80 research outputs found
A model of Poissonian interactions and detection of dependence
This paper proposes a model of interactions between two point processes,
ruled by a reproduction function h, which is considered as the intensity of a
Poisson process. In particular, we focus on the context of neurosciences to
detect possible interactions in the cerebral activity associated with two
neurons. To provide a mathematical answer to this specific problem of
neurobiologists, we address so the question of testing the nullity of the
intensity h. We construct a multiple testing procedure obtained by the
aggregation of single tests based on a wavelet thresholding method. This test
has good theoretical properties: it is possible to guarantee the level but also
the power under some assumptions and its uniform separation rate over weak
Besov bodies is adaptive minimax. Then, some simulations are provided, showing
the good practical behavior of our testing procedure.Comment: 27 page
Surrogate data methods based on a shuffling of the trials for synchrony detection: the centering issue
International audienceWe investigate several distribution-free dependence detection procedures, all based on a shuffling of the trials, from a statistical point of view. The mathematical justification of such procedures lies in the bootstrap principle and its approximation properties. In particular, we show that such a shuffling has mainly to be done on centered quantities-that is, quantities with zero mean under independence-to construct correct p-values, meaning that the corresponding tests control their false positive (FP) rate. Thanks to this study, we introduce a method, named permutation UE, which consists of a multiple testing procedure based on permutation of experimental trials and delayed coincidence count. Each involved single test of this procedure achieves the prescribed level, so that the corresponding multiple testing procedure controls the false discovery rate (FDR), and this with as few assumptions as possible on the underneath distribution, except independence and identical distribution across trials. The mathematical meaning of this assumption is discussed, and it is in particular argued that it does not mean what is commonly referred in neuroscience to as cross-trials stationarity. Some simulations show, moreover, that permutation UE outperforms the trial-shuffling of Pipa and Grün ( 2003 ) and the MTGAUE method of Tuleau-Malot et al. ( 2014 ) in terms of single levels and FDR, for a comparable amount of false negatives. Application to real data is also provided
Model selection for density estimation with L2-loss
We consider here estimation of an unknown probability density s belonging to
L2(mu) where mu is a probability measure. We have at hand n i.i.d. observations
with density s and use the squared L2-norm as our loss function. The purpose of
this paper is to provide an abstract but completely general method for
estimating s by model selection, allowing to handle arbitrary families of
finite-dimensional (possibly non-linear) models and any density s belonging to
L2(mu). We shall, in particular, consider the cases of unbounded densities and
bounded densities with unknown bound and investigate how the L-infinity-norm of
s may influence the risk. We shall also provide applications to adaptive
estimation and aggregation of preliminary estimators. Although of a purely
theoretical nature, our method leads to results that cannot presently be
reached by more concrete methods.Comment: 37 pages. Minor change
Detection of dependence patterns with delay
The Unitary Events (UE) method is a popular and efficient method used this
last decade to detect dependence patterns of joint spike activity among
simultaneously recorded neurons. The first introduced method is based on binned
coincidence count \citep{Grun1996} and can be applied on two or more
simultaneously recorded neurons. Among the improvements of the methods, a
transposition to the continuous framework has recently been proposed in
\citep{muino2014frequent} and fully investigated in \citep{MTGAUE} for two
neurons. The goal of the present paper is to extend this study to more than two
neurons. The main result is the determination of the limit distribution of the
coincidence count. This leads to the construction of an independence test
between neurons. Finally we propose a multiple test procedure via a
Benjamini and Hochberg approach \citep{Benjamini1995}. All the theoretical
results are illustrated by a simulation study, and compared to the UE method
proposed in \citep{Grun2002}. Furthermore our method is applied on real data
Online Detection Of Supply Chain Network Disruptions Using Sequential Change-Point Detection for Hawkes Processes
In this paper, we attempt to detect an inflection or change-point resulting
from the Covid-19 pandemic on supply chain data received from a large furniture
company. To accomplish this, we utilize a modified CUSUM (Cumulative Sum)
procedure on the company's spatial-temporal order data as well as a GLR
(Generalized Likelihood Ratio) based method. We model the order data using the
Hawkes Process Network, a multi-dimensional self and mutually exciting point
process, by discretizing the spatial data and treating each order as an event
that has a corresponding node and time. We apply the methodologies on the
company's most ordered item on a national scale and perform a deep dive into a
single state. Because the item was ordered infrequently in the state compared
to the nation, this approach allows us to show efficacy upon different degrees
of data sparsity. Furthermore, it showcases use potential across differing
levels of spatial detail.Comment: Accepted to AAAI 2023 Workshop on Graphs and more Complex structures
for Learning and Reasonin
Using the multivariate Hawkes process to study interactions between multiple species from camera trap data
DATA AVAILABILITY STATEMENT :
Data and code (Nicvert et al., 2023) are available on Figshare at https://doi.org/10.6084/m9.figshare.24552157.v5.Interspecific interactions can influence species' activity and movement patterns. In particular, species may avoid or attract each other through reactive responses in space and/or time. However, data and methods to study such reactive interactions have remained scarce and were generally limited to two interacting species. At this time, the deployment of camera traps opens new opportunities but adapted statistical techniques are still required to analyze interaction patterns with such data. We present the multivariate Hawkes process (MHP) and show how it can be used to analyze interactions between several species using camera trap data. Hawkes processes use flexible pairwise interaction functions, allowing us to consider asymmetries and variations over time when depicting reactive temporal interactions. After describing the theoretical foundations of the MHP, we outline how its framework can be used to study interspecific interactions with camera trap data. We design a simulation study to evaluate the performance of the MHP and of another existing method to infer interactions from camera trap-like data. We also use the MHP to infer reactive interactions from real camera trap data for five species from South African savannas (impala Aepyceros melampus, greater kudu Tragelaphus strepsiceros, lion Panthera leo, blue wildebeest Connochaetes taurinus and Burchell's zebra Equus quagga burchelli). The simulation study shows that the MHP can be used as a tool to benchmark other methods of interspecific interaction inference and that this model can reliably infer interactions when enough data are considered. The analysis of real data highlights evidence of predator avoidance by prey and herbivore–herbivore attraction. Lastly, we present the advantages and limits of the MHP and discuss how it can be improved to infer attraction/avoidance patterns more reliably. As camera traps are increasingly used, the multivariate Hawkes process provides a promising framework to decipher the complexity of interactions structuring ecological communities.The French National Research Agency ANR (project EcoNet).https://onlinelibrary.wiley.com/r/ecyhj2024Mammal Research InstituteZoology and EntomologySDG-15:Life on lan
Lasso and probabilistic inequalities for multivariate point processes
Due to its low computational cost, Lasso is an attractive regularization
method for high-dimensional statistical settings. In this paper, we consider
multivariate counting processes depending on an unknown function parameter to
be estimated by linear combinations of a fixed dictionary. To select
coefficients, we propose an adaptive -penalization methodology, where
data-driven weights of the penalty are derived from new Bernstein type
inequalities for martingales. Oracle inequalities are established under
assumptions on the Gram matrix of the dictionary. Nonasymptotic probabilistic
results for multivariate Hawkes processes are proven, which allows us to check
these assumptions by considering general dictionaries based on histograms,
Fourier or wavelet bases. Motivated by problems of neuronal activity inference,
we finally carry out a simulation study for multivariate Hawkes processes and
compare our methodology with the adaptive Lasso procedure proposed by Zou in
(J. Amer. Statist. Assoc. 101 (2006) 1418-1429). We observe an excellent
behavior of our procedure. We rely on theoretical aspects for the essential
question of tuning our methodology. Unlike adaptive Lasso of (J. Amer. Statist.
Assoc. 101 (2006) 1418-1429), our tuning procedure is proven to be robust with
respect to all the parameters of the problem, revealing its potential for
concrete purposes, in particular in neuroscience.Comment: Published at http://dx.doi.org/10.3150/13-BEJ562 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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