Conformal prediction bands for multivariate functional data

Diquigiovanni, Jacopo; Fontana, Matteo; Vantini, Simone

doi:10.1016/j.jmva.2021.104879

Cited by 11 publications

(2 citation statements)

References 25 publications

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“…Moreover, probabilistic univariate time series forecasting has been addressed in a similar context by Shang and Hyndman (2011). Conformal prediction for multivariate functional data has been proposed by Diquigiovanni et al (2022) and by Kelly and Chen (2022) for multiple functional regression.…”

Section: Functional Regressionmentioning

confidence: 99%

A review of predictive uncertainty estimation with machine learning

Tyralis,

Papacharalampous

2024

Artif Intell Rev

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Predictions and forecasts of machine learning models should take the form of probability distributions, aiming to increase the quantity of information communicated to end users. Although applications of probabilistic prediction and forecasting with machine learning models in academia and industry are becoming more frequent, related concepts and methods have not been formalized and structured under a holistic view of the entire field. Here, we review the topic of predictive uncertainty estimation with machine learning algorithms, as well as the related metrics (consistent scoring functions and proper scoring rules) for assessing probabilistic predictions. The review covers a time period spanning from the introduction of early statistical (linear regression and time series models, based on Bayesian statistics or quantile regression) to recent machine learning algorithms (including generalized additive models for location, scale and shape, random forests, boosting and deep learning algorithms) that are more flexible by nature. The review of the progress in the field, expedites our understanding on how to develop new algorithms tailored to users’ needs, since the latest advancements are based on some fundamental concepts applied to more complex algorithms. We conclude by classifying the material and discussing challenges that are becoming a hot topic of research.

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Section: Functional Regressionmentioning

confidence: 99%

A review of predictive uncertainty estimation with machine learning

Tyralis,

Papacharalampous

2024

Artif Intell Rev

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“…The method has also been extended to functional regression, where the predictors and responses are functions, rather than vectors, see for instance [Lei et al, 2015], [Fontana et al, 2020] and [Diquigiovanni et al, 2022]. In this case, the prediction regions take the form of functional envelopes that have a high probability of containing the true function.…”

Section: Introductionmentioning

confidence: 99%

Universally consistent estimation of the reach

Cholaquidis

Fraiman

Moreno

2023

Journal of Statistical Planning and Inference

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Multivariate Scalar on Multidimensional Distribution Regression With Application to Modeling the Association Between Physical Activity and Cognitive Functions

Ghosal,

Matabuena

2024

Biometrical J

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We develop a new method for multivariate scalar on multidimensional distribution regression. Traditional approaches typically analyze isolated univariate scalar outcomes or consider unidimensional distributional representations as predictors. However, these approaches are suboptimal because (i) they fail to utilize the dependence between the distributional predictors and (ii) neglect the correlation structure of the response. To overcome these limitations, we propose a multivariate distributional analysis framework that harnesses the power of multivariate density functions and multitask learning. We develop a computationally efficient semiparametric estimation method for modeling the effect of the latent joint density on the multivariate response of interest. Additionally, we introduce a new conformal prediction algorithm for quantifying the uncertainty of our multivariate predictions based on subject characteristics and individualized distributional predictors, providing valuable insights into the conditional distribution of the response. We validate the effectiveness of our proposed method through comprehensive numerical simulations, clearly demonstrating its superior performance compared to traditional methods. The application of the proposed method is demonstrated on triaxial accelerometer data from the National Health and Nutrition Examination Survey 2011–2014 for modeling the association between cognitive scores across various domains and distributional representation of physical activity among the older adult population. Our results highlight the advantages of the proposed approach, emphasizing the significance of incorporating multidimensional distributional information in the triaxial accelerometer data.

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Conformal prediction bands for multivariate functional data

Cited by 11 publications

References 25 publications

A review of predictive uncertainty estimation with machine learning

A review of predictive uncertainty estimation with machine learning

Universally consistent estimation of the reach

Multivariate Scalar on Multidimensional Distribution Regression With Application to Modeling the Association Between Physical Activity and Cognitive Functions

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