Improving clustering quality evaluation in noisy Gaussian mixtures Renato Cordeiro de Amorim Vladimir Makarenkov Abstract Clustering is a well-established technique in machine learning and data analysis, widely used across various domains. Cluster validity indices, such as the Average Silhouette Width, Calinski-Harabasz, and Davies-Bouldin indices, play a crucial role in assessing clustering quality when external ground truth labels are unavailable. However, these measures can be affected by the feature relevance issue, potentially leading to unreliable evaluations in high-dimensional or noisy data sets. We introduce a theoretically grounded Feature Importance Rescaling (FIR) method that enhances the quality of clustering validation by adjusting feature contributions based on their dispersion. It attenuates noise features, clarifies clustering compactness and separation, and thereby aligns clustering validation more closely with the ground truth. Through extensive experiments on synthetic data sets under different configurations, we demonstrate that FIR consistently improves the correlation between the values of cluster validity indices and the ground truth, particularly in settings with noisy or irrelevant features. The results show that FIR increases the robustness of clustering evaluation, reduces variability in performance across different data sets, and remains effective even when clusters exhibit significant overlap. These findings highlight the potential of FIR as a valuable enhancement of clustering validation, making it a practical tool for unsupervised learning tasks where labelled data is unavailable. Mila - Quebec AI Institute, Montreal, QC, Canada.Keywords: Cluster validity indices, data rescaling, noisy data. 1 Introduction Clustering is a fundamenta technique in machine learning and data analysis, which is central to many exploratory methods.

This paper reviews statistical methods for hypothesis testing and clustering in network models. We analyze the method by Bickel et al. (2016) for deriving the asymptotic null distribution of the largest eigenvalue, noting its slow convergence and the need for bootstrap corrections. The SCORE method by Jin et al. (2015) and the NCV method by Chen et al. (2018) are evaluated for their efficacy in clustering within Degree-Corrected Block Models, with NCV facing challenges due to its time-intensive nature. We suggest exploring eigenvector entry distributions as a potential efficiency improvement.

Automated Machine Learning (AutoML) has significantly advanced the efficiency of ML-focused software development by automating hyperparameter optimization and pipeline construction, reducing the need for manual intervention. Quantum Machine Learning (QML) offers the potential to surpass classical machine learning (ML) capabilities by utilizing quantum computing. However, the complexity of QML presents substantial entry barriers. We introduce \emph{AutoQML}, a novel framework that adapts the AutoML approach to QML, providing a modular and unified programming interface to facilitate the development of QML pipelines. AutoQML leverages the QML library sQUlearn to support a variety of QML algorithms. The framework is capable of constructing end-to-end pipelines for supervised learning tasks, ensuring accessibility and efficacy. We evaluate AutoQML across four industrial use cases, demonstrating its ability to generate high-performing QML pipelines that are competitive with both classical ML models and manually crafted quantum solutions.

We propose Microscopic Propagator Imaging (MPI) as a novel method to retrieve the indices of the microscopic propagator which is the probability density function of water displacements due to diffusion within the nervous tissue microstructures. Unlike the Ensemble Average Propagator indices or the Diffusion Tensor Imaging metrics, MPI indices are independent from the mesoscopic organization of the tissue such as the presence of multiple axonal bundle directions and orientation dispersion. As a consequence, MPI indices are more specific to the volumes, sizes, and types of microstructures, like axons and cells, that are present in the tissue. Thus, changes in MPI indices can be more directly linked to alterations in the presence and integrity of microstructures themselves. The methodology behind MPI is rooted on zonal modeling of spherical harmonics, signal simulation, and machine learning regression, and is demonstrated on both synthetic and Human Diffusion MRI data.

ABSTRACT Natural gas (NG) is relatively a clean source of energy, particularly compared to fossil fuels, and worldwide consumption of NG has been increasing almost linearly in the last two decades. A similar trend can also be seen in Turkey, while another similarity is the high dependence on impor ts for the continuous NG supply. It is crucial to accurately forecast future NG demand (NGD) in Turkey, especially, for import contracts; in this respect, forecasts of monthly NGD for the following year are of utmost importance. In the current study, the h istorical monthly NG consumption data between 2014 and 2024 provided by SOCAR, the local residential NG distribution company for two cities in Turkey, Bursa and Kayseri, was used to determine out - of - sample monthly NGD forecasts for a period of one year and nine months using various time series models, including SARIMA and ETS models, and a novel proposed machine learning method. The proposed method, named Just - in - Time - Learning - Gaussia n Process Regression (JITL - GPR), uses a novel feature representation for t he past NG demand values; instead of using past demand values as column - wise separate features, they are placed on a two - dimensional (2 - D) grid of year - month values. For each test point, a kernel function, tailored for the NGD predictions, is used in GPR t o predict the query point. Since a model is constructed separately for each test point, the proposed method is, indeed, an example of JITL. The JITL - GPR method is easy to use and optimize, and offers a reduction in forecast errors compared to traditional t ime series methods and a state - of - the - art combinat ion model; therefore, it is a promising tool for NGD forecasting in similar settings. INTRODUCTION In the last few decades, there has been a shift in energy sources from fossil fuels to cleaner energy sources, such as wind and solar energy, mainly due to environmental concerns and related government regulations . However, these latter sources are depend ent on w eather conditions and require integration with grid technologies for continuous power generation. Natural gas (NG), typically, consists of (up to) ~95% of methane and 2 - 2.5% ethane - hexane+, with the remain der consist ing of nitrogen, CO NG p ower plants are easy to build and highly reliable, mak ing them invaluable for "clean" energy production. On the other hand, m ost countries depend on imports to maintain t heir NG supplies, and there is a delicate balance between import s and domestic demand . S toring excess import ed gas above actual demand is difficult and would result in economic losses, while import ing less than actual demand could result in a nationwide sh ortage.

The advancement of smart grid technologies necessitates the integration of cutting-edge computational methods to enhance predictive energy optimization. This study proposes a multi-faceted approach by incorporating (1) Deep Reinforcement Learning (DRL) agents trained using data from Digital Twins (DTs) to optimize energy consumption in real time, (2) Physics-Informed Neural Networks (PINNs) to seamlessly embed physical laws within the optimization process, ensuring model accuracy and interpretability, and (3) Blockchain (BC) technology to facilitate secure and transparent communication across the smart grid infrastructure. The model was trained and validated using comprehensive datasets, including smart meter energy consumption data, renewable energy outputs, dynamic pricing, and user preferences collected from IoT devices. The proposed framework achieved superior predictive performance with a Mean Absolute Error (MAE) of 0.237 kWh, Root Mean Square Error (RMSE) of 0.298 kWh, and an R-squared (R2) value of 0.978, indicating a 97.8% explanation of data variance. Classification metrics further demonstrated the model's robustness, achieving 97.7% accuracy, 97.8% precision, 97.6% recall, and an F1 Score of 97.7%. Comparative analysis with traditional models like Linear Regression, Random Forest, SVM, LSTM, and XGBoost revealed the superior accuracy and real-time adaptability of the proposed method. In addition to enhancing energy efficiency, the model reduced energy costs by 35%, maintained a 96% user comfort index, and increased renewable energy utilization to 40%. This study demonstrates the transformative potential of integrating PINNs, DT, and Blockchain technologies to optimize energy consumption in smart grids, paving the way for sustainable, secure, and efficient energy management systems.

Curriculum learning is a training method in which an agent is first trained on a curriculum of relatively simple tasks related to a target task in an effort to shorten the time required to train on the target task. Autonomous curriculum design involves the design of such curriculum with no reliance on human knowledge and/or expertise. Finding an efficient and effective way of autonomously designing curricula remains an open problem. We propose a novel approach for automatically designing curricula by leveraging the learner's uncertainty to select curricula tasks. Our approach measures the uncertainty in the learner's policy using relative entropy, and guides the agent to states of high uncertainty to facilitate learning. Our algorithm supports the generation of autonomous curricula in a self-assessed manner by leveraging the learner's past and current policies but it also allows the use of teacher guided design in an instructive setting. We provide theoretical guarantees for the convergence of our algorithm using two time-scale optimization processes. Results show that our algorithm outperforms randomly generated curriculum, and learning directly on the target task as well as the curriculum-learning criteria existing in literature. We also present two additional heuristic distance measures that could be combined with our relative-entropy approach for further performance improvements.

Temporal networks have gained significant prominence in the past decade for modelling dynamic interactions within complex systems. A key challenge in this domain is Temporal Link Prediction (TLP), which aims to forecast future connections by analysing historical network structures across various applications including social network analysis. While existing surveys have addressed specific aspects of TLP, they typically lack a comprehensive framework that distinguishes between representation and inference methods. This survey bridges this gap by introducing a novel taxonomy that explicitly examines representation and inference from existing methods, providing a novel classification of approaches for TLP. We analyse how different representation techniques capture temporal and structural dynamics, examining their compatibility with various inference methods for both transductive and inductive prediction tasks. Our taxonomy not only clarifies the methodological landscape but also reveals promising unexplored combinations of existing techniques. This taxonomy provides a systematic foundation for emerging challenges in TLP, including model explainability and scalable architectures for complex temporal networks.

Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs) have led to significant progress in 2D body pose estimation. However, achieving a good balance between accuracy, efficiency, and robustness remains a challenge. For instance, CNNs are computationally efficient but struggle with long-range dependencies, while ViTs excel in capturing such dependencies but suffer from quadratic computational complexity. This paper proposes two ViT-based models for accurate, efficient, and robust 2D pose estimation. The first one, EViTPose, operates in a computationally efficient manner without sacrificing accuracy by utilizing learnable joint tokens to select and process a subset of the most important body patches, enabling us to control the trade-off between accuracy and efficiency by changing the number of patches to be processed. The second one, UniTransPose, while not allowing for the same level of direct control over the trade-off, efficiently handles multiple scales by combining (1) an efficient multi-scale transformer encoder that uses both local and global attention with (2) an efficient sub-pixel CNN decoder for better speed and accuracy. Moreover, by incorporating all joints from different benchmarks into a unified skeletal representation, we train robust methods that learn from multiple datasets simultaneously and perform well across a range of scenarios -- including pose variations, lighting conditions, and occlusions. Experiments on six benchmarks demonstrate that the proposed methods significantly outperform state-of-the-art methods while improving computational efficiency. EViTPose exhibits a significant decrease in computational complexity (30% to 44% less in GFLOPs) with a minimal drop of accuracy (0% to 3.5% less), and UniTransPose achieves accuracy improvements ranging from 0.9% to 43.8% across these benchmarks.

Algorithmic solutions have significant potential to improve decision-making across various domains, from healthcare to e-commerce. However, the widespread adoption of these solutions is hindered by a critical challenge: the lack of human-interpretable explanations. Current approaches to Explainable AI (XAI) predominantly focus on complex machine learning models, often producing brittle and non-intuitive explanations. This project proposes a novel approach to developing explainable algorithms by starting with optimization problems, specifically the assignment problem. The developed software library enriches basic algorithms with human-understandable explanations through four key methodologies: generating meaningful alternative solutions, creating robust solutions through input perturbation, generating concise decision trees and providing reports with comprehensive explanation of the results. Currently developed tools are often designed with specific clustering algorithms in mind, which limits their adaptability and flexibility to incorporate alternative techniques. Additionally, many of these tools fail to integrate expert knowledge, which could enhance the clustering process by providing valuable insights and context. This lack of adaptability and integration can hinder the effectiveness and robustness of the clustering outcomes in various applications. The represents a step towards making algorithmic solutions more transparent, trustworthy, and accessible. By collaborating with industry partners in sectors such as sales, we demonstrate the practical relevance and transformative potential of our approach.