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AuthorTempone, Raul (32)Alouini, Mohamed-Slim (11)Nobile, Fabio (8)Bagci, Hakan (7)Vilanova, Pedro (7)View MoreDepartment

Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division (69)

Applied Mathematics and Computational Science Program (44)Electrical Engineering Program (19)Physical Sciences and Engineering (PSE) Division (7)Mechanical Engineering Program (3)View MoreSubjectWireless (11)Bayesian (9)Sampling (9)CEM (7)SDE (6)View MoreTypePoster (54)Presentation (14)Meetings and Proceedings (1)Year (Issue Date)2016 (69)Item AvailabilityOpen Access (69)

Now showing items 61-69 of 69

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Hierarchical matrix approximation of large covariance matrices

Litvinenko, Alexander; Genton, Marc G.; Sun, Ying (2016-01-06) [Poster]

Surrogate based approaches to parameter inference in ocean models

Knio, Omar (2016-01-06) [Presentation]

This talk discusses the inference of physical parameters using model surrogates. Attention is focused on the use of sampling schemes to build suitable representations of the dependence of the model response on uncertain input data. Non-intrusive spectral projections and regularized regressions are used for this purpose. A Bayesian inference formalism is then applied to update the uncertain inputs based on available measurements or observations. To perform the update, we consider two alternative approaches, based on the application of Markov Chain Monte Carlo methods or of adjoint-based optimization techniques. We outline the implementation of these techniques to infer dependence of wind drag, bottom drag, and internal mixing coefficients.

Polynomial Chaos Surrogates for Bayesian Inference

Le Maitre, Olivier (2016-01-06) [Presentation]

The Bayesian inference is a popular probabilistic method to solve inverse problems, such as the identification of field parameter in a PDE model. The inference rely on the Bayes rule to update the prior density of the sought field, from observations, and derive its posterior distribution. In most cases the posterior distribution has no explicit form and has to be sampled, for instance using a Markov-Chain Monte Carlo method. In practice the prior field parameter is decomposed and truncated (e.g. by means of Karhunen- Lo´eve decomposition) to recast the inference problem into the inference of a finite number of coordinates. Although proved effective in many situations, the Bayesian inference as sketched above faces several difficulties requiring improvements. First, sampling the posterior can be a extremely costly task as it requires multiple resolutions of the PDE model for different values of the field parameter. Second, when the observations are not very much informative, the inferred parameter field can highly depends on its prior which can be somehow arbitrary. These issues have motivated the introduction of reduced modeling or surrogates for the (approximate) determination of the parametrized PDE solution and hyperparameters in the description of the prior field. Our contribution focuses on recent developments in these two directions: the acceleration of the posterior sampling by means of Polynomial Chaos expansions and the efficient treatment of parametrized covariance functions for the prior field. We also discuss the possibility of making such approach adaptive to further improve its efficiency.

A potpourri of results from the KAUST SRI-UQ

Tempone, Raul (2016-01-08) [Presentation]

As the KAUST Strategic Research Initiative for Uncertainty Quantification completes its fourth year of existence we recall several results produced during its exciting journey of discovery. These include, among others, contributions on Multi-level and Multi-index sampling techniques that address both direct and inverse problems. We may discuss also several techniques for Bayesian Inverse Problems and Optimal Experimental Design.

Secure Communications over Wireless Networks Even 1-bit Feedback Helps Achieving Security

Rezki, Zouheir (2016-01-06) [Presentation]

Recently, there have been a surge toward developing sophisticated security mechanisms based on a cross layer design. While an extensive progress has been realized toward establishing physical layer security as an important design paradigm to enhance security of existing wireless networks, only a little effort has been made toward designing practical coding schemes that achieve or approach the secrecy capacity. Most of existing results are tied to some simplifying assumptions that do not seem always reasonable (passive eavesdropper, perfect channel state information (CSI), etc.). Furthermore, it is still not very clear how to exploit physical layer security paradigms, together with existing cryptosystems, in order to add a supplementary level of protection for information transmission or to achieve key agreement. In this talk, we address the first part of the above problematic, i.e., the effect of channel uncertainty on network security. Particularly, we show that even a coarse estimate of the main channel (channel between the transmitter and the legitimate receiver) can help providing a positive secrecy rate. Specifically, we assume two types of channel uncertainty at the transmitter. The first one is a rate-limited feedback in a block fading channel where the feedback information can be proactive (at the beginning of the coherence block) or of ARQ-type. The second type of uncertainty takes the form of a noisy estimate of the main channel at the transmitter in a fast fading channel. In both cases, we provide upper and lower bounds on the secrecy capacity. We argue how our achievable schemes and upper bounding techniques extend to multi-user setting (broadcasting a single confidential message or multiple confidential messages to multiple legitimate receivers) and to multiple antenna channels.

An efficient forward-reverse expectation-maximization algorithm for statistical inference in stochastic reaction networks

Vilanova, Pedro (2016-01-07) [Presentation]

In this work, we present an extension of the forward-reverse representation introduced in Simulation of forward-reverse stochastic representations for conditional diffusions , a 2014 paper by Bayer and Schoenmakers to the context of stochastic reaction networks (SRNs). We apply this stochastic representation to the computation of efficient approximations of expected values of functionals of SRN bridges, i.e., SRNs conditional on their values in the extremes of given time-intervals. We then employ this SRN bridge-generation technique to the statistical inference problem of approximating reaction propensities based on discretely observed data. To this end, we introduce a two-phase iterative inference method in which, during phase I, we solve a set of deterministic optimization problems where the SRNs are replaced by their reaction-rate ordinary differential equations approximation; then, during phase II, we apply the Monte Carlo version of the Expectation-Maximization algorithm to the phase I output. By selecting a set of over-dispersed seeds as initial points in phase I, the output of parallel runs from our two-phase method is a cluster of approximate maximum likelihood estimates. Our results are supported by numerical examples.

Error Analysis for Fourier Methods for Option Pricing

Häppölä, Juho (2016-01-06) [Presentation]

We provide a bound for the error committed when using a Fourier method to price European options when the underlying follows an exponential Levy dynamic. The price of the option is described by a partial integro-differential equation (PIDE). Applying a Fourier transformation to the PIDE yields an ordinary differential equation that can be solved analytically in terms of the characteristic exponent of the Levy process. Then, a numerical inverse Fourier transform allows us to obtain the option price. We present a novel bound for the error and use this bound to set the parameters for the numerical method. We analyze the properties of the bound for a dissipative and pure-jump example. The bound presented is independent of the asymptotic behaviour of option prices at extreme asset prices. The error bound can be decomposed into a product of terms resulting from the dynamics and the option payoff, respectively. The analysis is supplemented by numerical examples that demonstrate results comparable to and superior to the existing literature.

A study of Monte Carlo methods for weak approximations of stochastic particle systems in the mean-field?

Haji Ali, Abdul Lateef (2016-01-08) [Presentation]

I discuss using single level and multilevel Monte Carlo methods to compute quantities of interests of a stochastic particle system in the mean-field. In this context, the stochastic particles follow a coupled system of Ito stochastic differential equations (SDEs). Moreover, this stochastic particle system converges to a stochastic mean-field limit as the number of particles tends to infinity. I start by recalling the results of applying different versions of Multilevel Monte Carlo (MLMC) for particle systems, both with respect to time steps and the number of particles and using a partitioning estimator. Next, I expand on these results by proposing the use of our recent Multi-index Monte Carlo method to obtain improved convergence rates.

Multilevel ensemble Kalman filtering

Hoel, Haakon; Chernov, Alexey; Law, Kody; Nobile, Fabio; Tempone, Raul (2016-01-08) [Presentation]

The ensemble Kalman filter (EnKF) is a sequential filtering method that uses an ensemble of particle paths to estimate the means and covariances required by the Kalman filter by the use of sample moments, i.e., the Monte Carlo method. EnKF is often both robust and efficient, but its performance may suffer in settings where the computational cost of accurate simulations of particles is high. The multilevel Monte Carlo method (MLMC) is an extension of classical Monte Carlo methods which by sampling stochastic realizations on a hierarchy of resolutions may reduce the computational cost of moment approximations by orders of magnitude. In this work we have combined the ideas of MLMC and EnKF to construct the multilevel ensemble Kalman filter (MLEnKF) for the setting of finite dimensional state and observation spaces. The main ideas of this method is to compute particle paths on a hierarchy of resolutions and to apply multilevel estimators on the ensemble hierarchy of particles to compute Kalman filter means and covariances. Theoretical results and a numerical study of the performance gains of MLEnKF over EnKF will be presented. Some ideas on the extension of MLEnKF to settings with infinite dimensional state spaces will also be presented.

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