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The Expectation-Maximization (EM) algorithm is a widely used method for maximum likelihood estimation in models with latent variables. For estimating mixtures of Gaussians, its iteration can be viewed as a soft version of the k-means…

Accurate weather forecasting holds significant importance, serving as a crucial tool for decision-making in various industrial sectors. The limitations of statistical models, assuming independence among data points, highlight the need for…

This document describes in detail a new hybrid ensemble-variational algorithm that generalizes existing ensemble or variational data assimilation approaches and would enable joint state/parameter estimations in ECMWF's Integrated…

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…

Seasonal climate forecasts are commonly based on model runs from fully coupled forecasting systems that use Earth system models to represent interactions between the atmosphere, ocean, land and other Earth-system components. Recently,…

Data-driven weather forecast based on machine learning (ML) has experienced rapid development and demonstrated superior performance in the global medium-range forecast compared to traditional physics-based dynamical models. However, most of…

Expectation-Maximization (EM) algorithm is a widely used iterative algorithm for computing (local) maximum likelihood estimate (MLE). It can be used in an extensive range of problems, including the clustering of data based on the Gaussian…

We present a new version of the truncated harmonic mean estimator (THAMES) for univariate or multivariate mixture models. The estimator computes the marginal likelihood from Markov chain Monte Carlo (MCMC) samples, is consistent,…

Time series forecasting models are increasingly scaled through large Transformer backbones, yet most existing approaches process all series through a shared dense computation path despite substantial heterogeneity in temporal structure.…

In order to enable the transition towards renewable energy sources, probabilistic energy forecasting is of critical importance for incorporating volatile power sources such as solar energy into the electrical grid. Solar energy forecasting…

Mixture models are a fundamental tool in applied statistics and machine learning for treating data taken from multiple subpopulations. The current practice for estimating the parameters of such models relies on local search heuristics…

Over the last three decades, ensemble forecasts have become an integral part of forecasting the weather. They provide users with more complete information than single forecasts as they permit to estimate the probability of weather events by…

Ensemble learning is a mainstay in modern data science practice. Conventional ensemble algorithms assign to base models a set of deterministic, constant model weights that (1) do not fully account for individual models' varying accuracy…

The Mixture-of-Experts (MoE) model has emerged as a prominent architecture in the field of Large Language Models (LLMs), providing a better balance between model performance and computational efficiency. However the General Matrix Multiply…

Weather forecasts sit upstream of high-stakes decisions in domains such as grid operations, aviation, agriculture, and emergency response. Yet forecast users often face a difficult trade-off. Many decision-relevant targets are functionals…

An ensemble post-processing method is developed to improve the probabilistic forecasts of extreme precipitation events across the conterminous United States (CONUS). The method combines a 3-D Vision Transformer (ViT) for bias correction…

Data clustering has received a lot of attention and numerous methods, algorithms and software packages are available. Among these techniques, parametric finite-mixture models play a central role due to their interesting mathematical…

The performance of ensemble-based data assimilation techniques that estimate the state of a dynamical system from partial observations depends crucially on the prescribed uncertainty of the model dynamics and of the observations. These are…

Classical Mixtures of Experts (MoE) are Machine Learning models that involve partitioning the input space, with a separate "expert" model trained on each partition. Recently, MoE-based model architectures have become popular as a means to…

Normal mean-variance mixture distributions are widely applied to simplify a model's implementation and improve their computational efficiency under the Maximum Likelihood (ML) approach. Especially for distributions with normal mean-variance…