\texttt{Mixture-Models} is an open-source Python library for fitting Gaussian Mixture Models (GMM) and their variants, such as Parsimonious GMMs, Mixture of Factor Analyzers, MClust models, Mixture of Student's t distributions, etc. It streamlines the implementation and analysis of these models using various first/second order optimization routines such as Gradient Descent and Newton-CG through automatic differentiation (AD) tools. This helps in extending these models to high-dimensional data, which is first of its kind among Python libraries. The library provides user-friendly model evaluation tools, such as BIC, AIC, and log-likelihood estimation. The source-code is licensed under MIT license and can be accessed at \url{https://github.com/kasakh/Mixture-Models}. The package is highly extensible, allowing users to incorporate new distributions and optimization techniques with ease. We conduct a large scale simulation to compare the performance of various gradient based approaches against Expectation Maximization on a wide range of settings and identify the corresponding best suited approach.

Through Ecological Momentary Assessment (EMA) studies, a number of time-series data is collected across multiple individuals, continuously monitoring various items of emotional behavior. Such complex data is commonly analyzed in an individual level, using personalized models. However, it is believed that additional information of similar individuals is likely to enhance these models leading to better individuals' description. Thus, clustering is investigated with an aim to group together the most similar individuals, and subsequently use this information in group-based models in order to improve individuals' predictive performance. More specifically, two model-based clustering approaches are examined, where the first is using model-extracted parameters of personalized models, whereas the second is optimized on the model-based forecasting performance. Both methods are then analyzed using intrinsic clustering evaluation measures (e.g. Silhouette coefficients) as well as the performance of a downstream forecasting scheme, where each forecasting group-model is devoted to describe all individuals belonging to one cluster. Among these, clustering based on performance shows the best results, in terms of all examined evaluation measures. As another level of evaluation, those group-models' performance is compared to three baseline scenarios, the personalized, the all-in-one group and the random group-based concept. According to this comparison, the superiority of clustering-based methods is again confirmed, indicating that the utilization of group-based information could be effectively enhance the overall performance of all individuals' data.

Water pollution is a major global environmental problem, and it poses a great environmental risk to public health and biological diversity. This work is motivated by assessing the potential environmental threat of coal mining through increased sulfate concentrations in river networks, which do not belong to any simple parametric distribution. However, existing network models mainly focus on binary or discrete networks and weighted networks with known parametric weight distributions. We propose a principled nonparametric weighted network model based on exponential-family random graph models and local likelihood estimation and study its model-based clustering with application to large-scale water pollution network analysis. We do not require any parametric distribution assumption on network weights. The proposed method greatly extends the methodology and applicability of statistical network models. Furthermore, it is scalable to large and complex networks in large-scale environmental studies and geoscientific research. The power of our proposed methods is demonstrated in simulation studies.