Just like power, water, and transportation systems, wireless networks are a crucial societal infrastructure. As natural and human-induced disruptions continue to grow, wireless networks must be resilient. This requires them to withstand and recover from unexpected adverse conditions, shocks, unmodeled disturbances and cascading failures. Unlike robustness and reliability, resilience is based on the understanding that disruptions will inevitably happen. Resilience, as elasticity, focuses on the ability to bounce back to favorable states, while resilience as plasticity involves agents and networks that can flexibly expand their states and hypotheses through real-time adaptation and reconfiguration. This situational awareness and active preparedness, adapting world models and counterfactually reasoning about potential system failures and the best responses, is a core aspect of resilience. This article will first disambiguate resilience from reliability and robustness, before delving into key mathematical foundations of resilience grounded in abstraction, compositionality and emergence. Subsequently, we focus our attention on a plethora of techniques and methodologies pertaining to the unique characteristics of resilience, as well as their applications through a comprehensive set of use cases. Ultimately, the goal of this paper is to establish a unified foundation for understanding, modeling, and engineering resilience in wireless communication systems, while laying a roadmap for the next-generation of resilient-native and intelligent wireless systems.

Bayesian decision theory advocates the Bayes classifier as the optimal approach for minimizing the risk in machine learning problems. Current deep learning algorithms usually solve for the optimal classifier by \emph{implicitly} estimating the posterior probabilities, \emph{e.g.}, by minimizing the Softmax cross-entropy loss. This simple methodology has been proven effective for meticulously balanced academic benchmark datasets. However, it is not applicable to the long-tailed data distributions in the real world, where it leads to the gradient imbalance issue and fails to ensure the Bayes optimal decision rule. To address these challenges, this paper presents a novel approach (BAPE) that provides a more precise theoretical estimation of the data distributions by \emph{explicitly} modeling the parameters of the posterior probabilities and solving them with point estimation. Consequently, our method directly learns the Bayes classifier without gradient descent based on Bayes' theorem, simultaneously alleviating the gradient imbalance and ensuring the Bayes optimal decision rule. Furthermore, we propose a straightforward yet effective \emph{distribution adjustment} technique. This method enables the Bayes classifier trained from the long-tailed training set to effectively adapt to the test data distribution with an arbitrary imbalance factor, thereby enhancing performance without incurring additional computational costs. In addition, we demonstrate the gains of our method are orthogonal to existing learning approaches for long-tailed scenarios, as they are mostly designed under the principle of \emph{implicitly} estimating the posterior probabilities. Extensive empirical evaluations on CIFAR-10-LT, CIFAR-100-LT, ImageNet-LT, and iNaturalist demonstrate that our method significantly improves the generalization performance of popular deep networks, despite its simplicity.

Consensus-based optimization (CBO) has established itself as an efficient gradient-free optimization scheme, with attractive mathematical properties, such as mean-field convergence results for non-convex loss functions. In this work, we study CBO in the context of closed-box adversarial attacks, which are imperceptible input perturbations that aim to fool a classifier, without accessing its gradient. Our contribution is to establish a connection between the so-called consensus hopping as introduced by Riedl et al. and natural evolution strategies (NES) commonly applied in the context of adversarial attacks and to rigorously relate both methods to gradient-based optimization schemes. Beyond that, we provide a comprehensive experimental study that shows that despite the conceptual similarities, CBO can outperform NES and other evolutionary strategies in certain scenarios.

We introduce BayesL, a novel logical framework for specifying, querying, and verifying the behaviour of Bayesian networks (BNs). BayesL (pronounced "Basil") is a structured language that allows for the creation of queries over BNs. It facilitates versatile reasoning concerning causal and evidence-based relationships, and permits comprehensive what-if scenario evaluations without the need for manual modifications to the model.

In this paper, we propose a unifying message-passing framework for training spiking neural networks (SNNs) using Expectation-Propagation. Our gradient-free method is capable of learning the marginal distributions of network parameters and simultaneously marginalizes nuisance parameters, such as the outputs of hidden layers. This framework allows for the first time, training of discrete and continuous weights, for deterministic and stochastic spiking networks, using batches of training samples. Although its convergence is not ensured, the algorithm converges in practice faster than gradient-based methods, without requiring a large number of passes through the training data. The classification and regression results presented pave the way for new efficient training methods for deep Bayesian networks.

We present `GL-LowPopArt`, a novel Catoni-style estimator for generalized low-rank trace regression. Building on `LowPopArt` (Jang et al., 2024), it employs a two-stage approach: nuclear norm regularization followed by matrix Catoni estimation. We establish state-of-the-art estimation error bounds, surpassing existing guarantees (Fan et al., 2019; Kang et al., 2022), and reveal a novel experimental design objective, $\mathrm{GL}(π)$. The key technical challenge is controlling bias from the nonlinear inverse link function, which we address by our two-stage approach. We prove a *local* minimax lower bound, showing that our `GL-LowPopArt` enjoys instance-wise optimality up to the condition number of the ground-truth Hessian. Applications include generalized linear matrix completion, where `GL-LowPopArt` achieves a state-of-the-art Frobenius error guarantee, and **bilinear dueling bandits**, a novel setting inspired by general preference learning (Zhang et al., 2024). Our analysis of a `GL-LowPopArt`-based explore-then-commit algorithm reveals a new, potentially interesting problem-dependent quantity, along with improved Borda regret bound than vectorization (Wu et al., 2024).

Cancer is a genetic disorder whose clonal evolution can be monitored by tracking noisy genome-wide copy number variants. We introduce the Copy Number Stochastic Block Model (CN-SBM), a probabilistic framework that jointly clusters samples and genomic regions based on discrete copy number states using a bipartite categorical block model. Unlike models relying on Gaussian or Poisson assumptions, CN-SBM respects the discrete nature of CNV calls and captures subpopulation-specific patterns through block-wise structure. Using a two-stage approach, CN-SBM decomposes CNV data into primary and residual components, enabling detection of both large-scale chromosomal alterations and finer aberrations. We derive a scalable variational inference algorithm for application to large cohorts and high-resolution data. Benchmarks on simulated and real datasets show improved model fit over existing methods. Applied to TCGA low-grade glioma data, CN-SBM reveals clinically relevant subtypes and structured residual variation, aiding patient stratification in survival analysis. These results establish CN-SBM as an interpretable, scalable framework for CNV analysis with direct relevance for tumor heterogeneity and prognosis.

Scientific information expresses human understanding of nature. This knowledge is largely disseminated in different forms of text, including scientific papers, news articles, and discourse among people on social media. While important for accelerating our pursuit of knowledge, not all scientific text is faithful to the underlying science. As the volume of this text has burgeoned online in recent years, it has become a problem of societal importance to be able to identify the faithfulness of a given piece of scientific text automatically. This thesis is concerned with the cultivation of datasets, methods, and tools for machine understanding of scientific language, in order to analyze and understand science communication at scale. To arrive at this, I present several contributions in three areas of natural language processing and machine learning: automatic fact checking, learning with limited data, and scientific text processing. These contributions include new methods and resources for identifying check-worthy claims, adversarial claim generation, multi-source domain adaptation, learning from crowd-sourced labels, cite-worthiness detection, zero-shot scientific fact checking, detecting exaggerated scientific claims, and modeling degrees of information change in science communication. Critically, I demonstrate how the research outputs of this thesis are useful for effectively learning from limited amounts of scientific text in order to identify misinformative scientific statements and generate new insights into the science communication process

To understand how genetic variants in human genomes manifest in phenotypes -- traits like height or diseases like asthma -- geneticists have sequenced and measured hundreds of thousands of individuals. Geneticists use this data to build models that predict how a genetic variant impacts phenotype given genomic features of the variant, like DNA accessibility or the presence of nearby DNA-bound proteins. As more data and features become available, one might expect predictive models to improve. Unfortunately, training these models is bottlenecked by the need to solve expensive linear algebra problems because variants in the genome are correlated with nearby variants, requiring inversion of large matrices. Previous methods have therefore been restricted to fitting small models, and fitting simplified summary statistics, rather than the full likelihood of the statistical model. In this paper, we leverage modern fast linear algebra techniques to develop DeepWAS (Deep genome Wide Association Studies), a method to train large and flexible neural network predictive models to optimize likelihood. Notably, we find that larger models only improve performance when using our full likelihood approach; when trained by fitting traditional summary statistics, larger models perform no better than small ones. We find larger models trained on more features make better predictions, potentially improving disease predictions and therapeutic target identification.

--Learning the structure of Bayesian networks (BNs) from data is challenging, especially for datasets involving a large number of variables. The recently proposed divide-and-conquer (D&D) strategies present a promising approach for learning large BNs. However, they still face a main issue of unstable learning accuracy across subproblems. In this work, we introduce the idea of employing structure learning ensemble (SLE), which combines multiple BN structure learning algorithms, to consistently achieve high learning accuracy. We further propose an automatic approach called Auto-SLE for learning near-optimal SLEs, addressing the challenge of manually designing high-quality SLEs. The learned SLE is then integrated into a D&D method. Extensive experiments firmly show the superiority of our method over D&D methods with single BN structure learning algorithm in learning large BNs, achieving accuracy improvement usually by 30% 225% on datasets involving 10,000 variables. These results indicate the significant potential of employing (automatic learning of) SLEs for scalable BN structure learning. Learning the structure of Bayesian networks (BNs) [1] from data has attracted much research interest, due to its wide applications in machine learning, statistical modeling, and causal inference [2]-[4].