In this paper, we derive an asymptotically optimal multi-layer coding scheme for entropy-coded scalar quantizers (SQ) that minimizes the weighted mean-squared error (WMSE). The optimal entropy-coded SQ is non-uniform in the case of WMSE. The conventional multi-layer coder quantizes the base-layer reconstruction error at the enhancement-layer, and is sub-optimal for the WMSE criterion. We consid...

Learning to predict future images from a video sequence involves the construction of an internal representation that models the image evolution accurately, and therefore, to some degree, its content and dynamics. This is why pixel-space video prediction is viewed as a promising avenue for unsupervised feature learning. In this work, we train a convolutional network to generate future frames giv...

Theory for jointly optimizing nonuniform analysis and synthesis FIR filter banks with arbitrary filter lengths and an arbitrary delay through the filter bank is developed. The FIR subband coder is optimized with respect to the minimum mean square error between the output and the input signals under a bit constraint. The subband quantizers are modeled as additive noise sources. Theoretical compa...

The aim of this paper is to find a multitaper-based spectrum estimator that is mean square error optimal for cepstrum coefficient estimation. The multitaper spectrum estimator consists of windowed periodograms which are weighted together, where the weights are optimized using the Taylor expansion of the log-spectrum variance and a novel approximation for the log-spectrum bias. A thorough discus...

Most of the real life classification problems have ill defined, imprecise or fuzzy class boundaries. Feedforward neural networks with conventional backpropagation learning algorithm are not tailored to this kind of classification problem. Hence, in this paper, feedforward neural networks, that use backpropagation learning algorithm with fuzzy objective functions, are investigated. A learning al...

This paper regards randomized discrete-time consensus systems that preserve the average on expectation. As a main result, we provide an upper bound on the mean square deviation of the consensus value from the initial average. Then, we particularize our result to systems where the interactions which take place simultaneously are few, or weakly correlated; these assumptions cover several algorith...

An adaptive scaled mean square error (SMSE) filter using a Hopfield neural-network-based algorithm is presented. We show the development of the original SMSE filter from the minimum mean square error (MMSE) filter and the parametric mean square error (PMSE) filter, both of which suffer from the oversmooth phenomena. The SMSE filter is more efficient than the PMSE filter in terms of noise remova...

We consider the compressed sensing problem, where the object x0 ∈ R is to be recovered from incomplete measurements y = Ax0 + z; here the sensing matrix A is an n × N random matrix with iid Gaussian entries and n < N . A popular method of sparsity-promoting reconstruction is `-penalized least-squares reconstruction (aka LASSO, Basis Pursuit). It is currently popular to consider the strict spars...

We propose a new method for evaluating the mean square error (mse) of a possibly biased estimator 1̂ θ , or, rather, the class of estimators to which it belongs. The method uses confidence intervals c of a corresponding unbiased estimator θ̂ and makes its assessment based on the extent to which c includes 1̂ θ . The method does not require an estimate, implicit or explicit, of the bias of 1̂ θ , is...

1School of Business Administration, Southwestern University of Finance and Economics No. 555, Liutai Ave, Wenjiang Zone, Chengdu 611130, China 2Yangtze Normal University, No. 98, Julong Ave, Fuling Zone, Chongqing, 408100, China 3School of Management and Economics University of Electronic Science and Technology of China No. 2006, Xiyuan Ave, West Hi-Tech Zone, Chengdu 611731, China e-mail: koug...