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Prediction curves (blue) with associated 95% credible intervals (grey) from GP regression (top), Magma (middle) and MagmaClust (bottom). The dashed lines represent the mean parameters from the mean processes estimates. Observed data points are in black, testing data points are in red. Backward points are the observations from the training data set, coloured relatively to individuals (middle) or clusters (bottom).
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A model involving Gaussian processes (GPs) is introduced to simultaneously handle multi-task learning, clustering, and prediction for multiple functional data. This procedure acts as a model-based clustering method for functional data as well as a learning step for subsequent predictions for new tasks. The
model is instantiated as a mixture of mult...
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Citations
... An increasing number of applications feature functional data collected at a discrete, random set of design points, also known as the random design framework. Examples include sports science Leroy et al. (2023), Warmenhoven (2024), oceanography Acar-Denizli et al. (2018), Yarger et al. (2022), medicine Sørensen et al. (2013), and spatial data Burbano-Moreno and Mayrink (2024). In these applications, a fundamental task in the functional data analysis pipeline is the approximation of integrals of functions of the sample paths (also called trajectories). ...
The computation of integrals is a fundamental task in the analysis of functional data, which are typically considered as random elements in a space of squared integrable functions. Borrowing ideas from recent advances in the Monte Carlo integration literature, we propose effective unbiased estimation and inference procedures for integrals of uni- and multivariate random functions. Several applications to key problems in functional data analysis (FDA) involving random design points are studied and illustrated. In the absence of noise, the proposed estimates converge faster than the sample mean and the usual algorithms for numerical integration. Moreover, the proposed estimator facilitates effective inference by generally providing better coverage with shorter confidence and prediction intervals, in both noisy and noiseless setups.
... For both models, the same GP kernel and initial hyperparameters were specified. Moreover, the number K of clusters was defined as 3, thanks to a model selection procedure based on the maximization of a variational Bayesian information criterion calculated for different values of K. 21 Once the 2 models were trained, the 2 associated predictions were made on the mean GPs obtained from the training step of the MAGMACLUST algorithm. ...
Purpose : To analyze the evolution of the world ranking in swimming over the last 10 years, with particular attention to the effects of COVID-19 on the different levels of participating athletes. Methods : The top 200 world-ranked entries in all swimming events (50-m pool) were collected from 2013 to 2022. A mathematical model (Gaussian model) was proposed to evaluate the ranking progression for different performance levels (clusters) according to distance, stroke, and gender. The model was applied both with and without the COVID season data. Results : Overall results indicated a general progression in world rankings over the last 10 years, except for the COVID season and the post-Olympic year(s), with peak results in the 2021 postpandemic (Olympic) year. The gender gap in World Aquatics points scoring has shown an increasing gap in favor of males since 2017, reaching 1.5% in 2022. The top 200 positions of world rankings were grouped into 3 different clusters defined by the 23.3%, 66.5%, and 100% of ranked male swimmers (or 31.5%, 72.5%, and 100% for females) and with average World Aquatics scores of 910 (12), 858 (10) and 816 (11) points (907 [13], 847 [11], and 802 [12] for females). The Gaussian model showed a gap averaging ∼21 to ∼36 points between performance curves with or without COVID season data, with larger gaps for female rankings and cluster-3 swimmers. Conclusions : These results suggest that, given the lower relative performance of female swimmers in the different clusters of world rankings, female events may provide an opportunity to enter international-level swimming.
... DOMINO dramatically improves on the MAGMA algorithm. A natural next step is to conduct a similar study on MAGMAClust [Leroy et al., 2023], a generalisation of MAGMA which learns cluster-specific means and infers clusters whilst learning the common means. ...
We consider time-series forecasting problems where data is scarce, difficult to gather, or induces a prohibitive computational cost. As a first attempt, we focus on short-term electricity consumption in France, which is of strategic importance for energy suppliers and public stakeholders. The complexity of this problem and the many levels of geospatial granularity motivate the use of an ensemble of Gaussian Processes (GPs). Whilst GPs are remarkable predictors, they are computationally expensive to train, which calls for a frugal few-shot learning approach. By taking into account performance on GPs trained on a dataset and designing a random walk on these, we mitigate the training cost of our entire Bayesian decision-making procedure. We introduce our algorithm called \textsc{Domino} (ranDOM walk on gaussIaN prOcesses) and present numerical experiments to support its merits.
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... Future enhancements for our models include incorporating additional features as covariates, adopting more advanced preprocessing techniques, considering error measurements in a heteroskedastic model and refining the kernel to make it more specific to the task at hand. Another potential next step would be to use MagmaClustR [12], a variant of the MAGMA algorithm that may reduce prediction uncertainty by performing clustering on profiles. These enhancements could establish GPs as highly effective models for spatial atmosphere analysis. ...
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