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In applications of group testing in networks, e.g. identifying individuals who are infected by a disease spread over a network, exploiting correlation among network nodes provides fundamental opportunities in reducing the number of tests needed. We model and analyze group testing on $n$ correlated nodes whose interactions are specified by a graph $G$. We model correlation through an edge-faulty random graph formed from $G$ in which each edge is dropped with probability $1-r$, and all nodes in the same component have the same state. We consider three classes of graphs: cycles and trees, $d$-regular graphs and stochastic block models or SBM, and obtain lower and upper bounds on the number of tests needed to identify the defective nodes. Our results are expressed in terms of the number of tests needed when the nodes are independent and they are in terms of $n$, $r$, and the target error. In particular, we quantify the fundamental improvements that exploiting correlation offers by the ratio between the total number of nodes $n$ and the equivalent number of independent nodes in a classic group testing algorithm. The lower bounds are derived by illustrating a strong dependence of the number of tests needed on the expected number of components. In this regard, we establish a new approximation for the distribution of component sizes in "$d$-regular trees" which may be of independent interest and leads to a lower bound on the expected number of components in $d$-regular graphs. The upper bounds are found by forming dense subgraphs in which nodes are more likely to be in the same state. When $G$ is a cycle or tree, we show an improvement by a factor of $log(1/r)$. For grid, a graph with almost $2n$ edges, the improvement is by a factor of ${(1-r) \log(1/r)}$, indicating drastic improvement compared to trees. When $G$ has a larger number of edges, as in SBM, the improvement can scale in $n$.

Treatment effect estimation from observational data is a central problem in causal inference. Methods based on potential outcomes framework solve this problem by exploiting inductive biases and heuristics from causal inference. Each existing technique addresses a specific aspect of treatment effect estimation, such as controlling propensity score, enforcing randomization, etc., by designing neural network architectures and regularizers. In this paper, we propose an adaptive method called Neurosymbolic Treatment Effect Estimator (NESTER), a generalized method for treatment effect estimation. NESTER brings together all the desiderata for treatment effect estimation into one framework. For this purpose, we design a Domain Specific Language (DSL) for the treatment effect estimation based on inductive biases used in literature. We also theoretically study NESTER's capability for the treatment effect estimation task. Our comprehensive empirical results show that NESTER performs better on benchmark datasets than state-of-the-art methods without compromising run time requirements.

Model-reference adaptive systems refer to a consortium of techniques that guide plants to track desired reference trajectories. Approaches based on theories like Lyapunov, sliding surfaces, and backstepping are typically employed to advise adaptive control strategies. The resulting solutions are often challenged by the complexity of the reference model and those of the derived control strategies. Additionally, the explicit dependence of the control strategies on the process dynamics and reference dynamical models may contribute in degrading their efficiency in the face of uncertain or unknown dynamics. A model-reference adaptive solution is developed here for autonomous systems where it solves the Hamilton-Jacobi-Bellman equation of an error-based structure. The proposed approach describes the process with an integral temporal difference equation and solves it using an integral reinforcement learning mechanism. This is done in real-time without knowing or employing the dynamics of either the process or reference model in the control strategies. A class of aircraft is adopted to validate the proposed technique.

The flock-guidance problem enjoys a challenging structure where multiple optimization objectives are solved simultaneously. This usually necessitates different control approaches to tackle various objectives, such as guidance, collision avoidance, and cohesion. The guidance schemes, in particular, have long suffered from complex tracking-error dynamics. Furthermore, techniques that are based on linear feedback strategies obtained at equilibrium conditions either may not hold or degrade when applied to uncertain dynamic environments. Pre-tuned fuzzy inference architectures lack robustness under such unmodeled conditions. This work introduces an adaptive distributed technique for the autonomous control of flock systems. Its relatively flexible structure is based on online fuzzy reinforcement learning schemes which simultaneously target a number of objectives; namely, following a leader, avoiding collision, and reaching a flock velocity consensus. In addition to its resilience in the face of dynamic disturbances, the algorithm does not require more than the agent position as a feedback signal. The effectiveness of the proposed method is validated with two simulation scenarios and benchmarked against a similar technique from the literature.

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.

We consider the problem of discovering $K$ related Gaussian directed acyclic graphs (DAGs), where the involved graph structures share a consistent causal order and sparse unions of supports. Under the multi-task learning setting, we propose a $l_1/l_2$-regularized maximum likelihood estimator (MLE) for learning $K$ linear structural equation models. We theoretically show that the joint estimator, by leveraging data across related tasks, can achieve a better sample complexity for recovering the causal order (or topological order) than separate estimations. Moreover, the joint estimator is able to recover non-identifiable DAGs, by estimating them together with some identifiable DAGs. Lastly, our analysis also shows the consistency of union support recovery of the structures. To allow practical implementation, we design a continuous optimization problem whose optimizer is the same as the joint estimator and can be approximated efficiently by an iterative algorithm. We validate the theoretical analysis and the effectiveness of the joint estimator in experiments.

Graph neural networks (GNNs) is widely used to learn a powerful representation of graph-structured data. Recent work demonstrates that transferring knowledge from self-supervised tasks to downstream tasks could further improve graph representation. However, there is an inherent gap between self-supervised tasks and downstream tasks in terms of optimization objective and training data. Conventional pre-training methods may be not effective enough on knowledge transfer since they do not make any adaptation for downstream tasks. To solve such problems, we propose a new transfer learning paradigm on GNNs which could effectively leverage self-supervised tasks as auxiliary tasks to help the target task. Our methods would adaptively select and combine different auxiliary tasks with the target task in the fine-tuning stage. We design an adaptive auxiliary loss weighting model to learn the weights of auxiliary tasks by quantifying the consistency between auxiliary tasks and the target task. In addition, we learn the weighting model through meta-learning. Our methods can be applied to various transfer learning approaches, it performs well not only in multi-task learning but also in pre-training and fine-tuning. Comprehensive experiments on multiple downstream tasks demonstrate that the proposed methods can effectively combine auxiliary tasks with the target task and significantly improve the performance compared to state-of-the-art methods.

While recent studies on semi-supervised learning have shown remarkable progress in leveraging both labeled and unlabeled data, most of them presume a basic setting of the model is randomly initialized. In this work, we consider semi-supervised learning and transfer learning jointly, leading to a more practical and competitive paradigm that can utilize both powerful pre-trained models from source domain as well as labeled/unlabeled data in the target domain. To better exploit the value of both pre-trained weights and unlabeled target examples, we introduce adaptive consistency regularization that consists of two complementary components: Adaptive Knowledge Consistency (AKC) on the examples between the source and target model, and Adaptive Representation Consistency (ARC) on the target model between labeled and unlabeled examples. Examples involved in the consistency regularization are adaptively selected according to their potential contributions to the target task. We conduct extensive experiments on several popular benchmarks including CUB-200-2011, MIT Indoor-67, MURA, by fine-tuning the ImageNet pre-trained ResNet-50 model. Results show that our proposed adaptive consistency regularization outperforms state-of-the-art semi-supervised learning techniques such as Pseudo Label, Mean Teacher, and MixMatch. Moreover, our algorithm is orthogonal to existing methods and thus able to gain additional improvements on top of MixMatch and FixMatch. Our code is available at //github.com/SHI-Labs/Semi-Supervised-Transfer-Learning.

Recently, contrastive learning (CL) has emerged as a successful method for unsupervised graph representation learning. Most graph CL methods first perform stochastic augmentation on the input graph to obtain two graph views and maximize the agreement of representations in the two views. Despite the prosperous development of graph CL methods, the design of graph augmentation schemes -- a crucial component in CL -- remains rarely explored. We argue that the data augmentation schemes should preserve intrinsic structures and attributes of graphs, which will force the model to learn representations that are insensitive to perturbation on unimportant nodes and edges. However, most existing methods adopt uniform data augmentation schemes, like uniformly dropping edges and uniformly shuffling features, leading to suboptimal performance. In this paper, we propose a novel graph contrastive representation learning method with adaptive augmentation that incorporates various priors for topological and semantic aspects of the graph. Specifically, on the topology level, we design augmentation schemes based on node centrality measures to highlight important connective structures. On the node attribute level, we corrupt node features by adding more noise to unimportant node features, to enforce the model to recognize underlying semantic information. We perform extensive experiments of node classification on a variety of real-world datasets. Experimental results demonstrate that our proposed method consistently outperforms existing state-of-the-art baselines and even surpasses some supervised counterparts, which validates the effectiveness of the proposed contrastive framework with adaptive augmentation.

Attributed graph clustering is challenging as it requires joint modelling of graph structures and node attributes. Recent progress on graph convolutional networks has proved that graph convolution is effective in combining structural and content information, and several recent methods based on it have achieved promising clustering performance on some real attributed networks. However, there is limited understanding of how graph convolution affects clustering performance and how to properly use it to optimize performance for different graphs. Existing methods essentially use graph convolution of a fixed and low order that only takes into account neighbours within a few hops of each node, which underutilizes node relations and ignores the diversity of graphs. In this paper, we propose an adaptive graph convolution method for attributed graph clustering that exploits high-order graph convolution to capture global cluster structure and adaptively selects the appropriate order for different graphs. We establish the validity of our method by theoretical analysis and extensive experiments on benchmark datasets. Empirical results show that our method compares favourably with state-of-the-art methods.