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Highdimensional additive hazard models and the Lasso
 Electronic Journal of Statistics
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Multiple Tests based on a Gaussian Approximation of the Unitary Events method with delayed coincidence count
, 2013
"... The Unitary Events (UE) method is one of the most popular and efficient methods used this last decade to detect patterns of coincident joint spike activity among simultaneously recorded neurons. The detection of coincidences is usually based on binned coincidence count (GrÃ¼n, 1996), which is known ..."
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The Unitary Events (UE) method is one of the most popular and efficient methods used this last decade to detect patterns of coincident joint spike activity among simultaneously recorded neurons. The detection of coincidences is usually based on binned coincidence count (GrÃ¼n, 1996), which is known to be subject to information loss (GrÃ¼n et al., 1999). This defect has been corrected by the multiple shift coincidence count (GrÃ¼n et al., 1999). The statistical properties of this count have not been further investigated until the present work, the formula being more difficult to deal with than the original binned count. First of all, we propose a new notion of coincidence count, the delayed coincidence count which is equal to the multiple shift coincidence count when discretized point processes are involved as models for the spike trains. Moreover, it generalizes this notion to non discretized point processes, allowing us to propose a new Gaussian approximation of the count. Since unknown parameters are involved in the approximation, we perform a plugin step, where unknown parameters are replaced by estimated ones,
BOOTSTRAP AND PERMUTATION TESTS OF INDEPENDENCE FOR POINT PROCESSES
, 2015
"... Motivated by a neuroscience question about synchrony detection in spike train analysis, we deal with the independence testing problem for point processes. We introduce nonparametric test statistics, which are rescaled general Ustatistics, whose corresponding critical values are constructed from boo ..."
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Motivated by a neuroscience question about synchrony detection in spike train analysis, we deal with the independence testing problem for point processes. We introduce nonparametric test statistics, which are rescaled general Ustatistics, whose corresponding critical values are constructed from bootstrap and randomization/permutation approaches, making as few assumptions as possible on the underlying distribution of the point processes. We derive general consistency results for the bootstrap and for the permutation w.r.t. Wasserstein’s metric, which induces weak convergence as well as convergence of secondorder moments. The obtained bootstrap or permutation independence tests are thus proved to be asymptotically of the prescribed size, and to be consistent against any reasonable alternative. A simulation study is performed to illustrate the derived theoretical results, and to compare the performance of our new tests with existing ones in the neuroscientific literature.
Nonparametric Markovian Learning of Triggering Kernels for Mutually Exciting and Mutually Inhibiting Multivariate Hawkes Processes
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HAWKES PROCESSES WITH VARIABLE LENGTH MEMORY AND AN INFINITE NUMBER OF COMPONENTS
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Posterior concentration rates for empirical Bayes procedures, with applications to Dirichlet Process mixtures Supplementary material
, 2014
"... 1 Gibbs algorithm We detail the algorithm used to sample from the posterior distribution (λ,A, γ)N in the Poisson process context, in the most complete case (with a hierarchical level on γ). In case where γ is set to a fixed value, then the corresponding part in the algorithm is removed. As a stand ..."
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1 Gibbs algorithm We detail the algorithm used to sample from the posterior distribution (λ,A, γ)N in the Poisson process context, in the most complete case (with a hierarchical level on γ). In case where γ is set to a fixed value, then the corresponding part in the algorithm is removed. As a standard Gibbs algorithm, the simulation is decomposed into three steps: [1] λA, γ,N [2] Aλ, γ,N [3] γA, λ,N. where N is the observed Poisson process over [0, T], namely a number of jumps N(T) and jump instants (T1,..., TN(T)). In order to avoid an artificial truncation in λ, we use the slice sampler strategy proposed by Fall and Barat (2012). More precisely, we consider the stick breaking representation of λ. Let ci be the affectation variable of data Wi. The DPM model is written as: Wici, θ ∗ ∼ hθ?ci, P (ci = k) = wk, ∀k ∈ N ∗ (wk)k∈N? ∼ Stick(A), (θ k)k∈N? ∼i.i.d Gγ. The slice sampler strategy consists in introducing a latent variable ui such that the joint distribution of (Wi, ui) is p(Wi, uiω, θ k=1 wkhθ∗k(Wi) 1 ξk 1l[0,ξk](ui) with ξk = min(wk, ζ), which can be reformulated as: p(Wi, uiω, θ 1
Hawkes Processes with Stochastic Excitations
"... Abstract We propose an extension to Hawkes processes by treating the levels of selfexcitation as a stochastic differential equation. Our new point process allows better approximation in application domains where events and intensities accelerate each other with correlated levels of contagion. We g ..."
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Abstract We propose an extension to Hawkes processes by treating the levels of selfexcitation as a stochastic differential equation. Our new point process allows better approximation in application domains where events and intensities accelerate each other with correlated levels of contagion. We generalize a recent algorithm for simulating draws from Hawkes processes whose levels of excitation are stochastic processes, and propose a hybrid Markov chain Monte Carlo approach for model fitting. Our sampling procedure scales linearly with the number of required events and does not require stationarity of the point process. A modular inference procedure consisting of a combination between Gibbs and Metropolis Hastings steps is put forward. We recover expectation maximization as a special case. Our general approach is illustrated for contagion following geometric Brownian motion and exponential Langevin dynamics.
THEME Optimization, Learning and Statistical Methods Table of contents
"... 3.1. Regression models of supervised learning 2 3.1.1. PACBayes inequalities 2 3.1.2. Sparsity and ℓ1–regularization 2 3.1.3. Pushing it to the extreme: no assumption on the data 2 3.2. Online aggregation of predictors for the prediction of time series, with or without stationarity assumptions 2 3 ..."
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3.1. Regression models of supervised learning 2 3.1.1. PACBayes inequalities 2 3.1.2. Sparsity and ℓ1–regularization 2 3.1.3. Pushing it to the extreme: no assumption on the data 2 3.2. Online aggregation of predictors for the prediction of time series, with or without stationarity assumptions 2 3.3. Multiarmed bandit problems, prediction with limited feedback 3 3.3.1. Bandit problems 3 3.3.2. A generalization of the regret: the approachability of sets 3
CONCENTRATION INEQUALITIES, COUNTING PROCESSES AND ADAPTIVE STATISTICS ∗
"... Abstract. Adaptive statistics for counting processes need particular concentration inequalities to define and calibrate the methods as well as to precise the theoretical performance of the statistical inference. The present article is a small (non exhaustive) review of existing concentration inequal ..."
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Abstract. Adaptive statistics for counting processes need particular concentration inequalities to define and calibrate the methods as well as to precise the theoretical performance of the statistical inference. The present article is a small (non exhaustive) review of existing concentration inequalities that are useful in this context. Résumé. Les statistiques adaptatives pour les processus de comptage nécessitent des inégalités de concentration particulières pour définir et calibrer les méthodes ainsi que pour comprendre les performances de l’inférence statistique. Cet article est une revue non exhaustive des inégalités de concentration qui sont utiles dans ce contexte.
Inference of functional connectivity in Neurosciences
, 2013
"... Abstract—We use Hawkes processes as models for spike trains analysis. A new Lasso method designed for general multivariate counting processes [1] enables us to estimate the functional connectivity graph between the different recorded neurons. I. ..."
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Abstract—We use Hawkes processes as models for spike trains analysis. A new Lasso method designed for general multivariate counting processes [1] enables us to estimate the functional connectivity graph between the different recorded neurons. I.