A new order parameter approximation to Random Boolean Networks RBN is introduced based on the concept of Boolean derivative A statistical argu ment involving an annealed approximation is used allowing to measure the order parameter in terms of the statistical properties of a random matrix Using the same formalism a Lyapunov exponent is calculated allowing to provide the onset of damage spreadin...

We introduce a one parameter family of hybrid operators and study quantitative convergence theorems for these operators e.g. local and weighted approximation results and simultaneous approximation of derivatives. Further, we discuss the statistical convergence of these operators. Lastly, we show the rate of convergence of these operators to a certain function by illustrative graphics in Matlab....

The Bethe approximation, discovered in statistical physics, gives an efficient algorithm called belief propagation (BP) for approximating a partition function. BP empirically gives an accurate approximation for many problems, e.g., low-density parity-check codes, compressed sensing, etc. Recently, Vontobel gives a novel characterization of the Bethe approximation using graph cover. In this pape...

Based on a statistical mechanics approach, we develop a method for approximately computing average case learning curves for Gaussian process regression models. The approximation works well in the large sample size limit and for arbitrary dimensionality of the input space. We explain how the approximation can be systematically improved and argue that similar techniques can be applied to general ...

The paper is concerned with stochastic approximation procedures having three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function. We study convergence and rate of convergence. Main results are supplemented with corollaries to establish various sets of sufficient conditions, with the main em...

Nonlinear approximation has recently found computational applications such as data compression, statistical estimation or adaptive schemes for partial diierential or integral equations, especially through the development of wavelet-based methods. The goal of this paper is to provide with a short survey of nonlinear wavelet approximation in the perspective of these applications , as well as to s...

We consider the space of analytic functions in the closed domain, where convergence is a uniform convergence in closed domain that contains the original domain strictly inside itself and prove the theorems on the approximation and statistical approximation of functions in this space by the sequences of linear operators.

In the present paper, we introduce a sequence of linear operators, which is a higher order generalization of positive linear operators defined by a class of Borel measures studied in [2]. Then, using the concept of A−statistical convergence we obtain some approximation results which are stronger than the aspects of the classical approximation theory.

I present a theory of mean field approximation based on information geometry. This theory includes in a consistent way the naive mean field approximation, as well as the TAP approach and the linear response theorem in statistical physics, giving clear information-theoretic interpretations to them.

Normal approximation confidence intervals are used in most commercial statistical package because they are easy to compute. However, the performance of such procedures could be poor when the sample size is not large or when there is heavy censoring. A transformation can be applied to avoid having confidence interval endpoints fall outside the parameter space and otherwise improves performance, ...