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).

Rapid evolution of territories due to climate change and human impact requires prompt and effective updates to geospatial databases maintained by the National Mapping Agency. This paper presents a comprehensive overview of change detection methods tailored for the operational updating of large-scale geographic databases. This review first outlines the fundamental definition of change, emphasizing its multifaceted nature, from temporal to semantic characterization. It categorizes automatic change detection methods into four main families: rule-based, statistical, machine learning, and simulation methods. The strengths, limitations, and applicability of every family are discussed in the context of various input data. Then, key applications for National Mapping Agencies are identified, particularly the optimization of geospatial database updating, change-based phenomena, and dynamics monitoring. Finally, the paper highlights the current challenges for leveraging change detection such as the variability of change definition, the missing of relevant large-scale datasets, the diversity of input data, the unstudied no-change detection, the human in the loop integration and the operational constraints. The discussion underscores the necessity for ongoing innovation in change detection techniques to address the future needs of geographic information systems for national mapping agencies.

The ability to display rich facial expressions is crucial for human-like robotic heads. While manually defining such expressions is intricate, there already exist approaches to automatically learn them. In this work one such approach is applied to evaluate and control a robot head different from the one in the original study. To improve the mapping of facial expressions from human actors onto a robot head, it is proposed to use 3D landmarks and their pairwise distances as input to the learning algorithm instead of the previously used facial action units. Participants of an online survey preferred mappings from our proposed approach in most cases, though there are still further improvements required.

Over the past decade, wearable computing devices (``smart glasses'') have undergone remarkable advancements in sensor technology, design, and processing power, ushering in a new era of opportunity for high-density human behavior data. Equipped with wearable cameras, these glasses offer a unique opportunity to analyze non-verbal behavior in natural settings as individuals interact. Our focus lies in predicting engagement in dyadic interactions by scrutinizing verbal and non-verbal cues, aiming to detect signs of disinterest or confusion. Leveraging such analyses may revolutionize our understanding of human communication, foster more effective collaboration in professional environments, provide better mental health support through empathetic virtual interactions, and enhance accessibility for those with communication barriers. In this work, we collect a dataset featuring 34 participants engaged in casual dyadic conversations, each providing self-reported engagement ratings at the end of each conversation. We introduce a novel fusion strategy using Large Language Models (LLMs) to integrate multiple behavior modalities into a ``multimodal transcript'' that can be processed by an LLM for behavioral reasoning tasks. Remarkably, this method achieves performance comparable to established fusion techniques even in its preliminary implementation, indicating strong potential for further research and optimization. This fusion method is one of the first to approach ``reasoning'' about real-world human behavior through a language model. Smart glasses provide us the ability to unobtrusively gather high-density multimodal data on human behavior, paving the way for new approaches to understanding and improving human communication with the potential for important societal benefits. The features and data collected during the studies will be made publicly available to promote further research.

The Fisher-Rao distance between two probability distributions of a statistical model is defined as the Riemannian geodesic distance induced by the Fisher information metric. In order to calculate the Fisher-Rao distance in closed-form, we need (1) to elicit a formula for the Fisher-Rao geodesics, and (2) to integrate the Fisher length element along those geodesics. We consider several numerically robust approximation and bounding techniques for the Fisher-Rao distances: First, we report generic upper bounds on Fisher-Rao distances based on closed-form 1D Fisher-Rao distances of submodels. Second, we describe several generic approximation schemes depending on whether the Fisher-Rao geodesics or pregeodesics are available in closed-form or not. In particular, we obtain a generic method to guarantee an arbitrarily small additive error on the approximation provided that Fisher-Rao pregeodesics and tight lower and upper bounds are available. Third, we consider the case of Fisher metrics being Hessian metrics, and report generic tight upper bounds on the Fisher-Rao distances using techniques of information geometry. Uniparametric and biparametric statistical models always have Fisher Hessian metrics, and in general a simple test allows to check whether the Fisher information matrix yields a Hessian metric or not. Fourth, we consider elliptical distribution families and show how to apply the above techniques to these models. We also propose two new distances based either on the Fisher-Rao lengths of curves serving as proxies of Fisher-Rao geodesics, or based on the Birkhoff/Hilbert projective cone distance. Last, we consider an alternative group-theoretic approach for statistical transformation models based on the notion of maximal invariant which yields insights on the structures of the Fisher-Rao distance formula which may be used fruitfully in applications.

Accurate vegetation models can produce further insights into the complex interaction between vegetation activity and ecosystem processes. Previous research has established that long-term trends and short-term variability of temperature and precipitation affect vegetation activity. Motivated by the recent success of Transformer-based Deep Learning models for medium-range weather forecasting, we adapt the publicly available pre-trained FourCastNet to model vegetation activity while accounting for the short-term dynamics of climate variability. We investigate how the learned global representation of the atmosphere's state can be transferred to model the normalized difference vegetation index (NDVI). Our model globally estimates vegetation activity at a resolution of \SI{0.25}{\degree} while relying only on meteorological data. We demonstrate that leveraging pre-trained weather models improves the NDVI estimates compared to learning an NDVI model from scratch. Additionally, we compare our results to other recent data-driven NDVI modeling approaches from machine learning and ecology literature. We further provide experimental evidence on how much data and training time is necessary to turn FourCastNet into an effective vegetation model. Code and models will be made available upon publication.

At its microscopic level, the universe follows the laws of quantum mechanics. Focusing on the quantum trajectories of particles as followed from the hydrodynamical formulation of quantum mechanics, we propose that under general requirements, quantum systems follow a disrupted version of the gradient descent model, a basic machine learning algorithm, where the learning is distorted due to the self-organizing process of the quantum system. Such a learning process is possible only when we assume dissipation, i.e., that the quantum system is open. The friction parameter determines the nonlinearity of the quantum system. We then provide an empirical demonstration of the proposed model.

Evaluating environmental variables that vary stochastically is the principal topic for designing better environmental management and restoration schemes. Both the upper and lower estimates of these variables, such as water quality indices and flood and drought water levels, are important and should be consistently evaluated within a unified mathematical framework. We propose a novel pair of Orlicz regrets to consistently bound the statistics of random variables both from below and above. Here, consistency indicates that the upper and lower bounds are evaluated with common coefficients and parameter values being different from some of the risk measures proposed thus far. Orlicz regrets can flexibly evaluate the statistics of random variables based on their tail behavior. The explicit linkage between Orlicz regrets and divergence risk measures was exploited to better comprehend them. We obtain sufficient conditions to pose the Orlicz regrets as well as divergence risk measures, and further provide gradient descent-type numerical algorithms to compute them. Finally, we apply the proposed mathematical framework to the statistical evaluation of 31-year water quality data as key environmental indicators in a Japanese river environment.

Emotional contagion refers to the sharing of emotional states between individuals, and it has been observed in both animal and human models that the infectivity of negative emotions is much greater than that of positive emotions [1]. Negative emotional contagion has a powerful effect on our relationships - family, friends, teams, etc. - and can lead, for example, to depressive behavior in healthy people who live with depressed individuals. It is urgent to understand the mechanism of emotional contagion, especially negative emotional contagion. Emotional contagion has long been regarded as reflecting a mimicry-based process, for which mimicry of emotional expressions and its consequent feedback function are assumed and can be evoked by higher-order social processes or by a simple emotion-to-action response as well as the primary mimicry-based process [2]. At present, the emotional contagion models mostly adopt behavioral analysis and questionnaires, which are often affected by subjects' subjective factors. They have mainly focused on behavioral experiment such as analysing people's posts containing emotional information to extract affective evidence [3], using the Positive And Negative Affective Schedule (PANAS) scale to measure positive and negative emotions as a quantitive research [4] and the mathematical simulation model of emotional contagion in crowd evacuation [5]. Although behavioral analysis and questionaires can provide valuable insights into emotional contagion, they have limitations in terms of capturing the neural mechanisms, timing, and subtleties of this phenomenon.