While most existing network embedding techniques focus solely on the network features, nodes in real-world networks are associated with a rich set of attributes. For example, in a social network, the user's posts are significantly correlated with trust and following relationships, and it has been shown that jointly exploiting both information sources improves learning performance [Tang et al., 2013]. Network embeddings for static attributed networks include frameworks based on matrix factorisation [Yang et al., 2015], or deep learning [Gao and Huang, 2018, Tu et al., 2017, Tan et al., 2023, Sun et al., 2016, Zhang et al., 2018, Li et al., 2021]. Some existing dynamic network embeddings leverage node attributes, but their exploitation of node attributes is rather limited, as they are usually solely used to initialise the first layer [Sankar et al., 2020, Dwivedi et al., 2023, Liu et al., 2021, Xu et al., 2020b,a]. Approaches that purposefully exploit node attributes include frameworks based on matrix factorisation [Liu et al., 2020, Li et al., 2017], deep learning [Tang et al., 2022, Ahmed et al., 2024, Wei et al., 2019], or Bayesian modelling [Luodi et al., 2024]. However, to the best of our knowledge, none of these methods have stability guarantees, which ensure that if two node/time pairs "behave the same" in the network, their representation is the same up to noise. Stability allows for the comparison of embeddings over time because the embedding space has a consistent interpretation. Attributed unfolded adjacency spectral embedding (AUASE) is a framework for unsupervised dynamic attributed network embedding with stability guarantees.

Recent works have shown a reduction from contextual bandits to online regression under a realizability assumption [Foster and Rakhlin, 2020, Foster and Krishnamurthy, 2021]. In this work, we investigate the use of neural networks for such online regression and associated Neural Contextual Bandits (NeuCBs). Using existing results for wide networks, one can readily show a ${\mathcal{O}}(\sqrt{T})$ regret for online regression with square loss, which via the reduction implies a ${\mathcal{O}}(\sqrt{K} T^{3/4})$ regret for NeuCBs. Departing from this standard approach, we first show a $\mathcal{O}(\log T)$ regret for online regression with almost convex losses that satisfy QG (Quadratic Growth) condition, a generalization of the PL (Polyak-\L ojasiewicz) condition, and that have a unique minima. Although not directly applicable to wide networks since they do not have unique minima, we show that adding a suitable small random perturbation to the network predictions surprisingly makes the loss satisfy QG with unique minima. Based on such a perturbed prediction, we show a ${\mathcal{O}}(\log T)$ regret for online regression with both squared loss and KL loss, and subsequently convert these respectively to $\tilde{\mathcal{O}}(\sqrt{KT})$ and $\tilde{\mathcal{O}}(\sqrt{KL^*} + K)$ regret for NeuCB, where $L^*$ is the loss of the best policy. Separately, we also show that existing regret bounds for NeuCBs are $\Omega(T)$ or assume i.i.d. contexts, unlike this work. Finally, our experimental results on various datasets demonstrate that our algorithms, especially the one based on KL loss, persistently outperform existing algorithms.

Nowadays, classification and Out-of-Distribution (OoD) detection in the few-shot setting remain challenging aims due to rarity and the limited samples in the few-shot setting, and because of adversarial attacks. Accomplishing these aims is important for critical systems in safety, security, and defence. In parallel, OoD detection is challenging since deep neural network classifiers set high confidence to OoD samples away from the training data. To address such limitations, we propose the Few-shot ROBust (FROB) model for classification and few-shot OoD detection. We devise FROB for improved robustness and reliable confidence prediction for few-shot OoD detection. We generate the support boundary of the normal class distribution and combine it with few-shot Outlier Exposure (OE). We propose a self-supervised learning few-shot confidence boundary methodology based on generative and discriminative models. The contribution of FROB is the combination of the generated boundary in a self-supervised learning manner and the imposition of low confidence at this learned boundary. FROB implicitly generates strong adversarial samples on the boundary and forces samples from OoD, including our boundary, to be less confident by the classifier. FROB achieves generalization to unseen OoD with applicability to unknown, in the wild, test sets that do not correlate to the training datasets. To improve robustness, FROB redesigns OE to work even for zero-shots. By including our boundary, FROB reduces the threshold linked to the model's few-shot robustness; it maintains the OoD performance approximately independent of the number of few-shots. The few-shot robustness analysis evaluation of FROB on different sets and on One-Class Classification (OCC) data shows that FROB achieves competitive performance and outperforms benchmarks in terms of robustness to the outlier few-shot sample population and variability.

We consider the problem of learning a sparse undirected graph underlying a given set of multivariate data. We focus on graph Laplacian-related constraints on the sparse precision matrix that encodes conditional dependence between the random variables associated with the graph nodes. Under these constraints the off-diagonal elements of the precision matrix are non-positive (total positivity), and the precision matrix may not be full-rank. We investigate modifications to widely used penalized log-likelihood approaches to enforce total positivity but not the Laplacian structure. The graph Laplacian can then be extracted from the off-diagonal precision matrix. An alternating direction method of multipliers (ADMM) algorithm is presented and analyzed for constrained optimization under Laplacian-related constraints and lasso as well as adaptive lasso penalties. Numerical results based on synthetic data show that the proposed constrained adaptive lasso approach significantly outperforms existing Laplacian-based approaches. We also evaluate our approach on real financial data.