Multiscale systems are ubiquitous in science and technology, but are notoriously challenging to simulate as short spatiotemporal scales must be appropriately linked to emergent bulk physics. When expensive high-dimensional dynamical systems are coarse-grained into low-dimensional models, the entropic loss of information leads to emergent physics which are dissipative, history-dependent, and stochastic. To machine learn coarse-grained dynamics from time-series observations of particle trajectories, we propose a framework using the metriplectic bracket formalism that preserves these properties by construction; most notably, the framework guarantees discrete notions of the first and second laws of thermodynamics, conservation of momentum, and a discrete fluctuation-dissipation balance crucial for capturing non-equilibrium statistics. We introduce the mathematical framework abstractly before specializing to a particle discretization. As labels are generally unavailable for entropic state variables, we introduce a novel self-supervised learning strategy to identify emergent structural variables. We validate the method on benchmark systems and demonstrate its utility on two challenging examples: (1) coarse-graining star polymers at challenging levels of coarse-graining while preserving non-equilibrium statistics, and (2) learning models from high-speed video of colloidal suspensions that capture coupling between local rearrangement events and emergent stochastic dynamics. We provide open-source implementations in both PyTorch and LAMMPS, enabling large-scale inference and extensibility to diverse particle-based systems.

Conformalized multiple testing offers a model-free way to control predictive uncertainty in decision-making. Existing methods typically use only part of the available data to build score functions tailored to specific settings. We propose a unified framework that puts data utilization at the center: it uses all available data-null, alternative, and unlabeled-to construct scores and calibrate p-values through a full permutation strategy. This unified use of all available data significantly improves power by enhancing non-conformity score quality and maximizing calibration set size while rigorously controlling the false discovery rate. Crucially, our framework provides a systematic design principle for conformal testing and enables automatic selection of the best conformal procedure among candidates without extra data splitting. Extensive numerical experiments demonstrate that our enhanced methods deliver superior efficiency and adaptability across diverse scenarios.

We study the fundamental problem of learning a marginally stable unknown nonlinear dynamical system. We describe an algorithm for this problem, based on the technique of spectral filtering, which learns a mapping from past observations to the next based on a spectral representation of the system. Using techniques from online convex optimization, we prove vanishing prediction error for any nonlinear dynamical system that has finitely many marginally stable modes, with rates governed by a novel quantitative control-theoretic notion of learnability. The main technical component of our method is a new spectral filtering algorithm for linear dynamical systems, which incorporates past observations and applies to general noisy and marginally stable systems. This significantly generalizes the original spectral filtering algorithm to both asymmetric dynamics as well as incorporating noise correction, and is of independent interest.

Multi-view evidential learning aims to integrate information from multiple views to improve prediction performance and provide trustworthy uncertainty esitimation. Most previous methods assume that view-specific evidence learning is naturally reliable. However, in practice, the evidence learning process tends to be biased. Through empirical analysis on real-world data, we reveal that samples tend to be assigned more evidence to support data-rich classes, thereby leading to unreliable uncertainty estimation in predictions. This motivates us to delve into a new Biased Evidential Multi-view Learning (BEML) problem. To this end, we propose Fairness-Aware Multi-view Evidential Learning (FAML). FAML first introduces an adaptive prior based on training trajectory, which acts as a regularization strategy to flexibly calibrate the biased evidence learning process. Furthermore, we explicitly incorporate a fairness constraint based on class-wise evidence variance to promote balanced evidence allocation. In the multi-view fusion stage, we propose an opinion alignment mechanism to mitigate view-specific bias across views, thereby encouraging the integration of consistent and mutually supportive evidence. Extensive experiments on five real-world multi-view datasets demonstrate that FAML achieves more balanced evidence allocation and improves both prediction performance and the reliability of uncertainty estimation compared to state-of-the-art methods.

Bhattacharya et al. (2015) introduce a novel prior, the Dirichlet-Laplace (DL) prior, and propose a Markov chain Monte Carlo (MCMC) method to simulate posterior draws under this prior in a conditionally Gaussian setting. The original algorithm samples from conditional distributions in the wrong order, i.e., it does not correctly sample from the joint posterior distribution of all latent variables. This note details the issue and provides two simple solutions: A correction to the original algorithm and a new algorithm based on an alternative, yet equivalent, formulation of the prior. This corrigendum does not affect the theoretical results in Bhattacharya et al. (2015). A slightly modified version of this article is included in Luis Gruber's master thesis (Gruber, 2025).

The minimum density power divergence estimator (MDPDE) has gained significant attention in the literature of robust inference due to its strong robustness properties and high asymptotic efficiency; it is relatively easy to compute and can be interpreted as a generalization of the classical maximum likelihood estimator. It has been successfully applied in various setups, including the case of independent and non-homogeneous (INH) observations that cover both classification and regression-type problems with a fixed design. While the local robustness of this estimator has been theoretically validated through the bounded influence function, no general result is known about the global reliability or the breakdown behavior of this estimator under the INH setup, except for the specific case of location-type models. In this paper, we extend the notion of asymptotic breakdown point from the case of independent and identically distributed data to the INH setup and derive a theoretical lower bound for the asymptotic breakdown point of the MDPDE, under some easily verifiable assumptions. These results are further illustrated with applications to some fixed design regression models and corroborated through extensive simulation studies.

Determining the optimal data mixture for large language model training remains a challenging problem with an outsized impact on performance. In practice, language model developers continue to rely on heuristic exploration since no learning-based approach has emerged as a reliable solution. In this work, we propose to view the selection of training data mixtures as a black-box hyperparameter optimization problem, for which Bayesian Optimization is a well-established class of appropriate algorithms. Firstly, we cast data mixture learning as a sequential decision-making problem, in which we aim to find a suitable trade-off between the computational cost of training exploratory (proxy-) models and final mixture performance. Secondly, we systematically explore the properties of transferring mixtures learned at a small scale to larger-scale experiments, providing insights and highlighting opportunities for research at a modest scale. By proposing Multi-fidelity Bayesian Optimization as a suitable method in this common scenario, we introduce a natural framework to balance experiment cost with model fit, avoiding the risks of overfitting to smaller scales while minimizing the number of experiments at high cost. We present results for pre-training and instruction finetuning across models ranging from 1 million to 7 billion parameters, varying from simple architectures to state-of-the-art models and benchmarks spanning dozens of datasets. We demonstrate consistently strong results relative to a wide range of baselines, resulting inspeed-ups of over 500% in determining the best data mixture on our largest experiments. In addition, we broaden access to research by sharing ADMIRE IFT Runs, a dataset of 460 full training & evaluation runs worth over 13,000 GPU hours, greatly reducing the cost of conducting research in this area.

An overarching objective in contemporary statistical network analysis is extracting salient information from datasets consisting of multiple networks. To date, considerable attention has been devoted to node and network clustering, while comparatively less attention has been devoted to downstream connectivity estimation and parsimonious embedding dimension selection. Given a sample of potentially heterogeneous networks, this paper proposes a method to simultaneously estimate a latent matrix of connectivity probabilities and its embedding dimensionality or rank after first pre-estimating the number of communities and the node community memberships. The method is formulated as a convex optimization problem and solved using an alternating direction method of multipliers algorithm. We establish estimation error bounds under the Frobenius norm and nuclear norm for settings in which observable networks have blockmodel structure, even when node memberships are imperfectly recovered. When perfect membership recovery is possible and dimensionality is much smaller than the number of communities, the proposed method outperforms conventional averaging-based methods for estimating connectivity and dimensionality. Numerical studies empirically demonstrate the accuracy of our method across various scenarios. Additionally, analysis of a primate brain dataset demonstrates that posited connectivity is not necessarily full rank in practice, illustrating the need for flexible methodology.

This paper presents Constrained Centroid Clustering (CCC), a method that extends classical centroid-based clustering by enforcing a constraint on the maximum distance between the cluster center and the farthest point in the cluster. Using a Lagrangian formulation, we derive a closed-form solution that maintains interpretability while controlling cluster spread. To evaluate CCC, we conduct experiments on synthetic circular data with radial symmetry and uniform angular distribution. Using ring-wise, sector-wise, and joint entropy as evaluation metrics, we show that CCC achieves more compact clusters by reducing radial spread while preserving angular structure, outperforming standard methods such as K-means and GMM. The proposed approach is suitable for applications requiring structured clustering with spread control, including sensor networks, collaborative robotics, and interpretable pattern analysis.

Multivariate Hawkes process provides a powerful framework for modeling temporal dependencies and event-driven interactions in complex systems. While existing methods primarily focus on uncovering causal structures among observed subprocesses, real-world systems are often only partially observed, with latent subprocesses posing significant challenges. In this paper, we show that continuous-time event sequences can be represented by a discrete-time model as the time interval shrinks, and we leverage this insight to establish necessary and sufficient conditions for identifying latent subprocesses and the causal influences. Accordingly, we propose a two-phase iterative algorithm that alternates between inferring causal relationships among discovered subprocesses and uncovering new latent subprocesses, guided by path-based conditions that guarantee identifiability. Experiments on both synthetic and real-world datasets show that our method effectively recovers causal structures despite the presence of latent subprocesses.