An accuracy-runtime trade-off comparison of scalable Gaussian process approximations for spatial data

Gaussian processes (GPs) are flexible, probabilistic, non-parametric models widely employed in various fields such as spatial statistics, time series analysis, and machine learning. A drawback of Gaussian processes is their computational cost having $\mathcal{O}(N^3)$ time and $\mathcal{O}(N^2)$ memory complexity which makes them prohibitive for large datasets. Numerous approximation techniques have been proposed to address this limitation. In this work, we systematically compare the accuracy of different Gaussian process approximations concerning marginal likelihood evaluation, parameter estimation, and prediction taking into account the time required to achieve a certain accuracy. We analyze this trade-off between accuracy and runtime on multiple simulated and large-scale real-world datasets and find that Vecchia approximations consistently emerge as the most accurate in almost all experiments. However, for certain real-world data sets, low-rank inducing point-based methods, i.e., full-scale and modified predictive process approximations, can provide more accurate predictive distributions for extrapolation.

A spectral clustering-type algorithm for the consistent estimation of the Hurst distribution in moderately high dimensions

Scale invariance (fractality) is a prominent feature of the large-scale behavior of many stochastic systems. In this work, we construct an algorithm for the statistical identification of the Hurst distribution (in particular, the scaling exponents) undergirding a high-dimensional fractal system. The algorithm is based on wavelet random matrices, modified spectral clustering and a model selection step for picking the value of the clustering precision hyperparameter. In a moderately high-dimensional regime where the dimension, the sample size and the scale go to infinity, we show that the algorithm consistently estimates the Hurst distribution. Monte Carlo simulations show that the proposed methodology is efficient for realistic sample sizes and outperforms another popular clustering method based on mixed-Gaussian modeling. We apply the algorithm in the analysis of real-world macroeconomic time series to unveil evidence for cointegration.

Qwen2.5-VL Technical Report

We introduce Qwen2.5-VL, the latest flagship model of Qwen vision-language series, which demonstrates significant advancements in both foundational capabilities and innovative functionalities. Qwen2.5-VL achieves a major leap forward in understanding and interacting with the world through enhanced visual recognition, precise object localization, robust document parsing, and long-video comprehension. A standout feature of Qwen2.5-VL is its ability to localize objects using bounding boxes or points accurately. It provides robust structured data extraction from invoices, forms, and tables, as well as detailed analysis of charts, diagrams, and layouts. To handle complex inputs, Qwen2.5-VL introduces dynamic resolution processing and absolute time encoding, enabling it to process images of varying sizes and videos of extended durations (up to hours) with second-level event localization. This allows the model to natively perceive spatial scales and temporal dynamics without relying on traditional normalization techniques. By training a native dynamic-resolution Vision Transformer (ViT) from scratch and incorporating Window Attention, we reduce computational overhead while maintaining native resolution. As a result, Qwen2.5-VL excels not only in static image and document understanding but also as an interactive visual agent capable of reasoning, tool usage, and task execution in real-world scenarios such as operating computers and mobile devices. Qwen2.5-VL is available in three sizes, addressing diverse use cases from edge AI to high-performance computing. The flagship Qwen2.5-VL-72B model matches state-of-the-art models like GPT-4o and Claude 3.5 Sonnet, particularly excelling in document and diagram understanding. Additionally, Qwen2.5-VL maintains robust linguistic performance, preserving the core language competencies of the Qwen2.5 LLM.

Explaining the Success of Nearest Neighbor Methods in Prediction

Many modern methods for prediction leverage nearest neighbor search to find past training examples most similar to a test example, an idea that dates back in text to at least the 11th century and has stood the test of time. This monograph aims to explain the success of these methods, both in theory, for which we cover foundational nonasymptotic statistical guarantees on nearest-neighbor-based regression and classification, and in practice, for which we gather prominent methods for approximate nearest neighbor search that have been essential to scaling prediction systems reliant on nearest neighbor analysis to handle massive datasets. Furthermore, we discuss connections to learning distances for use with nearest neighbor methods, including how random decision trees and ensemble methods learn nearest neighbor structure, as well as recent developments in crowdsourcing and graphons. In terms of theory, our focus is on nonasymptotic statistical guarantees, which we state in the form of how many training data and what algorithm parameters ensure that a nearest neighbor prediction method achieves a user-specified error tolerance. We begin with the most general of such results for nearest neighbor and related kernel regression and classification in general metric spaces. In such settings in which we assume very little structure, what enables successful prediction is smoothness in the function being estimated for regression, and a low probability of landing near the decision boundary for classification. In practice, these conditions could be difficult to verify for a real dataset. We then cover recent guarantees on nearest neighbor prediction in the three case studies of time series forecasting, recommending products to people over time, and delineating human organs in medical images by looking at image patches. In these case studies, clustering structure enables successful prediction.

Two-Stage Representation Learning for Analyzing Movement Behavior Dynamics in People Living with Dementia

In remote healthcare monitoring, time series representation learning reveals critical patient behavior patterns from high-frequency data. This study analyzes home activity data from individuals living with dementia by proposing a two-stage, self-supervised learning approach tailored to uncover low-rank structures. The first stage converts time-series activities into text sequences encoded by a pre-trained language model, providing a rich, high-dimensional latent state space using a PageRank-based method. This PageRank vector captures latent state transitions, effectively compressing complex behaviour data into a succinct form that enhances interpretability. This low-rank representation not only enhances model interpretability but also facilitates clustering and transition analysis, revealing key behavioral patterns correlated with clinicalmetrics such as MMSE and ADAS-COG scores. Our findings demonstrate the framework's potential in supporting cognitive status prediction, personalized care interventions, and large-scale health monitoring.

LLMER: Crafting Interactive Extended Reality Worlds with JSON Data Generated by Large Language Models

The integration of Large Language Models (LLMs) like GPT-4 with Extended Reality (XR) technologies offers the potential to build truly immersive XR environments that interact with human users through natural language, e.g., generating and animating 3D scenes from audio inputs. However, the complexity of XR environments makes it difficult to accurately extract relevant contextual data and scene/object parameters from an overwhelming volume of XR artifacts. It leads to not only increased costs with pay-per-use models, but also elevated levels of generation errors. Moreover, existing approaches focusing on coding script generation are often prone to generation errors, resulting in flawed or invalid scripts, application crashes, and ultimately a degraded user experience. To overcome these challenges, we introduce LLMER, a novel framework that creates interactive XR worlds using JSON data generated by LLMs. Unlike prior approaches focusing on coding script generation, LLMER translates natural language inputs into JSON data, significantly reducing the likelihood of application crashes and processing latency. It employs a multi-stage strategy to supply only the essential contextual information adapted to the user's request and features multiple modules designed for various XR tasks. Our preliminary user study reveals the effectiveness of the proposed system, with over 80% reduction in consumed tokens and around 60% reduction in task completion time compared to state-of-the-art approaches. The analysis of users' feedback also illuminates a series of directions for further optimization.

Logarithmic Memory Networks (LMNs): Efficient Long-Range Sequence Modeling for Resource-Constrained Environments

Long-range sequence modeling is a crucial aspect of natural language processing and time series analysis. However, traditional models like Recurrent Neural Networks (RNNs) and Transformers suffer from computational and memory inefficiencies, especially when dealing with long sequences. This paper introduces Logarithmic Memory Networks (LMNs), a novel architecture that leverages a hierarchical logarithmic tree structure to efficiently store and retrieve past information. LMNs dynamically summarize historical context, significantly reducing the memory footprint and computational complexity of attention mechanisms from O(n2) to O(log(n)). The model employs a single-vector, targeted attention mechanism to access stored information, and the memory block construction worker (summarizer) layer operates in two modes: a parallel execution mode during training for efficient processing of hierarchical tree structures and a sequential execution mode during inference, which acts as a memory management system. It also implicitly encodes positional information, eliminating the need for explicit positional encodings. These features make LMNs a robust and scalable solution for processing long-range sequences in resource-constrained environments, offering practical improvements in efficiency and scalability. The code is publicly available under the MIT License on GitHub: https://github.com/AhmedBoin/LogarithmicMemory.

XMTC: Explainable Early Classification of Multivariate Time Series in Reach-to-Grasp Hand Kinematics

Hand kinematics can be measured in Human-Computer Interaction (HCI) with the intention to predict the user's intention in a reach-to-grasp action. Using multiple hand sensors, multivariate time series data are being captured. Given a number of possible actions on a number of objects, the goal is to classify the multivariate time series data, where the class shall be predicted as early as possible. Many machine-learning methods have been developed for such classification tasks, where different approaches produce favorable solutions on different data sets. We, therefore, employ an ensemble approach that includes and weights different approaches. To provide a trustworthy classification production, we present the XMTC tool that incorporates coordinated multiple-view visualizations to analyze the predictions. Temporal accuracy plots, confusion matrix heatmaps, temporal confidence heatmaps, and partial dependence plots allow for the identification of the best trade-off between early prediction and prediction quality, the detection and analysis of challenging classification conditions, and the investigation of the prediction evolution in an overview and detail manner. We employ XMTC to real-world HCI data in multiple scenarios and show that good classification predictions can be achieved early on with our classifier as well as which conditions are easy to distinguish, which multivariate time series measurements impose challenges, and which features have most impact.

Navigating Tomorrow: Reliably Assessing Large Language Models Performance on Future Event Prediction

Predicting future events is an important activity with applications across multiple fields and domains. For example, the capacity to foresee stock market trends, natural disasters, business developments, or political events can facilitate early preventive measures and uncover new opportunities. Multiple diverse computational methods for attempting future predictions, including predictive analysis, time series forecasting, and simulations have been proposed. This study evaluates the performance of several large language models (LLMs) in supporting future prediction tasks, an under-explored domain. We assess the models across three scenarios: Affirmative vs. Likelihood questioning, Reasoning, and Counterfactual analysis. For this, we create a dataset1 by finding and categorizing news articles based on entity type and its popularity. We gather news articles before and after the LLMs training cutoff date in order to thoroughly test and compare model performance. Our research highlights LLMs potential and limitations in predictive modeling, providing a foundation for future improvements.

Deterministic Reservoir Computing for Chaotic Time Series Prediction

Reservoir Computing was shown in recent years to be useful as efficient to learn networks in the field of time series tasks. Their randomized initialization, a computational benefit, results in drawbacks in theoretical analysis of large random graphs, because of which deterministic variations are an still open field of research. Building upon Next-Gen Reservoir Computing and the Temporal Convolution Derived Reservoir Computing, we propose a deterministic alternative to the higher-dimensional mapping therein, TCRC-LM and TCRC-CM, utilizing the parametrized but deterministic Logistic mapping and Chebyshev maps. To further enhance the predictive capabilities in the task of time series forecasting, we propose the novel utilization of the Lobachevsky function as non-linear activation function. As a result, we observe a new, fully deterministic network being able to outperform TCRCs and classical Reservoir Computing in the form of the prominent Echo State Networks by up to $99.99\%$ for the non-chaotic time series and $87.13\%$ for the chaotic ones.