Spurious correlation as an approximation of the mutual information between redundant outputs and an unknown input

Stochastic resonance (SR) is a counterintuitive phenomenon, observed in a wide variety of nonlinear systems, for which the addition of noise of opportune magnitude can improve signal detection. Tuning the noise for maximizing the SR effect is important both for artificial and biological systems. In the case of artificial systems, full exploitation of the SR effect opens the possibility of measuring otherwise unmeasurable signals. In biology, identification of possible SR maximization mechanisms is of great interest for explaining the low-energy high-sensitivity perception capabilities often observed in animals. SR maximization approaches presented in literature use knowledge on the input signal (or stimulus, in the case of living beings), and maximize the mutual information between the input and the output signal. The input signal, however, is unknown in many practical settings. To cope with this problem, this paper introduces an approximation of the input–output mutual information based on the spurious correlation among a set of redundant units. A proof of the approximation, as well as numerical examples of its application are given.     

A new algorithm for variance based importance analysis of models with correlated inputs

Importance analysis is aimed at finding the contributions of the inputs to the output uncertainty. For structural models involving correlated input variables, the variance contribution by an individual input variable is decomposed into correlated contribution and uncorrelated contribution in this study. Based on point estimate, this work proposes a new algorithm to conduct variance based importance analysis for correlated input variables. Transformation of the input variables from correlation space to independence space and the computation of conditional distribution in the process ensure that the correlation information is inherited correctly. Different point estimate methods can be employed in the proposed algorithm, thus the algorithm is adaptable and evolvable. Meanwhile, the proposed algorithm is also applicable to uncertainty systems with multiple modes. The proposed algorithm avoids the sampling procedure, which usually consumes a heavy computational cost. Results of several examples in this work have proven the proposed algorithm can be used as an effective tool to deal with uncertainty analysis involving correlated inputs.     

Sampling Schemes for Bayesian Variable Selection in Generalized Linear Models

Bayesian approaches to prediction and the assessment of predictive uncertainty in generalized linear models are often based on averaging predictions over different models, and this requires methods for accounting for model uncertainty. When there are linear dependencies among potential predictor variables in a generalized linear model, existing Markov chain Monte Carlo algorithms for sampling from the posterior distribution on the model and parameter space in Bayesian variable selection problems may not work well. This article describes a sampling algorithm based on the Swendsen-Wang algorithm for the Ising model, and which works well when the predictors are far from orthogonality. In problems of variable selection for generalized linear models we can index different models by a binary parameter vector, where each binary variable indicates whether or not a given predictor variable is included in the model. The posterior distribution on the model is a distribution on this collection of binary strings, and by thinking of this posterior distribution as a binary spatial field we apply a sampling scheme inspired by the Swendsen-Wang algorithm for the Ising model in order to sample from the model posterior distribution. The algorithm we describe extends a similar algorithm for variable selection problems in linear models. The benefits of the algorithm are demonstrated for both real and simulated data.     

Jitter and Measurement Errors in Approximation and Integration of Lipschitz Functions

The goal of this paper is to point out the differences between jitter (the perturbations in sampling points reading) and the measurement errors. In some cases jitter may have significantly smaller influence on the radius of information than the measurement error. The class of Lipschitz functions is considered and two problems, integration and approximation, are studied.     

Application of particle swarm optimization in chaos synchronization in noisy environment in presence of unknown parameter uncertainty

In this paper, particle swarm optimization (PSO) is applied to synchronize chaotic systems in presence of parameter uncertainties and measurement noise. Particle swarm optimization is an evolutionary algorithm which is introduced by Kennedy and Eberhart. This algorithm is inspired by birds flocking. Optimization algorithms can be applied to control by defining an appropriate cost function that guarantees stability of system. In presence of environment noise and parameter uncertainty, robustness plays a crucial role in succeed of controller. Since PSO needs only rudimentary information about the system, it can be a suitable algorithm for this case. Simulation results confirm that the proposed controller can handle the uncertainty and environment noise without any extra information about them. A comparison with some earlier works is performed during simulations.     

Nonlinear Dynamical Systems and Adaptive Filters in Biomedicine

In this paper we present the application of a method of adaptive estimation using an algebra–geometric approach, to the study of dynamic processes in the brain. It is assumed that the brain dynamic processes can be described by nonlinear or bilinear lattice models. Our research focuses on the development of an estimation algorithm for a signal process in the lattice models with background additive white noise, and with different assumptions regarding the characteristics of the signal process. We analyze the estimation algorithm and implement it as a stochastic differential equation under the assumption that the Lie algebra, associated with the signal process, can be reduced to a finite dimensional nilpotent algebra. A generalization is given for the case of lattice models, which belong to a class of causal lattices with certain restrictions on input and output signals. The application of adaptive filters for state estimation of the CA3 region of the hippocampus (a common location of the epileptic focus) is discussed. Our areas of application involve two problems: (1) an adaptive estimation of state variables of the hippocampal network, and (2) space identification of the coupled ordinary equation lattice model for the CA3 region.     

Un exemple d'application des grandes déviations à l'approximation stochastique

We present an application of the large deviations theory to stochastic approximation, for the one-stage Robbins-Monro algorithm, as well as for the averaging method (Polyak-Ruppert). The study deals with a continuous time linear regression model where the noise is a continuous local martingale.     

Limiting optimal adaptive filtering with unknown disturbance covariance

The accuracy of estimating the variance of the Kalman-Bucy filter depends essentially on disturbance covariance matrices and measurement noise. The main difficulty in filter design is the lack of necessary statistical information about the useful signal and the disturbance. Filters whose parameters are tuned during active estimation are classified with adaptive filters. The problem of adaptive filtering under parametric uncertainty conditions is studied. A method for designing limiting optimal Kalman-Bucy filters in the case of unknown disturbance covariance is presented. An adaptive algorithm for estimating disturbance covariance matrices based on stochastic approximation is described. Convergence conditions for this algorithm are investigated. The operation of a limiting adaptive filter is exemplified.     

Localized sampling in the presence of noise

When the sampled values are corrupted by noise, error estimates for the localized sampling series for approximating a band-limited function are obtained. The result provides error bounds for practical cases including error caused by average sampling, jitter error and amplitude error.     

Cost efficiency measures in data envelopment analysis with data uncertainty

This paper extends the classical cost efficiency (CE) models to include data uncertainty. We believe that many research situations are best described by the intermediate case, where some uncertain input and output data are available. In such cases, the classical cost efficiency models cannot be used, because input and output data appear in the form of ranges. When the data are imprecise in the form of ranges, the cost efficiency measure calculated from the data should be uncertain as well. So, in the current paper, we develop a method for the estimation of upper and lower bounds for the cost efficiency measure in situations of uncertain input and output data. Also, we develop the theory of efficiency measurement so as to accommodate incomplete price information by deriving upper and lower bounds for the cost efficiency measure. The practical application of these bounds is illustrated by a numerical example.     

加权再生核空间中信号的平均采样与重构

主要讨论L_v~p的加权再生核子空间中信号的平均采样与重构.首先,针对两种平均采样泛函建立了采样稳定性;其次,基于概率测度给出一个一般的迭代算法,将迭代逼近投影算法和迭代标架算法统一起来;最后,针对被白噪声污染的平均样本给出了信号重构的渐进点态误差估计.     

Blind Channel Identification Based on Noisy Observation by Stochastic Approximation Method

A stochastic approximation algorithm for estimating multichannel coefficients is proposed, and the estimate is proved to converge to the true parameters a.s. up-to a constant scaling factor. The estimate is updated after receiving each new observation, so the output data need not be collected in advance. The input signal is allowed to be dependent and the observation is allowed to be corrupted by noise, but no noise statistics are used in the estimation algorithm.     

Bayesian subset selection for threshold autoregressive moving-average models

Optimal subset selection among a general family of threshold autoregressive moving-average (TARMA) models is considered. The usual complexity of model/order selection is increased by capturing the uncertainty of unknown threshold levels and an unknown delay lag. The Monte Carlo method of Bayesian model averaging provides a possible way to overcome such model uncertainty. Incorporating with the idea of Bayesian model averaging, a modified stochastic search variable selection method is adapted to consider subset selection in TARMA models, by adding latent indicator variables for all potential model lags as part of the proposed Markov chain Monte Carlo sampling scheme. Metropolis–Hastings methods are employed to deal with the well-known difficulty of including moving-average terms in the model and a novel proposal mechanism is designed for this purpose. Bayesian comparison of two hyper-parameter settings is carried out via a simulation study. The results demonstrate that the modified method has favourable performance under reasonable sample size and appropriate settings of the necessary hyper-parameters. Finally, the application to four real datasets illustrates that the proposed method can provide promising and parsimonious models from more than 16 million possible subsets.     

Estimation of second-order properties from jittered time series

This paper considers spectral and autocovariance estimation for a zero-mean, band-limited, stationary process that has been sampled at time points jittered from a regular, equi-interval, sampling scheme. The case of interest is where the sampling scheme is near regular so that the jitter standard deviation is small compared to the sampling interval. Such situations occur with many time series collected in the physical sciences including, in particular, oceanographic profiles.Spectral estimation procedures are developed for the case of independent jitter and autocovariance estimation procedures for both independent and dependent jitter. These are typically modifications of general estimation procedures proposed elsewhere, but tailored to the particular jittered sampling scheme considered. The theoretical properties of these estimators are developed and their relative efficiencies compared.The properties of the jittered sampling point process are also developed. These lead to a better understanding, in this situation, of more general techniques available for processes sampled by stationary point processes.     

“Chaos” in superregenerative receivers

The superregenerative principle has been known since the early 1920s. The circuit is extremely simple and extremely sensitive. Today, superheterodyne receivers generally supplant superregenerative receivers in most applications because there are several undesirable characteristics: poor selectivity, reradiation, etc. Superregenerative receivers undergo a revival in recent papers for wireless systems, where low cost and very low power consumption are relevant: house/building meters (such as water, energy, gas counter), personal computer environment (keyboard, mouse), etc. Another drawback is the noise level which is higher than that of a well-designed superheterodyne receiver; without an antenna input signal, the output of the receiver hears in an earphone as a waterfall noise; this sound principally is the inherent input noise amplified and detected by the circuit; however, when the input noise is negligible with respect of an antenna input signal, we are faced to an other source of “noise” self-generated by the superregenerative working. The main objective of this paper concerns this self-generated noise coming from an exponential growing followed by a re-injection process for which the final state is a function of the phase of the input signal.     

RCMARS: Robustification of CMARS with different scenarios under polyhedral uncertainty set

Our recently developed CMARS is powerful in handling complex and heterogeneous data. We include into CMARS the existence of uncertainty about the scenarios. Indeed, data include noise in both output and input variables. Therefore, solutions of the optimization problem may reveal a remarkable sensitivity to perturbations in the parameters of the problem. The data uncertainty results in uncertain constraints and objective function. To overcome this difficulty, we refine our CMARS algorithm by a robust optimization technique proposed to cope with data uncertainty. In our previous study, we present the new robust CMARS (RCMARS) in theory and method and illustrate it with a numerical example. In this study, we present RCMARS results with different uncertainty scenarios for our numerical example.     

On stability of sampling-reconstruction models

A useful sampling-reconstruction model should be stable with respect to different kind of small perturbations, regardless whether they result from jitter, measurement errors, or simply from a small change in the model assumptions. In this paper we prove this result for a large class of sampling models. We define different classes of perturbations and present a way of quantifying the robustness of a model with respect to them. We also use the theory of localized frames to study the dual frame method for recovering the original signal from its samples.     

What is the role of stochastic resonance?

The role of stochastic resonance (SR) in the detection of signals is discussed. It is shown that when a signal is not detectable using traditional methods, such as spectral analysis or averaging, it cannot be detected using SR. In other words by adding noise a far-from detectable signal cannot become detectable.     

Compressive Sampling via Random Convolution

Several recent results in compressive sampling show that a sparse signal (i.e. a signal which can be compressed in a known orthobasis) can be efficiently acquired by taking linear measurements against random test functions. In this paper, we show that these results can be extended to measurements taken by convolving with a random pulse and then subsampling. The measurement scheme is universal in that it complements (with high probability) any fixed orthobasis we use to represent the signal. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于噪声先验知识的LMS自适应噪声对消法的水声微弱信号提取

讲述了LMS自适应噪声对消法的数学原理,设计了一种基于噪声参考信号的噪声对消原理结构图,并对初步提取的信号做Fourier变换,设计合理的系数阈值经行滤波,Fourier逆变换的信号与理想信号做性能对比.仿真实验表明:基于噪声参考信号的噪声对消算法呈现出滤波阶数少,收敛速度快,精度良好,提取信号效果良好等优点.汾河二库湖试测试实验结果也验证了该算法具有良好的高效性和实用性.