A central challenge in dynamic network analysis is to represent temporal evolution in a way that is both geometrically meaningful and statistically identifiable. One approach embeds a sequence of network snapshots as trajectories in a Euclidean space and relates these trajectories to node embeddings. In multilayer and unfolded spectral constructions, however, node embeddings and their underlying latent positions are identifiable only up to general linear transformations. Although this ambiguity preserves edge probabilities, it can distort geometry and invalidate distance based temporal comparisons at both the trajectory and node-levels. We develop Multiscale Euclidean Network Trajectories (MENT), a framework for multiscale temporal trajectories based on second-moment geometry. By imposing an isotropic normalization on the anchor latent positions, we reduce the relevant ambiguity to orthogonal transformations and prevent distortion of the second-moment geometry. In this canonical representation, we define a trace variation distance and mode-wise variation distances along orthogonal directions, and use multidimensional scaling to obtain low-dimensional trajectories of time points at both global and mode-wise levels. The resulting trajectories support interpretation and inference. They admit mode-wise decompositions, support attribution of global and mode-wise temporal changes to nodes, and enable change point detection through 1D trajectories. We prove consistency of the proposed unfolded spectral embedding and of the induced temporal trajectories. Experiments on two synthetic and two real dynamic networks illustrate stable and interpretable recovery of temporal structure and show strong performance against existing change point detection baselines.

We study expected generalization bounds for the Hierarchical Federated Learning (HFL) setup using Wasserstein distance. We introduce a generalized framework in which data is sampled hierarchically, and we model it with a multi-layered tree structure that induces dependencies among the clients' datasets. We derive generalization bounds in terms of Wasserstein distance under the Lipschitz assumption on the loss function, by applying a supersample construction that allows us to measure the sensitivity of the algorithm to the change of a single node in the sampling tree. By leveraging the FL structure, we recover and strictly imply existing state-of-the-art conditional mutual information (CMI) bounds in the case of bounded losses. We also show that our bound can be applied together with Differential Privacy assumptions, to recover generalization bounds based on algorithmic privacy. To assess the tightness of our bounds, we study the Gaussian Location Model (GLM) and show that we recover the actual asymptotic rate of the generalization error.

Consideranews recommendation website that, when presented with a new user, sequentially offers a selection of currently trending articles. Such asystem may only haveafewopportunities tomakerecommendations before the user decides to navigate away, leaving little time to correct for misspecified or underspecified prior knowledge.

Thesetting isarepeated game between the Player and Nature, where at each stage both pick actions based on the contexts.

In this paper, we find an appealing way to synthesize [JO19] and [CLM19] to give the best of both worlds: an algorithm which runs in polynomial time and can exploit structure in the underlying distribution to achieve sublinear sample complexity.

Many generative models have to combat missing modes .

Survey researchers face two key challenges: the rising costs of probability samples and missing data (e.g., non-response or attrition), which can undermine inference and increase the use of convenience samples. Recent work explores using large language models (LLMs) to simulate respondents via persona-based prompts, often without labeled data. We study a more practical setting where partial survey responses exist: we fine-tune LLMs on available data to impute self-reported vote choice under both random and systematic nonresponse, using the German Longitudinal Election Study. We compare zero-shot prompting and supervised fine-tuning against tabular classifiers (e.g., CatBoost) and test how different convenience samples (e.g., students) used for fine-tuning affect generalization. Our results show that when data are missing completely at random, fine-tuned LLMs match tabular classifiers but outperform zero-shot approaches. When only biased convenience samples are available, fine-tuning small (3B to 8B) open-source LLMs can recover both individual-level predictions and population-level distributions more accurately than zero-shot and often better than tabular methods. This suggests fine-tuned LLMs offer a promising strategy for researchers working with non-probability samples or systematic missing-ness, and may enable new survey designs requiring only easily accessible subpopulations.