Multidimensional adaptive P-splines with application to neurons' activity studies

María Xosé Rodríguez-Álvarez*, María Durbán, Paul H.C. Eilers, Dae Jin Lee, Francisco Gonzalez

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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The receptive field (RF) of a visual neuron is the region of the space that elicits neuronal responses. It can be mapped using different techniques that allow inferring its spatial and temporal properties. Raw RF maps (RFmaps) are usually noisy, making it difficult to obtain and study important features of the RF. A possible solution is to smooth them using P-splines. Yet, raw RFmaps are characterized by sharp transitions in both space and time. Their analysis thus asks for spatiotemporal adaptive P-spline models, where smoothness can be locally adapted to the data. However, the literature lacks proposals for adaptive P-splines in more than two dimensions. Furthermore, the extra flexibility afforded by adaptive P-spline models is obtained at the cost of a high computational burden, especially in a multidimensional setting. To fill these gaps, this work presents a novel anisotropic locally adaptive P-spline model in two (e.g., space) and three (space and time) dimensions. Estimation is based on the recently proposed SOP (Separation of Overlapping Precision matrices) method, which provides the speed we look for. Besides the spatiotemporal analysis of the neuronal activity data that motivated this work, the practical performance of the proposal is evaluated through simulations, and comparisons with alternative methods are reported.

Original languageEnglish
Publication statusE-pub ahead of print - 5 Sep 2022

Bibliographical note

Funding Information:
This research was funded by projects MTM2017‐82379‐R (AEI/FEDER, UE) and PID2019‐104901RB‐I00 (AEI), by the Ramon y Cajal Grant RYC2019‐027534‐I, by the Basque Government (BERC 2018‐2021 program), by the Spanish Ministry of Science, Innovation, and Universities (BCAM Severo Ochoa accreditation SEV‐2017‐0718), by ISCIII (RETICS RD16/0008/0003), Xunta de Galicia (Accreditation ED431G 2019/02), and the European Regional Development Fund. We are grateful to Vanda Inácio for helpful comments and discussions. We are also grateful to the peer referees and associate editor for their constructive comments of the paper.

Funding Information:
Funding for open access charge was provided by Universidade de Vigo/CISUG.

Funding information:
Instituto de Salud Carlos III, Spain,
Grant/Award Number: RETICS
RD16/0008/0003; Xunta de Galicia,
Grant/Award Numbers: Accreditation
2019-2022, ED431G 2019/02; Spanish
Ministry of Science, Innovation, and
Universities, Grant/Award Number:
BCAM Severo Ochoa accreditation
SEV-2017-0718; Eusko Jaurlaritza,
Grant/Award Number: BERC 2018-2021
program; Agencia Estatal de Investigacion
(AEI), Spain, Grant/Award Numbers:
PID2019-104901RB-I00; Ministerio
de Ciencia e Innovación, Grant/Award
Number: Ramon y Cajal Grant

Publisher Copyright:
© 2022 The Authors. Biometrics published by Wiley Periodicals LLC on behalf of International Biometric Society.


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