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Additive Error

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Dror Baron – One of the best experts on this subject based on the ideXlab platform.

  • Performance Limits With Additive Error Metrics in Noisy Multimeasurement Vector Problems
    IEEE Transactions on Signal Processing, 2018
    Co-Authors: Junan Zhu, Dror Baron

    Abstract:

    Real-world applications such as magnetic resonance imaging with multiple coils, multiuser communication, and diffuse optical tomography often assume a linear model, where several sparse signals sharing common sparse supports are acquired by several measurement matrices and then contaminated by noise. Multimeasurement vector (MMV) problems consider the estimation or reconstruction of such signals. In different applications, the estimation Error that we want to minimize could be the mean squared Error or other metrics, such as the mean absolute Error and the support set Error. Seeing that minimizing different Error metrics is useful in MMV problems, we study information-theoretic performance limits for MMV signal estimation with arbitrary Additive Error metrics. We also propose a message passing algorithmic framework that achieves the optimal performance, and rigorously prove the optimality of our algorithm for a special case. We further conjecture the optimality of our algorithm for some general cases and back it up through numerical examples. As an application of our MMV algorithm, we propose a novel setup for active user detection in multiuser communication and demonstrate the promise of our proposed setup.

  • signal estimation with Additive Error metrics in compressed sensing
    IEEE Transactions on Information Theory, 2014
    Co-Authors: Jin Tan, Danielle Carmon, Dror Baron

    Abstract:

    Compressed sensing typically deals with the estimation of a system input from its noise-corrupted linear measurements, where the number of measurements is smaller than the number of input components. The performance of the estimation process is usually quantified by some standard Error metric such as squared Error or support set Error. In this correspondence, we consider a noisy compressed sensing problem with any Additive Error metric. Under the assumption that the relaxed belief propagation method matches Tanaka’s fixed point equation, we propose a general algorithm that estimates the original signal by minimizing the Additive Error metric defined by the user. The algorithm is a pointwise estimation process, and thus simple and fast. We verify that our algorithm is asymptotically optimal, and we describe a general method to compute the fundamental information-theoretic performance limit for any Additive Error metric. We provide several example metrics, and give the theoretical performance limits for these cases. Experimental results show that our algorithm outperforms methods such as relaxed belief propagation (relaxed BP) and compressive sampling matching pursuit (CoSaMP), and reaches the suggested theoretical limits for our example metrics.

  • Signal Estimation with Additive Error Metrics in Compressed Sensing
    IEEE Transactions on Information Theory, 2014
    Co-Authors: Jin Tan, Danielle Carmon, Dror Baron

    Abstract:

    Compressed sensing typically deals with the estimation of a system input from its noise-corrupted linear measurements, where the number of measurements is smaller than the number of input components. The performance of the estimation process is usually quantified by some standard Error metric such as squared Error or support set Error. In this correspondence, we consider a noisy compressed sensing problem with any arbitrary Error metric. We propose a simple, fast, and highly general algorithm that estimates the original signal by minimizing the Error metric defined by the user. We verify that our algorithm is optimal owing to the decoupling principle, and we describe a general method to compute the fundamental information-theoretic performance limit for any Error metric. We provide two example metrics — minimum mean absolute Error and minimum mean support Error — and give the theoretical performance limits for these two cases. Experimental results show that our algorithm outperforms methods such as relaxed belief propagation (relaxed BP) and compressive sampling matching pursuit (CoSaMP), and reaches the suggested theoretical limits for our two example metrics.

Jiapeng Zhang – One of the best experts on this subject based on the ideXlab platform.

  • improved noisy population recovery and reverse bonami beckner inequality for sparse functions
    Symposium on the Theory of Computing, 2015
    Co-Authors: Shachar Lovett, Jiapeng Zhang

    Abstract:

    The noisy population recovery problem is a basic statistical inference problem. Given an unknown distribution in {0,1}n with support of size k, and given access only to noisy samples from it, where each bit is flipped independently with probability (1-μ)/2, estimate the original probability up to an Additive Error of e. We give an algorithm which solves this problem in time polynomial in (klog log k, n, 1/e). This improves on the previous algorithm of Wigderson and Yehudayoff [FOCS 2012] which solves the problem in time polynomial in (klog k, n, 1/e). Our main technical contribution, which facilitates the algorithm, is a new reverse Bonami-Beckner inequality for the L1 norm of sparse functions.

  • STOC – Improved Noisy Population Recovery, and Reverse Bonami-Beckner Inequality for Sparse Functions
    Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing – STOC '15, 2015
    Co-Authors: Shachar Lovett, Jiapeng Zhang

    Abstract:

    The noisy population recovery problem is a basic statistical inference problem. Given an unknown distribution in {0,1}n with support of size k, and given access only to noisy samples from it, where each bit is flipped independently with probability (1-μ)/2, estimate the original probability up to an Additive Error of e. We give an algorithm which solves this problem in time polynomial in (klog log k, n, 1/e). This improves on the previous algorithm of Wigderson and Yehudayoff [FOCS 2012] which solves the problem in time polynomial in (klog k, n, 1/e). Our main technical contribution, which facilitates the algorithm, is a new reverse Bonami-Beckner inequality for the L1 norm of sparse functions.

Tapati Basak – One of the best experts on this subject based on the ideXlab platform.

  • an application of non linear cobb douglas production function to selected manufacturing industries in bangladesh
    Open Journal of Statistics, 2012
    Co-Authors: Md Moyazzem Hossain, Ajit Kumar Majumder, Tapati Basak

    Abstract:

    Recently, businessmen as well as industrialists are very much concerned about the theory of firm in order to make correct decisions regarding what items, how much and how to produce them. All these decisions are directly related with the cost considerations and market situations where the firm is to be operated. In this regard, this paper should be helpful in suggesting the most suitable functional form of production process for the major manufacturing industries in Bangladesh. This paper considers Cobb-Douglas (C-D) production function with Additive Error and multiplicative Error term. The main purpose of this paper is to select the appropriate Cobb-Douglas production model for measuring the production process of some selected manufacturing industries in Bangladesh. We use different model selection criteria to compare the Cobb-Douglas production function with Additive Error term to Cobb-Douglas production function with multiplicative Error term. Finally, we estimate the parameters of the production function by using optimization subroutine.

  • An Application of Non–Linear Cobb-Douglas Production Function to Selected Manufacturing Industries in Bangladesh
    Open Journal of Statistics, 2012
    Co-Authors: Moyazzem Hossain, Ajit Kumar Majumder, Tapati Basak

    Abstract:

    Recently, businessmen as well as industrialists are very much concerned about the theory of firm in order to make correct decisions regarding what items, how much and how to produce them. All these decisions are directly related with the cost considerations and market situations where the firm is to be operated. In this regard, this paper should be helpful in suggesting the most suitable functional form of production process for the major manufacturing industries in Bangladesh. This paper considers Cobb-Douglas (C-D) production function with Additive Error and multiplicative Error term. The main purpose of this paper is to select the appropriate Cobb-Douglas production model for measuring the production process of some selected manufacturing industries in Bangladesh. We use different model selection criteria to compare the Cobb-Douglas production function with Additive Error term to Cobb-Douglas production function with multiplicative Error term. Finally, we estimate the parameters of the production function by using optimization subroutine.