Generalized Mahalanobis depth in point process and its application in neural coding

Liu, Shuyi; Wu, Wei

doi:10.1214/17-aoas1030

Cited by 13 publications

(27 citation statements)

References 23 publications

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“…As we have emphasized in Introduction, there are two types of randomness in a point process: (1) the number of events in each process, and (2) the conditional distribution of these event times. In (Liu and Wu, 2017), the number of events is modeled by a normalized Poisson mass function and the event times are modeled by a multivariate Gaussian distribution. The depth framework of a point process s is then defined as a weighted product of two terms -the normalized probability of having |s| events and the conditional depth using the Mahalanobis depth.…”

Section: Notation and Depth Definitionmentioning

confidence: 99%

“…As a summary, we list the properties of all proposed Dirichlet depths in Table 1, where "T" denotes "true" and "F" denotes "false". For comparative purpose, we also include the properties of the Mahalanobis depth Liu and Wu (2017).…”

Section: Propertiesmentioning

confidence: 99%

“…This is an under-explored area. The only previous work is given in (Liu and Wu, 2017), where the authors introduced the notion of depth in point process using a generalized Mahalanobis depth. Note that given the number of the events in a point process, the distribution of these events follow a multivariate framework.…”

Section: Introductionmentioning

confidence: 99%

“…A depth function needs to take into account two types of randomness in a temporal point process S:(1) the number of events, or cardinality, in the process, denoted as |S|, and (2) the conditional distribution of these events given |S|. The notion of depth for point process was first studied by Liu and Wu (2017), where the authors defined a new depth framework as a weighted product of two terms:…”

Section: Introductionmentioning

confidence: 99%

“…The goal of this paper is to develop a new depth framework for point processes systematically. Based on Liu and Wu (2017), our proposed framework of depth function for point processes is also defined as a weighted product of two terms aforementioned. In this paper, we focus on introducing new conditional depth functions based on the Dirichlet distribution.…”

Section: Introductionmentioning

confidence: 99%

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Dirichlet depths for point process

Chen

2021

Electron. J. Statist.

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Statistical depths have been well studied for multivariate and functional data over the past few decades, but remain under-explored for point processes. A first attempt on the notion of point process depth was conducted recently where the depth was defined as a weighted product of two terms: (1) the probability of the number of events in each process and (2) the depth of the event times conditioned on the number of events by using a Mahalanobis depth. We point out that multivariate depths such as the Mahalanobis depth cannot be directly used because they often neglect the important ordering property in the point process events. To deal with this problem, we propose a model-based approach for point process systematically. In particular, we develop a Dirichlet-distribution-based framework on the conditional depth term, where the new methods are referred to as Dirichlet depths. We examine mathematical properties of the new depths and conduct asymptotic analysis. In addition, we illustrate the new methods using various simulated and real experiment data. It is found that the proposed framework provides a reasonable center-outward rank and the new methods have accurate decoding in one neural spike train dataset.

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Section: Notation and Depth Definitionmentioning

confidence: 99%

Section: Propertiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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