Approximation Complexity of Additive Random Fields Mikhail Lifshits and Marguerite Zani Let X(t, ω), (t, ω) ∈ [0, 1]d × Ω be an additive random field. We investigate the complexity of finite rank approximation X(t, ω) ≈
n X
ξk (ω)ϕk (t).
k=1
The results obtained in asymptotic setting d → ∞, as suggested H.Wo´zniakowski, provide quantitative version of dimension curse phenomenon: we show that the number of terms in the series needed to obtain a given relative approximation error depends exponentially on d and find the explosion coefficients.
Curse of Dimensionality in Approximation of Random Fields. Mikhail Lifshits and Ekaterina Tulyakova. Consider a random field of tensor product type X(t),t â [0 ...
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We call the equivalence classes under this measure of relative randomness K-degrees. We give proofs that there is a random real so that lim supn K( n) â K(.
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We investigate small deviation properties of Gaussian random fields in the space Lq(RN ,µ) where µ is an arbitrary finite compactly supported Borel measure. Of special interest are hereby âthinâ measures µ, i.e., those which are singular with
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Georgia Institute of Technology, 75 Fifth Street NW, Atlanta, GA 30308. AbstractâThis paper ... result, variable word length data samples are produced by the ... Successive Sine Matching Pursuit (SSMP) is proposed to recover. spectrally ...
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Statistical Parametric Mapping (SPM) for these two situations be developed separately. In ... Mapping (SPM) approach based on Random Field Theory (RFT).
1Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton,. NJ 08544â1000 ... the spin variables, to be specified each time.
synthetic data set to discuss the conditions under which higher order features ..... In our experiment, we used the Automatic Content Extraction (ACE) data [9], ...
on a segmentation approach to be (1) robust to noise, (2) able to handle large variances ... cation [24]. Recent years have seen the emergence of Conditional Random Fields .... The Dice index measures the degree of spatial overlap between ...
5. References. 6. 1. Finite fields. Suppose that F is a finite field and consider the canonical homomorphism. Z â F. Since F is a field its kernel is a prime ideal of Z ...
not always generates non-additivity (see reviews by Gartner &. Cardon 2004; Hättenschwiler et al. 2005). Specifically, non- additive dynamics arising from ...
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