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In recent years, Deep-Learning Earth System Models (DL-ESMs) have emerged as promising, computationally efficient complements to traditional Earth system models. Here, we present an evaluation framework for testing DL-ESMs from a…

This study tackles the efficient estimation of Kullback-Leibler (KL) Divergence in Dirichlet Mixture Models (DMM), crucial for clustering compositional data. Despite the significance of DMMs, obtaining an analytically tractable solution for…

We propose a new method to test the effectiveness of a spatial point process forecast based on a log-likelihood score for predicted point density and the information gain for events that actually occurred in the test period. The method…

The EM algorithm is a widely used methodology for penalized likelihood estimation. Provable monotonicity and convergence are the hallmarks of the EM algorithm and these properties are well established for smooth likelihood and smooth…

We examine the integrated squared difference, also known as the L2 distance (L2D), between two probability densities. Such a distance metric allows for comparison of differences between pairs of distributions or changes in a distribution…

Climate model evaluation plays a crucial role in ensuring the accuracy of climatological predictions. However, existing statistical evaluation methods often overlook time misalignment of events in a system's evolution, which can lead to a…

Clustering is widely used in unsupervised learning to find homogeneous groups of observations within a dataset. However, clustering mixed-type data remains a challenge, as few existing approaches are suited for this task. This study…

A recurrent question in climate risk analysis is determining how climate change will affect heavy precipitation patterns. Dividing the globe into homogeneous sub-regions should improve the modelling of heavy precipitation by inferring…

Clustering algorithms have long been the topic of research, representing the more popular side of unsupervised learning. Since clustering analysis is one of the best ways to find some clarity and structure within raw data, this paper…

Clustering is one of the most fundamental tasks in machine learning, and the k-means clustering algorithm is perhaps one of the most widely used clustering algorithms. However, it suffers from several limitations, such as sensitivity to…

Different distance measures have been used for efficiently predicting software faults at early stages of software development. One stereotyped approach for software fault prediction due to its computational efficiency is K-means clustering,…

We consider the problem of clustering noisy finite-length observations of stationary ergodic random processes according to their generative models without prior knowledge of the model statistics and the number of generative models. Two…

The development of robust Early Warning Signals (EWS) is necessary to quantify the risk of crossing tipping points in the present-day climate change. Classically, EWS are statistical measures based on time series of climate state variables,…

In location-based resource allocation scenarios, the distances between each individual and the facility are desired to be approximately equal, thereby ensuring fairness. Individually fair clustering is often employed to achieve the…

Assignment methods are at the heart of many algorithms for unsupervised learning and clustering - in particular, the well-known K-means and Expectation-Maximization (EM) algorithms. In this work, we study several different methods of…

Existing approaches remain largely constrained by traditional distance metrics, limiting their effectiveness in handling random data. In this work, we introduce the first k-means variant in the literature that operates within a…

In this paper, we outline the use of Mixture Models in density estimation of large astronomical databases. This method of density estimation has been known in Statistics for some time but has not been implemented because of the large…

The conditional extremes (CE) framework has proven useful for analysing the joint tail behaviour of random vectors. However, when applied across many locations or variables, it can be difficult to interpret or compare the resulting extremal…

In the field of psychopathology, Ecological Momentary Assessment (EMA) methodological advancements have offered new opportunities to collect time-intensive, repeated and intra-individual measurements. This way, a large amount of data has…

In this paper an approach based on expectation maximization (EM) clustering to find the climate regions and a support vector machine to build a predictive model for each of these regions is proposed. To minimize the biases in the…