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Estimation of functions of d variables is considered using ridge combinations of the form Σmk=1 c1, kφ(Σdj=1c0, j, kxj-bk) where the activation function φ is a function with bounded value and derivative. These include single-hidden layer neural networks, polynomials, and sinusoidal models. From a sample of size n of possibly noisy values at random sites X ∊ B = [−1, 1]d, the minimax mean square error...
For the additive white Gaussian noise channel with average codeword power constraint, sparse superposition codes are developed. These codes are based on the statistical high-dimensional regression framework. In a previous paper, we investigated decoding using the optimal maximum-likelihood decoding scheme. Here, a fast decoding algorithm, called the adaptive successive decoder, is developed. For any...
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