We propose fast and communication-efficient optimization algorithms for multi-robot rotation averaging and translation estimation problems that arise from collaborative simultaneous localization and mapping (SLAM), structure-from-motion (SfM), and camera network localization applications. Our methods are based on theoretical relations between the Hessians of the underlying Riemannian optimization problems and the Laplacians of suitably weighted graphs. We leverage these results to design a collaborative solver in which robots coordinate with a central server to perform approximate second-order optimization, by solving a Laplacian system at each iteration. Crucially, our algorithms permit robots to employ spectral sparsification to sparsify intermediate dense matrices before communication, and hence provide a mechanism to trade off accuracy with communication efficiency with provable guarantees. We perform rigorous theoretical analysis of our methods and prove that they enjoy (local) linear rate of convergence. Furthermore, we show that our methods can be combined with graduated non-convexity to achieve outlier-robust estimation. Extensive experiments on real-world SLAM and SfM scenarios demonstrate the superior convergence rate and communication efficiency of our methods.

A key technique of machine learning and computer vision is to embed discrete weighted graphs into continuous spaces for further downstream processing. Embedding discrete hierarchical structures in hyperbolic geometry has proven very successful since it was shown that any weighted tree can be embedded in that geometry with arbitrary low distortion. Various optimization methods for hyperbolic embeddings based on common models of hyperbolic geometry have been studied. In this paper, we consider Hilbert geometry for the standard simplex which is isometric to a vector space equipped with the variation polytope norm. We study the representation power of this Hilbert simplex geometry by embedding distance matrices of graphs. Our findings demonstrate that Hilbert simplex geometry is competitive to alternative geometries such as the Poincar\'e hyperbolic ball or the Euclidean geometry for embedding tasks while being fast and numerically robust.

This paper studies an adaptive approach for probabilistic wind power forecasting (WPF) including offline and online learning procedures. In the offline learning stage, a base forecast model is trained via inner and outer loop updates of meta-learning, which endows the base forecast model with excellent adaptability to different forecast tasks, i.e., probabilistic WPF with different lead times or locations. In the online learning stage, the base forecast model is applied to online forecasting combined with incremental learning techniques. On this basis, the online forecast takes full advantage of recent information and the adaptability of the base forecast model. Two applications are developed based on our proposed approach concerning forecasting with different lead times (temporal adaptation) and forecasting for newly established wind farms (spatial adaptation), respectively. Numerical tests were conducted on real-world wind power data sets. Simulation results validate the advantages in adaptivity of the proposed methods compared with existing alternatives.

In this paper, we investigate the in-context learning ability of retrieval-augmented encoder-decoder language models. We first conduct a comprehensive analysis of the state-of-the-art ATLAS model and identify its limitations in in-context learning, primarily due to a mismatch between pretraining and testing, as well as a restricted context length. To address these issues, we propose RAVEN, a model that combines retrieval-augmented masked language modeling and prefix language modeling. We further introduce Fusion-in-Context Learning to enhance the few-shot performance by enabling the model to leverage more in-context examples without requiring additional training or model modifications. Through extensive experiments, we demonstrate that RAVEN significantly outperforms ATLAS and achieves results comparable to the most advanced language models in certain scenarios, despite having substantially fewer parameters. Our work underscores the potential of retrieval-augmented encoder-decoder language models for in-context learning and encourages further research in this direction.

In recent years, there has been a surge in effort to formalize notions of fairness in machine learning. We focus on clustering -- one of the fundamental tasks in unsupervised machine learning. We propose a new axiom ``proportional representation fairness'' (PRF) that is designed for clustering problems where the selection of centroids reflects the distribution of data points and how tightly they are clustered together. Our fairness concept is not satisfied by existing fair clustering algorithms. We design efficient algorithms to achieve PRF both for unconstrained and discrete clustering problems. Our algorithm for the unconstrained setting is also the first known polynomial-time approximation algorithm for the well-studied Proportional Fairness (PF) axiom (Chen, Fain, Lyu, and Munagala, ICML, 2019). Our algorithm for the discrete setting also matches the best known approximation factor for PF.

Making inference with spatial extremal dependence models can be computationally burdensome since they involve intractable and/or censored likelihoods. Building on recent advances in likelihood-free inference with neural Bayes estimators, that is, neural networks that approximate Bayes estimators, we develop highly efficient estimators for censored peaks-over-threshold models that encode censoring information in the neural network architecture. Our new method provides a paradigm shift that challenges traditional censored likelihood-based inference methods for spatial extremal dependence models. Our simulation studies highlight significant gains in both computational and statistical efficiency, relative to competing likelihood-based approaches, when applying our novel estimators to make inference with popular extremal dependence models, such as max-stable, $r$-Pareto, and random scale mixture process models. We also illustrate that it is possible to train a single neural Bayes estimator for a general censoring level, precluding the need to retrain the network when the censoring level is changed. We illustrate the efficacy of our estimators by making fast inference on hundreds-of-thousands of high-dimensional spatial extremal dependence models to assess extreme particulate matter 2.5 microns or less in diameter (PM2.5) concentration over the whole of Saudi Arabia.

We propose a novel multivariate nonparametric multiple change point detection method using classifiers. We construct a classifier log-likelihood ratio that uses class probability predictions to compare different change point configurations. We propose a computationally feasible search method that is particularly well suited for random forests, denoted by changeforest. However, the method can be paired with any classifier that yields class probability predictions, which we illustrate by also using a k-nearest neighbor classifier. We prove that it consistently locates change points in single change point settings when paired with a consistent classifier. Our proposed method changeforest achieves improved empirical performance in an extensive simulation study compared to existing multivariate nonparametric change point detection methods. An efficient implementation of our method is made available for R, Python, and Rust users in the changeforest software package.

Various approaches based on supervised or unsupervised machine learning (ML) have been proposed for evaluating IoT data trust. However, assessing their real-world efficacy is hard mainly due to the lack of related publicly-available datasets that can be used for benchmarking. Since obtaining such datasets is challenging, we propose a data synthesis method, called random walk infilling (RWI), to augment IoT time-series datasets by synthesizing untrustworthy data from existing trustworthy data. Thus, RWI enables us to create labeled datasets that can be used to develop and validate ML models for IoT data trust evaluation. We also extract new features from IoT time-series sensor data that effectively capture its auto-correlation as well as its cross-correlation with the data of the neighboring (peer) sensors. These features can be used to learn ML models for recognizing the trustworthiness of IoT sensor data. Equipped with our synthesized ground-truth-labeled datasets and informative correlation-based feature, we conduct extensive experiments to critically examine various approaches to evaluating IoT data trust via ML. The results reveal that commonly used ML-based approaches to IoT data trust evaluation, which rely on unsupervised cluster analysis to assign trust labels to unlabeled data, perform poorly. This poor performance can be attributed to the underlying unsubstantiated assumption that clustering provides reliable labels for data trust, a premise that is found to be untenable. The results also show that the ML models learned from datasets augmented via RWI while using the proposed features generalize well to unseen data and outperform existing related approaches. Moreover, we observe that a semi-supervised ML approach that requires only about 10% of the data labeled offers competitive performance while being practically more appealing compared to the fully-supervised approaches.

Automatic assessment of the quality of scholarly documents is a difficult task with high potential impact. Multimodality, in particular the addition of visual information next to text, has been shown to improve the performance on scholarly document quality prediction (SDQP) tasks. We propose the multimodal predictive model MultiSChuBERT. It combines a textual model based on chunking full paper text and aggregating computed BERT chunk-encodings (SChuBERT), with a visual model based on Inception V3.Our work contributes to the current state-of-the-art in SDQP in three ways. First, we show that the method of combining visual and textual embeddings can substantially influence the results. Second, we demonstrate that gradual-unfreezing of the weights of the visual sub-model, reduces its tendency to ovefit the data, improving results. Third, we show the retained benefit of multimodality when replacing standard BERT$_{\textrm{BASE}}$ embeddings with more recent state-of-the-art text embedding models. Using BERT$_{\textrm{BASE}}$ embeddings, on the (log) number of citations prediction task with the ACL-BiblioMetry dataset, our MultiSChuBERT (text+visual) model obtains an $R^{2}$ score of 0.454 compared to 0.432 for the SChuBERT (text only) model. Similar improvements are obtained on the PeerRead accept/reject prediction task. In our experiments using SciBERT, scincl, SPECTER and SPECTER2.0 embeddings, we show that each of these tailored embeddings adds further improvements over the standard BERT$_{\textrm{BASE}}$ embeddings, with the SPECTER2.0 embeddings performing best.

Multi-source Domain Generalization (DG) measures a classifier's ability to generalize to new distributions of data it was not trained on, given several training domains. While several multi-source DG methods have been proposed, they incur additional complexity during training by using domain labels. Recent work has shown that a well-tuned Empirical Risk Minimization (ERM) training procedure, that is simply minimizing the empirical risk on the source domains, can outperform most existing DG methods. We identify several key candidate techniques to further improve ERM performance, such as better utilization of training data, model parameter selection, and weight-space regularization. We call the resulting method ERM++, and show it significantly improves the performance of DG on five multi-source datasets by over 5% compared to standard ERM, and beats state-of-the-art despite being less computationally expensive. Additionally, we demonstrate the efficacy of ERM++ on the WILDS-FMOW dataset, a challenging DG benchmark. We hope that ERM++ becomes a strong baseline for future DG research. Code is released at https://github.com/piotr-teterwak/erm_plusplus.