Locally stationary processes (LSPs) provide a robust framework for modeling time-varying phenomena, allowing for smooth variations in statistical properties such as mean and variance over time. In this paper, we address the estimation of the conditional probability distribution of LSPs using Nadaraya-Watson (NW) type estimators. The NW estimator approximates the conditional distribution of a target variable given covariates through kernel smoothing techniques. We establish the convergence rate of the NW conditional probability estimator for LSPs in the univariate setting under the Wasserstein distance and extend this analysis to the multivariate case using the sliced Wasserstein distance. Theoretical results are supported by numerical experiments on both synthetic and real-world datasets, demonstrating the practical usefulness of the proposed estimators.

In this theoretical article, a sociotechnical approach is proposed to characterize. First, the business ecosystem, focusing on the relationships among Providers, Enterprise, and Customers through SCM, ERP, and CRM platforms to align: (1) Business Intelligence (BI), Fuzzy Logic (FL), and TRIZ (Theory of Inventive Problem Solving), through the OID model, and (2) Knowledge Management (KM) and Imperfect Knowledge Management (IKM), through the OIDK model. Second, the article explores the E-GenAI business ecosystem, which integrates GenAI-based platforms for SCM, ERP, and CRM with GenAI-based platforms for BI, FL, TRIZ, KM, and IKM, to align Large Language Models (LLMs) through the E-GenAI (OID) model. Finally, to understand the dynamics of LLMs, we utilize finite automata to model the relationships between Followers and Followees. This facilitates the construction of LLMs that can identify specific characteristics of users on a social media platform.

Clustering, as an unsupervised technique, plays a pivotal role in various data analysis applications. Among clustering algorithms, Spectral Clustering on Euclidean Spaces has been extensively studied. However, with the rapid evolution of data complexity, Euclidean Space is proving to be inefficient for representing and learning algorithms. Although Deep Neural Networks on hyperbolic spaces have gained recent traction, clustering algorithms or non-deep machine learning models on non-Euclidean Spaces remain underexplored. In this paper, we propose a spectral clustering algorithm on Hyperbolic Spaces to address this gap. Hyperbolic Spaces offer advantages in representing complex data structures like hierarchical and tree-like structures, which cannot be embedded efficiently in Euclidean Spaces. Our proposed algorithm replaces the Euclidean Similarity Matrix with an appropriate Hyperbolic Similarity Matrix, demonstrating improved efficiency compared to clustering in Euclidean Spaces. Our contributions include the development of the spectral clustering algorithm on Hyperbolic Spaces and the proof of its weak consistency. We show that our algorithm converges at least as fast as Spectral Clustering on Euclidean Spaces. To illustrate the efficacy of our approach, we present experimental results on the Wisconsin Breast Cancer Dataset, highlighting the superior performance of Hyperbolic Spectral Clustering over its Euclidean counterpart. This work opens up avenues for utilizing non-Euclidean Spaces in clustering algorithms, offering new perspectives for handling complex data structures and improving clustering efficiency.

Time-series anomaly detection deals with the problem of detecting anomalous timesteps by learning normality from the sequence of observations. However, the concept of normality evolves over time, leading to a "new normal problem", where the distribution of normality can be changed due to the distribution shifts between training and test data. This paper highlights the prevalence of the new normal problem in unsupervised time-series anomaly detection studies. To tackle this issue, we propose a simple yet effective test-time adaptation strategy based on trend estimation and a self-supervised approach to learning new normalities during inference. Extensive experiments on real-world benchmarks demonstrate that incorporating the proposed strategy into the anomaly detector consistently improves the model's performance compared to the baselines, leading to robustness to the distribution shifts.

Monitoring wildfires is an essential step in minimizing their impact on the planet, understanding the many negative environmental, economic, and social consequences. Recent advances in remote sensing technology combined with the increasing application of artificial intelligence methods have improved real-time, high-resolution fire monitoring. This study explores two proposed approaches based on the U-Net model for automating and optimizing the burned-area mapping process. Denoted 128 and AllSizes (AS), they are trained on datasets with a different class balance by cropping input images to different sizes. They are then applied to Landsat imagery and time-series data from two fire-prone regions in Chile. The results obtained after enhancement of model performance by hyperparameter optimization demonstrate the effectiveness of both approaches. Tests based on 195 representative images of the study area show that increasing dataset balance using the AS model yields better performance. More specifically, AS exhibited a Dice Coefficient (DC) of 0.93, an Omission Error (OE) of 0.086, and a Commission Error (CE) of 0.045, while the 128 model achieved a DC of 0.86, an OE of 0.12, and a CE of 0.12. These findings should provide a basis for further development of scalable automatic burned-area mapping tools.