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- W2184865678 abstract "This work was partially supported by the German Research Founda tion (DFG) within the Research Training Group GRK 1194 Self-organizing Sensor-Actuator-Networks. . densities are a popular representation of non-Gaussian densi ties. They are a universal function approximator in that, given a sufficient number of components, they can approximate any smooth function to arbitrary accuracy [6]. They also tend to be a useful representation in practice for multivariate densities. However, there is no known closed-form solution to dif ferential entropy for Gaussian mixtures. There exist several approximations in the literature, including loose upper and lower bounds, but the only existent approximation that can be demonstrated to converge to the true entropy relies on expensive random sampling methods. Other approximations offer either very loose bounds or can be shown to deviate from the true entropy in an arbitrary fashion and hence, are of limited usefulness. In this paper, we present a novel approximation to differen tial entropy for Gaussian mixture random vectors based on Taylor-series expansions. For each Gaussian mixture com ponent, a Taylor-series expansion of the logarithm of the Gaussian mixture is determined as described in Section IV, which facilitates an analytical evaluation of the entropy measure. Additionally, a splitting technique for Gaussian densities is employed in Section IV-B in order to avoid Gaus sian components with high variance, which would require computationally expensive higher order expansion terms. Through the use of higher-order terms or component splitting it is possible to obtain an entropy approximation, which is of practical usefulness and versatile applicability as it • permits a tradeoff between computational demand and accuracy" @default.
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- W2184865678 date "2008-01-01" @default.
- W2184865678 modified "2023-09-27" @default.
- W2184865678 title "On Entropy Approxilllation for Gaussian Mixture Randolll Vectors" @default.
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