Assumed Distribution

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Srinivas Shakkottai - One of the best experts on this subject based on the ideXlab platform.

  • Mean Field Games in Nudge Systems for Societal Networks
    arXiv: Computer Science and Game Theory, 2015
    Co-Authors: Jian Li, Xinbo Geng, Hao Ming, Srinivas Shakkottai, Vijay G. Subramanian
    Abstract:

    We consider the general problem of resource sharing in societal networks, consisting of interconnected communication, transportation, energy and other networks important to the functioning of society. Participants in such network need to take decisions daily, both on the quantity of resources to use as well as the periods of usage. With this in mind, we discuss the problem of incentivizing users to behave in such a way that society as a whole benefits. In order to perceive societal level impact, such incentives may take the form of rewarding users with lottery tickets based on good behavior, and periodically conducting a lottery to translate these tickets into real rewards. We will pose the user decision problem as a mean field game (MFG), and the incentives question as one of trying to select a good mean field equilibrium (MFE). In such a framework, each agent (a participant in the societal network) takes a decision based on an Assumed Distribution of actions of his/her competitors, and the incentives provided by the social planner. The system is said to be at MFE if the agent's action is a sample drawn from the Assumed Distribution. We will show the existence of such an MFE under different settings, and also illustrate how to choose an attractive equilibrium using as an example demand-response in energy networks.

  • A mean field game approach to scheduling in cellular systems
    IEEE INFOCOM 2014 - IEEE Conference on Computer Communications, 2014
    Co-Authors: Mayank Manjrekar, Vinod Ramaswamy, Srinivas Shakkottai
    Abstract:

    We study auction-theoretic scheduling in cellular networks using the idea of mean field equilibrium (MFE). Here, agents model their opponents through a Distribution over their action spaces and play the best response. The system is at an MFE if this action is itself a sample drawn from the Assumed Distribution. In our setting, the agents are smart phone apps that generate service requests, experience waiting costs, and bid for service from base stations. We show that if we conduct a second-price auction at each base station, there exists an MFE that would schedule the app with the longest queue at each time. The result suggests that auctions can attain the same desirable results as queue-length-based scheduling. We present results on the asymptotic convergence of a system with a finite number of agents to the mean field case, and conclude with simulation results illustrating the simplicity of computation of the MFE.

T.l. Landers - One of the best experts on this subject based on the ideXlab platform.

  • iscretizing Approach for Stress/Strength Analvsis
    1996
    Co-Authors: T.l. Landers
    Abstract:

    Summary & Conclusions - This paper implements & evaluates a discretizing approach for estimating the reliability of systems for which complex functions define strength or stress and where the derivation of reliability exceed analytic techniques. The discretizing approach predicts system reliability with reasonably high accuracy. Specifically, there is little difference in the accuracy of predictions for three engineering problems when compared to simulation results. The reliability predictions are near the 95% confidence intervals of the simulation results and are best in the high reliability and low reliability regions. The small errors observed are attributed to the estimation errors of the discretizing approach. The mid-range reliability values (eg, 50% reliability) are not generally of interest in engineering applications, and even for these value, the errors are small. There is little improvement in increasing the number of points in the pmf from 3 to 6. Due to this small difference, 3 discretizing points are recommended for reliability predictions when computational ease is of concern and limited to 4 points when more accurate reliability predictions are required. This paper models three systems and evaluates the robustness (departures from Assumed Distributions) of the discretizing approach. The discretizing approach is not too sensitive to departures from the Assumed Distribution of the underlying random variables. Specifically, estimated reliability predictions using the discretizing approach are close to both the Gaussian & nearGaussian cases, but as more severe departures are encountered, only the high reliability regions are accurately estimated. Therefore, if we are concerned with high-reliability regions, this approach is effective, and as less reliable systems are analyzed, more attention should be dedicated to changing the design &an on the details of slight parameter adjustments.

  • A discretizing approach for stress/strength analysis
    IEEE Transactions on Reliability, 1996
    Co-Authors: J.r. English, T. Sargent, T.l. Landers
    Abstract:

    This paper implements and evaluates a discretizing approach for estimating the reliability of systems for which complex functions define strength or stress and where the derivation of reliability exceed analytic techniques. The discretizing approach predicts system reliability with reasonably high accuracy. Specifically, there is little difference in the accuracy of predictions for three engineering problems when compared to simulation results. The reliability predictions are near the 95% confidence intervals of the simulation results and are best in the high reliability and low reliability regions. The small errors observed are attributed to the estimation errors of the discretizing approach. The mid-range reliability values (e.g. 50% reliability) are not generally of interest in engineering applications, and even for these value, the errors are small. There is little improvement in increasing the number of points in the pmf from 3 to 6. Due to this small difference, 3 discretizing points are recommended for reliability predictions when computational ease is of concern and limited to 4 points when more accurate reliability predictions are required. This paper models three systems and evaluates the robustness (departures from Assumed Distributions) of the discretizing approach. The discretizing approach is not too sensitive to departures from the Assumed Distribution of the underlying random variables regions are accurately estimated.

J N Wang - One of the best experts on this subject based on the ideXlab platform.

  • an approach for determining an appropriate Assumed Distribution of fatigue life under limited data
    Reliability Engineering & System Safety, 2000
    Co-Authors: Y X Zhao, J N Wang
    Abstract:

    Abstract The case of limited data implies that some unknown uncertainties may be involved in fatigue reliability analysis. For the sake of statistical convenience, for consistency with the relevant physical arguments and, most importantly, to ensure the safety in design evaluation, an approach is developed to determine an appropriate Distribution, from four possible Assumed Distributions—three-parameter Weibull, two-parameter Weibull, lognormal and extreme maximum-value Distributions. The approach makes allowance for consistency with the fatigue physics and checking tail fit effects. An application to nine groups of fatigue life data of 16Mn steel (Chinese steel) welded plate specimens shows that the lognormal Distribution and the extreme maximum-value Distribution may be the appropriate Distributions of the fatigue life under limited data.

Richard Heusdens - One of the best experts on this subject based on the ideXlab platform.

  • On linear versus non-linear magnitude-DFT estimators and the influence of super-Gaussian speech priors
    2010 IEEE International Conference on Acoustics Speech and Signal Processing, 2010
    Co-Authors: Richard C. Hendriks, Richard Heusdens
    Abstract:

    Although the linear mean-squared error (MSE) complex-DFT estimator, i.e., the Wiener filter, is well-known, its magnitude-DFT (MDFT) counterpart has never been considered in the context of speech enhancement. Therefore, certain theoretical questions regarding MDFT estimators remained unanswered. For example, it is unknown to which extend the performance of existing MSE MDFT estimators depends on the chosen speech prior, or on the non-linearity of the estimators. In this paper we present linear MSE MDFT estimators for speech enhancement. In contrast to the linear complex-DFT estimator, the presented linear MSE MDFT estimators do depend on the Assumed Distribution of the speech DFT coefficients. Based on objective and subjective experiments, it can be concluded that the chosen speech prior, i.e., Gaussian versus super-Gaussian has a significant effect on the performance of MDFT estimators, while the linearity as compared to non-linearity has only a minor influence.

  • On robustness of multi-channel minimum mean-squared error estimators under super-Gaussian priors
    2009 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics, 2009
    Co-Authors: Richard C. Hendriks, Richard Heusdens, Jesper Jensen
    Abstract:

    The use of microphone arrays in speech enhancement applications offer additional features, like directivity, over the classical single-channel speech enhancement algorithms. An often used strategy for multi-microphone noise reduction is to apply the multi-channel Wiener filter, which is often claimed to be mean-squared error optimal. However, this is only true if the estimator is constrained to be linear, or, if the speech and noise process are Assumed to be Gaussian. Based on histograms of speech DFT coefficients it can be argued that optimal multi-channel minimum mean-squared error (MMSE) estimators should be derived under super-Gaussian speech priors instead. In this paper we investigate the robustness of these estimators when the steering vector is affected by estimation errors. Further, we discuss the sensitivity of the estimators when the true underlying Distribution of speech DFT coefficients deviates from the Assumed Distribution.

Prabir Barooah - One of the best experts on this subject based on the ideXlab platform.

  • Maximum-likelihood localization of a camera network from heterogeneous relative measurements
    2013 American Control Conference, 2013
    Co-Authors: Joseph Knuth, Prabir Barooah
    Abstract:

    This paper proposes an algorithm for estimating the absolute pose (position and orientation) of n cameras using relative measurements between pairs of cameras. Our work is inspired by the recent work [1] where the same problem was considered and a distributed algorithm was proposed. In contrast to [1], which fused relative measurements of orientation and bearing between camera pairs, and produced a least squares estimate, we make two novel contributions. First, our algorithm is capable of fusing any type of relative measurement between cameras: relative orientation, relative position, relative bearing, or relative distance, or any combination thereof. Second, the algorithm determines a maximum likelihood estimate of the camera poses when the measurement noises Distributions are Gaussian-like in their corresponding Riemannian manifolds. A gradient descent method on the product manifold (SO(3) × R3)n is used to compute the estimates. Unlike past probabilistic techniques, our Assumed Distribution for measurement noise on orientation and bearings are defined on the natural manifolds rather then any parameterization. Though the proposed algorithm is centralized in its computation, we discuss how the computations can be distributed among the cameras. Performance of the proposed algorithm is examined through simulations. Comparison with the algorithm in [1] with non-uniform sensor accuracy reveals which algorithm is most appropriate for a given scenario.