Bernard Delyon
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View article: Stochastic mirror descent for nonparametric adaptive importance sampling
Stochastic mirror descent for nonparametric adaptive importance sampling Open
This paper addresses the problem of approximating an unknown probability distribution with density $f$ -- which can only be evaluated up to an unknown scaling factor -- with the help of a sequential algorithm that produces at each iteratio…
View article: Boundedness of the Optimal State Estimator Rejecting Unknown Inputs
Boundedness of the Optimal State Estimator Rejecting Unknown Inputs Open
International audience
View article: On the Optimality of the Kitanidis Filter
On the Optimality of the Kitanidis Filter Open
As a natural extension of the Kalman filter to systems subject to arbitrary unknown inputs, the Kitanidis filter has been designed by one-step minimization of the trace of the state estimation error covariance matrix. This optimality does …
View article: Mixing properties and central limit theorem for associated point processes
Mixing properties and central limit theorem for associated point processes Open
Positively (resp. negatively) associated point processes are a class of point processes that induce attraction (resp. inhibition) between the points. As an important example, determinantal point processes (DPPs) are negatively associated. …
View article: Adaptive importance sampling by kernel smoothing
Adaptive importance sampling by kernel smoothing Open
A key determinant of the success of Monte Carlo simulation is the sampling policy, the sequence of distribution used to generate the particles, and allowing the sampling policy to evolve adaptively during the algorithm provides considerabl…
View article: Safe and adaptive importance sampling: a mixture approach
Safe and adaptive importance sampling: a mixture approach Open
This paper investigates adaptive importance sampling algorithms for which the policy, the sequence of distributions used to generate the particles, is a mixture distribution between a flexible kernel density estimate (based on the previous…
View article: On the Asymptotic Normality of Adaptive Multilevel Splitting
On the Asymptotic Normality of Adaptive Multilevel Splitting Open
Adaptive Multilevel Splitting (AMS for short) is a generic Monte Carlo method for Markov processes that simulates rare events and estimates associated probabilities. Despite its practical efficiency, there are almost no theoretical results…
View article: Integral estimation based on Markovian design
Integral estimation based on Markovian design Open
Suppose that a mobile sensor describes a Markovian trajectory in the ambient space and at each time the sensor measures an attribute of interest, e.g. the temperature. Using only the location history of the sensor and the associated measur…
View article: Efficiency of adaptive importance sampling
Efficiency of adaptive importance sampling Open
Adaptive importance sampling (AIS) uses past samples to update the \textit{sampling policy} $q_t$ at each stage $t$. Each stage $t$ is formed with two steps : (i) to explore the space with $n_t$ points according to $q_t$ and (ii) to exploi…
View article: Asymptotic optimality of adaptive importance sampling
Asymptotic optimality of adaptive importance sampling Open
Adaptive importance sampling (AIS) uses past samples to update the \textit{sampling policy} $q_t$ at each stage $t$. Each stage $t$ is formed with two steps : (i) to explore the space with $n_t$ points according to $q_t$ and (ii) to exploi…
View article: A Central Limit Theorem for Fleming-Viot Particle Systems with Hard\n Killing
A Central Limit Theorem for Fleming-Viot Particle Systems with Hard\n Killing Open
Fleming-Viot type particle systems represent a classical way to approximate\nthe distribution of a Markov process with killing, given that it is still alive\nat a final deterministic time. In this context, each particle evolves\nindependen…
View article: A Central Limit Theorem for Fleming-Viot Particle Systems with Hard Killing
A Central Limit Theorem for Fleming-Viot Particle Systems with Hard Killing Open
Fleming-Viot type particle systems represent a classical way to approximate the distribution of a Markov process with killing, given that it is still alive at a final deterministic time. In this context, each particle evolves independently…
View article: Convergence rate of the powers of an operator. Applications to stochastic systems
Convergence rate of the powers of an operator. Applications to stochastic systems Open
We extend the traditional operator theoretic approach for the study of dynamical systems in order to handle the problem of non-geometric convergence. We show that the probabilistic treatment developed and popularized under Richard Tweedie’…
View article: Mixing properties and central limit theorem for associated point\n processes
Mixing properties and central limit theorem for associated point\n processes Open
Positively (resp. negatively) associated point processes are a class of point\nprocesses that induce attraction (resp. inhibition) between the points. As an\nimportant example, determinantal point processes (DPPs) are negatively\nassociate…
View article: A Central Limit Theorem for Fleming-Viot Particle Systems with Soft Killing
A Central Limit Theorem for Fleming-Viot Particle Systems with Soft Killing Open
The distribution of a Markov process with killing, conditioned to be still alive at a given time, can be approximated by a Fleming-Viot type particle system. In such a system, each particle is simulated independently according to the law o…
View article: Robust selection of parametric motion models in image sequences
Robust selection of parametric motion models in image sequences Open
International audience
View article: Integral approximation by kernel smoothing
Integral approximation by kernel smoothing Open
Let $(X_1,\\ldots,X_n)$ be an i.i.d. sequence of random variables in\n$\\mathbb{R}^d$, $d\\geq 1$. We show that, for any function $\\varphi\n:\\mathbb{R}^d\\rightarrow\\mathbb{R}$, under regularity conditions, \\[n^\n{1/2}\\Biggl(n^{-1}\\s…