The role of intrinsic dimension in high-resolution player tracking data—Insights in basketball

Santos–Fernández, Edgar; Denti, Francesco; Mengersen, Kerrie; Mira, Antonietta

doi:10.1214/21-aoas1506

Cited by 5 publications

(4 citation statements)

References 31 publications

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“…In this paper, we illustrated intRinsic, an R package that implements novel routines for the ID estimation according to the models recently developed in Facco et al (2017); Allegra et al (2020); Denti et al (2022), andSantos-Fernandez et al (2022). intRinsic consists of a collection of high-level, user-friendly functions that, in turn, rely on efficient, low-level routines implemented in R and C++.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…For example, when the nominal dimension D is low, the unbounded support of a Gamma prior may provide unrealistic results, where the posterior distribution assigns positive density to the interval (D, +∞). Santos-Fernandez, Denti, Mengersen, and Mira (2022) proposed to employ a more informative prior for d:…”

Section: Hidalgo: the Heterogeneous Intrinsic Dimension Algorithmmentioning

confidence: 99%

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intRinsic: An R Package for Model-Based Estimation of the Intrinsic Dimension of a Dataset

Denti

2023

J. Stat. Soft.

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This article illustrates intRinsic, an R package that implements novel state-of-the-art likelihood-based estimators of the intrinsic dimension of a dataset, an essential quantity for most dimensionality reduction techniques. In order to make these novel estimators easily accessible, the package contains a small number of high-level functions that rely on a broader set of efficient, low-level routines. Generally speaking, intRinsic encompasses models that fall into two categories: homogeneous and heterogeneous intrinsic dimension estimators. The first category contains the two nearest neighbors estimator, a method derived from the distributional properties of the ratios of the distances between each data point and its first two closest neighbors. The functions dedicated to this method carry out inference under both the frequentist and Bayesian frameworks. In the second category, we find the heterogeneous intrinsic dimension algorithm, a Bayesian mixture model for which an efficient Gibbs sampler is implemented. After presenting the theoretical background, we demonstrate the performance of the models on simulated datasets. This way, we can facilitate the exposition by immediately assessing the validity of the results. Then, we employ the package to study the intrinsic dimension of the Alon dataset, obtained from a famous microarray experiment. Finally, we show how the estimation of homogeneous and heterogeneous intrinsic dimensions allows us to gain valuable insights into the topological structure of a dataset.

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Section: Summary and Discussionmentioning

confidence: 99%

Section: Hidalgo: the Heterogeneous Intrinsic Dimension Algorithmmentioning

confidence: 99%

intRinsic: An R Package for Model-Based Estimation of the Intrinsic Dimension of a Dataset

Denti

2023

J. Stat. Soft.

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“…However, it is essential to note that ED does not account for points in a dataset lying on low-dimensional manifolds. Thus, identifying the ID is generally more valuable as it accounts for inherent structures in the data and remains a more accurate representation of underlying structural complexity in a dataset (Santos-Fernandez et al, 2021;Eneva et al, 2002). This research work will seek to bridge this gap and provide valuable information towards understanding the complexity and dimensionality of the Covid-19 pandemic in different countries and develop a deeper understanding of the spread of the pandemic.…”

Section: Introductionmentioning

confidence: 99%

“…Hidalgo extends this framework, allowing the presence of multiple manifolds characterised by different ID values in the same dataset. The Bayesian local ID estimator has been applied successfully to a diverse range of datasets for scenarios such as financial markets, neuroimaging, proteomics (Allegra et al, 2019), genomics (Denti, 2022), and high-resolution player tracking data (Santos-Fernandez et al, 2021). Here, we seek to organise the pandemic dynamics of different countries into groups with similar ID to help us unveil non-trivial patterns related to the dynamics of the Covid-19 pandemic.…”

Section: Introductionmentioning

confidence: 99%

On the intrinsic dimensionality of Covid-19 data: a global perspective

Varghese¹,

Santos–Fernández²,

Denti³

et al. 2022

Preprint

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This paper aims to develop a global perspective of the complexity of the relationship between the standardised per-capita growth rate of Covid-19 cases, deaths, and the OxCGRT Covid-19 Stringency Index, a measure describing a country's stringency of lockdown policies. To achieve our goal, we use a heterogeneous intrinsic dimension estimator implemented as a Bayesian mixture model, called Hidalgo. We identify that the Covid-19 dataset may project onto two low-dimensional manifolds without significant information loss. The low dimensionality suggests strong dependency among the standardised growth rates of cases and deaths per capita and the OxCGRT Covid-19 Stringency Index for a country over 2020-2021. Given the low dimensional structure, it may be feasible to model observable Covid-19 dynamics with few parameters. Importantly, we identify spatial autocorrelation in the intrinsic dimension distribution worldwide. Moreover, we highlight that high-income countries are more likely to lie on low-dimensional manifolds, likely arising from aging populations, comorbidities, and increased per capita mortality burden from Covid-19. Finally, we temporally stratify the dataset to examine the intrinsic dimension at a more granular level throughout the Covid-19 pandemic.

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Relationships between tail entropies and local intrinsic dimensionality and their use for estimation and feature representation

Bailey

Houle

2023

Information Systems

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The role of intrinsic dimension in high-resolution player tracking data—Insights in basketball

Cited by 5 publications

References 31 publications

intRinsic: An R Package for Model-Based Estimation of the Intrinsic Dimension of a Dataset

intRinsic: An R Package for Model-Based Estimation of the Intrinsic Dimension of a Dataset

On the intrinsic dimensionality of Covid-19 data: a global perspective

Relationships between tail entropies and local intrinsic dimensionality and their use for estimation and feature representation

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