarial attacks, which refer to imperceptible perturbation on the graph structure and node features. Among various GNN models, graph contrastive learning (GCL) based methods specifically suffer from adversarial attacks due to their inherent design that highly depends on the self-supervision signals derived from the original graph, which however already contains noise when the graph is attacked. To achieve adversarial robustness against such attacks, existing methods adopt adversarial training (AT) to the GCL framework, which considers the attacked graph as an augmentation under the GCL framework. However, we find that existing adversarially trained GCL methods achieve robustness at the expense of not being able to preserve the node feature similarity. In this paper, we propose a similarity-preserving adversarial graph contrastive learning (SP-AGCL) framework that contrasts the clean graph with two auxiliary views of different properties (i.e., the node similarity-preserving view and the adversarial view). Extensive experiments demonstrate that SP-AGCL achieves a competitive performance on several downstream tasks, and shows its effectiveness in various scenarios, e.g., a network with adversarial attacks, noisy labels, and heterophilous neighbors. Our code is available at //github.com/yeonjun-in/torch-SP-AGCL.

Learning on big data brings success for artificial intelligence (AI), but the annotation and training costs are expensive. In future, learning on small data is one of the ultimate purposes of AI, which requires machines to recognize objectives and scenarios relying on small data as humans. A series of machine learning models is going on this way such as active learning, few-shot learning, deep clustering. However, there are few theoretical guarantees for their generalization performance. Moreover, most of their settings are passive, that is, the label distribution is explicitly controlled by one specified sampling scenario. This survey follows the agnostic active sampling under a PAC (Probably Approximately Correct) framework to analyze the generalization error and label complexity of learning on small data using a supervised and unsupervised fashion. With these theoretical analyses, we categorize the small data learning models from two geometric perspectives: the Euclidean and non-Euclidean (hyperbolic) mean representation, where their optimization solutions are also presented and discussed. Later, some potential learning scenarios that may benefit from small data learning are then summarized, and their potential learning scenarios are also analyzed. Finally, some challenging applications such as computer vision, natural language processing that may benefit from learning on small data are also surveyed.

The adaptive processing of structured data is a long-standing research topic in machine learning that investigates how to automatically learn a mapping from a structured input to outputs of various nature. Recently, there has been an increasing interest in the adaptive processing of graphs, which led to the development of different neural network-based methodologies. In this thesis, we take a different route and develop a Bayesian Deep Learning framework for graph learning. The dissertation begins with a review of the principles over which most of the methods in the field are built, followed by a study on graph classification reproducibility issues. We then proceed to bridge the basic ideas of deep learning for graphs with the Bayesian world, by building our deep architectures in an incremental fashion. This framework allows us to consider graphs with discrete and continuous edge features, producing unsupervised embeddings rich enough to reach the state of the art on several classification tasks. Our approach is also amenable to a Bayesian nonparametric extension that automatizes the choice of almost all model's hyper-parameters. Two real-world applications demonstrate the efficacy of deep learning for graphs. The first concerns the prediction of information-theoretic quantities for molecular simulations with supervised neural models. After that, we exploit our Bayesian models to solve a malware-classification task while being robust to intra-procedural code obfuscation techniques. We conclude the dissertation with an attempt to blend the best of the neural and Bayesian worlds together. The resulting hybrid model is able to predict multimodal distributions conditioned on input graphs, with the consequent ability to model stochasticity and uncertainty better than most works. Overall, we aim to provide a Bayesian perspective into the articulated research field of deep learning for graphs.

Federated Learning (FL) is a decentralized machine-learning paradigm, in which a global server iteratively averages the model parameters of local users without accessing their data. User heterogeneity has imposed significant challenges to FL, which can incur drifted global models that are slow to converge. Knowledge Distillation has recently emerged to tackle this issue, by refining the server model using aggregated knowledge from heterogeneous users, other than directly averaging their model parameters. This approach, however, depends on a proxy dataset, making it impractical unless such a prerequisite is satisfied. Moreover, the ensemble knowledge is not fully utilized to guide local model learning, which may in turn affect the quality of the aggregated model. Inspired by the prior art, we propose a data-free knowledge distillation} approach to address heterogeneous FL, where the server learns a lightweight generator to ensemble user information in a data-free manner, which is then broadcasted to users, regulating local training using the learned knowledge as an inductive bias. Empirical studies powered by theoretical implications show that, our approach facilitates FL with better generalization performance using fewer communication rounds, compared with the state-of-the-art.

Mining graph data has become a popular research topic in computer science and has been widely studied in both academia and industry given the increasing amount of network data in the recent years. However, the huge amount of network data has posed great challenges for efficient analysis. This motivates the advent of graph representation which maps the graph into a low-dimension vector space, keeping original graph structure and supporting graph inference. The investigation on efficient representation of a graph has profound theoretical significance and important realistic meaning, we therefore introduce some basic ideas in graph representation/network embedding as well as some representative models in this chapter.

Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such a graph-structure is available. In practice, however, real-world graphs are often noisy and incomplete or might not be available at all. With this work, we propose to jointly learn the graph structure and the parameters of graph convolutional networks (GCNs) by approximately solving a bilevel program that learns a discrete probability distribution on the edges of the graph. This allows one to apply GCNs not only in scenarios where the given graph is incomplete or corrupted but also in those where a graph is not available. We conduct a series of experiments that analyze the behavior of the proposed method and demonstrate that it outperforms related methods by a significant margin.

Deep learning has been shown successful in a number of domains, ranging from acoustics, images to natural language processing. However, applying deep learning to the ubiquitous graph data is non-trivial because of the unique characteristics of graphs. Recently, a significant amount of research efforts have been devoted to this area, greatly advancing graph analyzing techniques. In this survey, we comprehensively review different kinds of deep learning methods applied to graphs. We divide existing methods into three main categories: semi-supervised methods including Graph Neural Networks and Graph Convolutional Networks, unsupervised methods including Graph Autoencoders, and recent advancements including Graph Recurrent Neural Networks and Graph Reinforcement Learning. We then provide a comprehensive overview of these methods in a systematic manner following their history of developments. We also analyze the differences of these methods and how to composite different architectures. Finally, we briefly outline their applications and discuss potential future directions.