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Learning Triggering Kernels for Multidimensional Hawkes Processes
"... How does the activity of one person affect that of another person? Does the strength of influence remain periodic or decay exponentially over time? In this paper, we study these critical questions in social networkanalysisquantitativelyundertheframework of multidimensional Hawkes processes. In part ..."
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How does the activity of one person affect that of another person? Does the strength of influence remain periodic or decay exponentially over time? In this paper, we study these critical questions in social networkanalysisquantitativelyundertheframework of multidimensional Hawkes processes. In particular, we focus on the nonparametric learning of the triggering kernels, and propose an algorithm MMEL that combines the idea of decoupling the parameters through constructing a tight upperbound of the objective function and application of EulerLagrange equations for optimization in infinite dimensional functional space. We show that the proposed method performs significantly better than alternatives in experiments on both synthetic and real world datasets. 1.
An “Estimate and Score Algorithm” for simultaneous parameter estimation and reconstruction of missing data on social networks, 2012. Available from
"... reconstruction of missing data on social networks ..."
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Nonparametric Markovian Learning of Triggering Kernels for Mutually Exciting and Mutually Inhibiting Multivariate Hawkes Processes
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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.
Linear processes in highdimension: phase space and critical properties
"... Abstract In this work we investigate the generic properties of a stochastic linear model in the regime of highdimensionality. We consider in particular the Vector AutoRegressive model (VAR) and the multivariate Hawkes process. We analyze both deterministic and random versions of these models, show ..."
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Abstract In this work we investigate the generic properties of a stochastic linear model in the regime of highdimensionality. We consider in particular the Vector AutoRegressive model (VAR) and the multivariate Hawkes process. We analyze both deterministic and random versions of these models, showing the existence of a stable and an unstable phase. We find that along the transition region separating the two regimes, the correlations of the process decay slowly, and we characterize the conditions under which these slow correlations are expected to become powerlaws. We check our findings with numerical simulations showing remarkable agreement with our predictions. We finally argue that real systems with a strong degree of selfinteraction are naturally characterized by this type of slow relaxation of the correlations.
RESEARCH Open Access An “Estimate & Score Algorithm ” for
"... simultaneous parameter estimation and reconstruction of incomplete data on social networks ..."
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simultaneous parameter estimation and reconstruction of incomplete data on social networks
unknown title
, 2011
"... EPJ manuscript No. (will be inserted by the editor) Nonparametric kernel estimation for symmetric Hawkes processes. Application to high frequency financial data. ..."
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EPJ manuscript No. (will be inserted by the editor) Nonparametric kernel estimation for symmetric Hawkes processes. Application to high frequency financial data.