Entropy-metric estimation of the small data models with stochastic parameters

In this paper, we propose a fast and versatile blind source separation including closed-form estimation of sources' probability density functions (PDFs), where the ICA's activation function is automatically adapted to various noise conditions. In the proposed method, closed-form second-order ICA and closed-form PDF estimation are introduced as a computational-cost-efficient preprocessing to extract sources' PDFs. Compared with various type of conventional ICAs, e.g., fixed activation-function type and ML-based type, our proposed algorithm can give a faster and higher convergence. Experimental assessment reveals that the proposed method is versatile for handling non-speech sound sources.

The non-line-of-sight (NLOS) propagation caused by intermittently blocking of the direct path between the base station and the mobile station is the main difficulty for mobile user location in cellular wireless communication system. So it is indispensable to investigate the techniques about the NLOS error identification and correction. In this paper, we suggest a robust and accurate approach using probability density function (PDF) estimator to identify the NLOS situation, and then an improved biased Kalman filter which depends on PDF estimator as the nonlinearity weighting coefficient in recursive operation is used to mitigate the NLOS error for time of arrival (TOA) measurements. As the PDF estimator is calculated from actual TOA samples, it is adaptive for the complex practical NLOS environments. The simulation results also indicate that with the less prior information about communication environments, the approach we present has a good location performance even in severe NLOS situations.

The error estimate of Borgonovo's moment-independent index δi is considered, and it shows that the possible computational complexity of δi is mainly due to the probability density function (PDF) estimate because the PDF estimate is an ill-posed problem and its convergence rate is quite slow. So it reminds us to compute Borgonovo's index using other methods. To avoid the PDF estimate, δi, which is based on the PDF, is first approximatively represented by the cumulative distribution function (CDF). The CDF estimate is well posed and its convergence rate is always faster than that of the PDF estimate. From the representation, a stable approach is proposed to compute δi with an adaptive procedure. Since the small probability multidimensional integral needs to be computed in this procedure, a computational strategy named asymptotic space integration is introduced to reduce a high-dimensional integral to a one-dimensional integral. Then we can compute the small probability multidimensional integral by adaptive numerical integration in one dimension with an improved convergence rate. From the comparison of numerical error analysis of some examples, it can be shown that the proposed method is an effective approach to uncertainty importance measure computation.

Identification of Heterogeneous Parameters in an Intracellular Reaction Network from Population Snapshot Measurements through Sensitivity Analysis and Neural Network

The main part of the noise in digital images arises when taking pictures or transmission. There is noise in the images captured by the image sensors of the real world. Noise, based on its causes can have different probability density functions. For example, such a model is called the Poisson distribution function of the random nature of photon arrival process that is consistent with the distribution of pixel values measured. The parameters of the noise probability density function (PDF) can be achieved to some extent the properties of the sensor. But, we need to estimate the parameters for imaging settings. If we assume that the PDF of noise is approximately Gaussian, then we need only to estimate the mean and variance because the Gaussian PDF with only two parameters is determined. In fact, in many cases, PDF of noise is not Gaussian and it has unknown distribution. In this study, we introduce a generalized probability density function for modeling noise in images and propose a method to estimate its parameters. Because the generalized probability density function has multiple parameters, so use common parameter estimation techniques such as derivative method to maximize the likelihood function would be extremely difficult. In this study, we propose the use of evolutionary algorithms for global optimization. The results show that this method accurately estimates the probability density function parameters.

Probability density function (PDF) estimation is a fundamentally important problem for statistical pattern recognition. Independent component analysis (ICA) can be applied to the feature vectors so that the PDF estimation of a high dimensional vector can be converted to the PDF estimation of several 1-dimensional variables. However in practice we find that this PDF is in poor generalization ability for pattern classification because of the implied noise. Hence, this paper proposes an improvement of ICA based PDF estimation method. A latent variable model is built to separate the noise from the feature vector so that the pattern information and the noise can be dealt with respectively. Based on the latent variable model, a modified ICA based PDF is deduced. The validity of our proposed method is demonstrated by the experiments of off-line handwritten numeral recognition.

Ogle and his colleagues proposed two measures of oculomotor linkage called the accommodative convergence to accommodation (AC/A) ratio. This ratio provided a clinically useful assessment of the drive of accommodation, or focusing system, on vergence, or binocular fixation system. The phoria method measured the relatively large deviation in eye alignment under the monocular condition, whereas the fixation disparity method measured the relatively small misalignment of the eyes under the binocular condition to obtain the AC/A ratio. Ogle et al. indicated that these two measures should be equal. However, experimental results showed a substantial difference between the AC/A ratios obtained by the two methods. To quantitatively assess the difference between the two methods, a linear static model was first evaluated. This model was based on an earlier successful model of the accommodation and vergence system. The linear-model solution showed that these two methods were equivalent and thus could not account for the differences found. Then, a nonlinear static model, containing the deadspace operators depth of field and Panum's fusional area (PFA), was evaluated. Since two solutions were possible for each deadspace operator, there were four basic solutions. However, there were two binocular-viewing paradigms. This resulted in four prism-viewing and four lens-viewing solutions. Finally, a difference was taken between the prism- and lens-viewing measures, giving a total combination of 16 solutions. Only four of these solutions were equal to that using the phoria method. Some of the other solution lines were widely separated, thus providing a range of possible data values across different solution lines. Calculations showed that the variation in AC/A ratio values for data across difference solution lines was comparable to that found experimentally. Thus, the deadspace operators in the nonlinear model were able to account for the discrepancy between the AC/A ratio determined by the phoria and fixation disparity methods.

Multivariate online kernel density estimation with Gaussian kernels

The existence of many different dynamic large eddy simulation (LES) methods leads to questions about the theoretical foundation of dynamic LES methods. It was shown recently that the use of stochastic analysis enables a theoretically well based systematic derivation of a realizable linear dynamic model (LDM) and a realizable nonlinear dynamic model (NDM). A priori and a posteriori analyses of turbulent channel flow are used here to study the characteristic properties of these dynamic models. The LDM and NDM are compared with other dynamic models: the non-stabilized and stabilized dynamic Smagorinsky model (DSM), which is used in many applications of LES, and Wang-Bergstrom's dynamic model (WBDM), which represents an extension of the DSM. The DSM and WBDM do not represent realizable models because they are not derived as consequences of a realizable stochastic process. The comparisons reported here show that the LDM and NDM are based on a dynamic model formulation that avoids shortcomings of existing concepts. The LDM and NDM account for backscatter, and they are computationally stable without any modification. The LDM and NDM represent the instantaneous small scale structure of turbulence very well. Compared to the DSM and WBDM, respectively, the LDM and NDM are computationally more efficient.

Block-oriented nonlinear systems are represented by a certain composition of linear dynamical and nonlinear static models. Hence, a block-oriented system is defined by the pair (λ ,m(∙)), where λ defines infinite-dimensional parameter representing impulse response sequences of linear dynamical subsystems, whereas m(∙) is a vector of nonparametric multidimensional functions describing nonlinear elements.KeywordsNonparametric EstimateSemiparametric ModelMean Integrate Square ErrorLinear SubsystemParametric PartThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

A hierarchical gain scheduling (HGS) approach is proposed to model the nonlinear dynamics of NOx emissions of a utility boiler. At the lower level of HGS, a nonlinear static model is used to schedule the static parameters of local linear dynamic models (LDMs), such as static gains and static operating conditions. According to upper level scheduling variables, a multi-model method is used to calculate the predictive output based on lower-level LDMs. Both static and dynamic experiments are carried out at a 360 MW pulverized coal-fired boiler. Based on these data, a nonlinear static model using artificial neural network (ANN) and a series of linear dynamic models are obtained. Then, the performance of the HGS model is compared to the common multi-model in predicting NOx emissions, and experimental results indicate that the proposed HGS model is much better than the multi-model in predicting NOx emissions in the dynamic process.

Application of steady-state and dynamic modeling for the prediction of the BOD of an aerated lagoon at a pulp and paper millPart I. Linear approaches

The temporal fluctuations of CW receptions at frequencies of 16, 29.5, and 115 Hz on a horizontal array have been analyzed to obtain a statistical description of the instantaneous power at both the individual hydrophone outputs and a frequency domain beamformer output. The signals were transmitted from a towed source and received en a ten-hydrophone bottom-mounted array in deep water. Fine resolution spectra of the individual hydrophone signals are compared with the beam-former frequency-azimuth spectra. Time series of instantaneous signal power from the individual hydrophones as well as the beamformer are obtained as the outputs of both wideband filters (350 mHz) and narrowband filters (50 mHz) which are realized using FFT processing techniques. The narrow bandwidth is selected to pass only the slow signal fluctuations and to reject the fast variations which appear in the spectra as the surface interaction sidebands, whereas the wide bandwidth is selected to pass the total signal. Noise power in comparable bandwidths is also measured to generate time series of signal-to-noise and array gain. Estimates of probability density functions, fluctuation spectra, and correlation functions are presented for selected time series and comparisons are made between the hydrophone and the beam statistics for the different transmitted frequencies.

This article presents an original analytical expression for an upper bound on the optimum joint decoding capacity of Wyner circular Gaussian cellular multiple access channel (C-GCMAC) for uniformly distributed mobile terminals (MTs). This upper bound is referred to as Hadamard upper bound (HUB) and is a novel application of the Hadamard inequality established by exploiting the Hadamard operation between the channel fading matrix G and the channel path gain matrix Ω. This article demonstrates that the actual capacity converges to the theoretical upper bound under the constraints like low signal-to-noise ratios and limiting channel path gain among the MTs and the respective base station of interest. In order to determine the usefulness of the HUB, the behavior of the theoretical upper bound is critically observed specially when the inter-cell and the intra-cell time sharing schemes are employed. In this context, we derive an analytical form of HUB by employing an approximation approach based on the estimation of probability density function of trace of Hadamard product of two matrices, i.e., G and Ω. A closed form of expression has been derived to capture the effect of the MT distribution on the optimum joint decoding capacity of C-GCMAC. This article demonstrates that the analytical HUB based on the proposed approximation approach converges to the theoretical upper bound results in the medium to high signal to noise ratio regime and shows a reasonably tighter bound on optimum joint decoding capacity of Wyner GCMAC.

Goodness of fit tests for weighted histograms