Prediction Error Criterion Research Articles

Sensor Failure Detection of FASSIP System using Principal Component Analysis

In the nuclear reactor accident of Fukushima Daiichi in Japan, the damages of core and pressure vessel were caused by the failure of its active cooling system (diesel generator was inundated by tsunami). Thus researches on passive cooling system for Nuclear Power Plant are performed to improve the safety aspects of nuclear reactors. The FASSIP system (Passive System Simulation Facility) is an installation used to study the characteristics of passive cooling systems at nuclear power plants. The accuracy of sensor measurement of FASSIP system is essential, because as the basis for determining the characteristics of a passive cooling system. In this research, a sensor failure detection method for FASSIP system is developed, so the indication of sensor failures can be detected early. The method used is Principal Component Analysis (PCA) to reduce the dimension of the sensor, with the Squarred Prediction Error (SPE) and statistic Hotteling criteria for detecting sensor failure indication. The results shows that PCA method is capable to detect the occurrence of a failure at any sensor.

New results on estimation bandwidth adaptation

The problem of identification of a nonstationary autoregressive signal using non-causal estimation schemes is considered. Noncausal estimators can be used in applications that are not time-critical, i.e., do not require real-time processing. A new adaptive estimation bandwidth selection rule based on evaluation of pseudoprediction errors is proposed, allowing one to adjust tracking characteristics of noncausal estimators to unknown and/or time-varying degree of signal nonstationary. The new rule is compared with the previously proposed one, based on the generalized Akaike’s final prediction error criterion.

Medical image analysis of abdominal X-ray CT images by deep multi-layered GMDH-type neural network

In this study, a deep multi-layered group method of data handling (GMDH)-type neural network is applied to the medical image analysis of the abdominal X-ray computed tomography (CT) images. The deep neural network architecture which has many hidden layers are automatically organized using the deep multi-layered GMDH-type neural network algorithm so as to minimize the prediction error criterion defined as Akaike’s information criterion (AIC) or prediction sum of squares (PSS). The characteristics of the medical images are very complex and therefore the deep neural network architecture is very useful for the medical image diagnosis and medical image recognition. In this study, it is shown that this deep multi-layered GMDH-type neural network is useful for the medical image analysis of abdominal X-ray CT images.

Deep feedback GMDH-type neural network and its application to medical image analysis of MRI brain images

The deep feedback group method of data handling (GMDH)-type neural network is applied to the medical image analysis of MRI brain images. In this algorithm, the complexity of the neural network is increased gradually using the feedback loop calculations. The deep neural network architecture is automatically organized so as to fit the complexity of the medical images using the prediction error criterion defined as Akaike's information criterion (AIC) or prediction sum of squares (PSS). The recognition results show that the deep feedback GMDH-type neural network algorithm is useful for the medical image analysis of MRI brain images, because the optimum neural network architectures fitting the complexity of the medical images are automatically organized so as to minimize the prediction error criterion defined as AIC or PSS.

Deep multi-layered GMDH-type neural network using revised heuristic self-organization and its application to medical image diagnosis of liver cancer

In this study, the deep multi-layered group method of data handling (GMDH)-type neural network algorithm using revised heuristic self-organization method is proposed and applied to medical image diagnosis of liver cancer. The deep GMDH-type neural network can automatically organize the deep neural network architecture which has many hidden layers. The structural parameters such as the number of hidden layers, the number of neurons in hidden layers and useful input variables are automatically selected to minimize prediction error criterion defined as Akaike’s information criterion (AIC) or prediction sum of squares (PSS). The architecture of the deep neural network is automatically organized using the revised heuristic self-organization method which is a type of the evolutionary computation. This new neural network algorithm is applied to the medical image diagnosis of the liver cancer and the recognition results are compared with the conventional 3-layered sigmoid function neural network.

Model Order Selection in Errors-in-Variables System Identification

This work studies the problem of model order selection in errors-in-variables (EIV) system identification. Two criteria, the final correlated prediction error (FCPE) criterion and the final correlated output error (FCOE) criterion are developed for estimating the order of EIV systems. The criteria are extensions of the final prediction error (FPE) criterion and the final output error (FOE) criterion. To eliminate the influence of the input noise in FPE criterion and FOE criterion, the idea of the new criteria is to correlate the prediction error and the output error with the output signal respectively. Simulations are used to illustrate the performance of the criteria.

An adaptive sampling approach for Kriging metamodeling by maximizing expected prediction error

As a well-known approximation method, Kriging is widely used in process engineering design and optimization for saving computational budget. The Kriging model for a target function is fitted to a set of sample points, the responses of which are expensive to obtain in practice and the sample distribution of which has a great impact on the model prediction quality. Therefore, a main task in adaptive sampling for Kriging metamodeling is to gather informative points in order to build an accurate model with as few points as possible. To this end, we propose an adaptive sampling approach under the bias-variance decomposition framework. This novel sampling approach sequentially selects new points by maximizing an expected prediction error criterion that considers both the bias and variance information. Particularly, it presents an adaptive balance strategy to dynamically balance the local exploitation and global exploration via the error information from the previous iteration. Four benchmark cases and four engineering cases from low to high dimensions are used to assess the performance of the proposed approach. Numerical results reveal that this adaptive sampling approach is very promising for constructing accurate Kriging models for problems with diverse characteristics.

On adaptive covariance and spectrum estimation of locally stationary multivariate processes

When estimating the correlation/spectral structure of a locally stationary process, one has to make two important decisions. First, one should choose the so-called estimation bandwidth, inversely proportional to the effective width of the local analysis window, in the way that complies with the degree of signal nonstationarity. Too small bandwidth may result in an excessive estimation bias, while too large bandwidth may cause excessive estimation variance. Second, but equally important, one should choose the appropriate order of the spectral representation of the signal so as to correctly model its resonant structure–when the order is too small, the estimated spectrum may not reveal some important signal components (resonances), and when it is too high, it may indicate the presence of some nonexistent components. When the analyzed signal is not stationary, with a possibly time-varying degree of nonstationarity, both the bandwidth and order parameters should be adjusted in an adaptive fashion. The paper presents and compares three approaches allowing for unified treatment of the problem of adaptive bandwidth and order selection for the purpose of identification of nonstationary vector autoregressive processes: the cross-validation approach, the full cross-validation approach, and the approach that incorporates the multivariate version of the generalized Akaike’s final prediction error criterion. It is shown that the latter solution yields the best results and, at the same time, is very attractive from the computational viewpoint.

Medical image diagnosis of kidney regions by deep feedback GMDH-type neural network using principal component-regression analysis

The deep feedback Group Method of Data Handling (GMDH)-type neural network is applied to the medical image recognition of kidney regions. In this algorithm, the principal component-regression analysis is used for the learning calculation of the neural network, and the accurate and stable predicted values are obtained. The neural network architecture is automatically organized so as to fit the complexity of the medical images using the prediction error criterion defined as Akaike's Information Criterion (AIC) or Prediction Sum of Squares (PSS). The recognition results show that the deep feedback GMDH-type neural network algorithm is useful for the medical image recognition of kidney regions, because the optimum neural network architecture is automatically organized.

Factor Modelling for High‐Dimensional Time Series: Inference and Model Selection

Analysis of high‐dimensional time series data is of increasing interest among different fields. This article studies high‐dimensional time series from a dimension reduction perspective using factor modelling. Statistical inference is conducted using eigen‐analysis of a certain non‐negative definite matrix related to autocovariance matrices of the time series, which is applicable to fixed or increasing dimension. When the dimension goes to infinity, the rate of convergence and limiting distributions of estimated factors are established. Using the limiting distributions of estimated factors, a high‐dimensional final prediction error criterion is proposed to select the number of factors. Asymptotic properties of the criterion are illustrated by simulation studies and real applications.

Designing combined physical and computer experiments to maximize prediction accuracy

Combined designs for experiments involving a physical system and a simulator of the physical system are evaluated in terms of their accuracy of predicting the mean of the physical system. Comparisons are made among designs that are (1) locally optimal under the minimum integrated mean squared prediction error criterion for the combined physical system and simulator experiments, (2) locally optimal for the physical or simulator experiments, with a fixed design for the component not being optimized, (3) maximin augmented nested Latin hypercube, and (4) I-optimal for the physical system experiment and maximin Latin hypercube for the simulator experiment. Computational methods are proposed for constructing the designs of interest. For a large test bed of examples, the empirical mean squared prediction errors are compared at a grid of inputs for each test surface using a statistically calibrated Bayesian predictor based on the data from each design. The prediction errors are also studied for a test bed that varies only the calibration parameter of the test surface. Design recommendations are given.

Using a Prediction Error Criterion for Model Selection in Forecasting Option Prices

The common way to measure the performance of a volatility prediction model is to assess its ability to predict future volatility. However, as volatility is unobservable, there is no natural metric for measuring the accuracy of any particular model. Noh et al. (1994) assessed the performance of a volatility prediction model by devising trading rules to trade options on a daily basis and using forecasts of option prices obtained by the Black & Scholes (BS) option pricing formula. (An option is a security that gives its owner the right, not the obligation, to buy or sell an asset at a fixed price within a specified period of time, subject to certain conditions. The BS formula amounts to buying (selling) an option when its price forecast for tomorrow is higher (lower) than today’s market settlement price.)In this paper, adopting Noh et al.’s (1994) idea, we assess the performance of a number of Autoregressive Conditional Heteroscedasticity (ARCH) models. For, each trading day, the ARCH model, selected on the basis of the prediction error criterion (PEC) introduced by Xekalaki et al. (2003) and suggested by Degiannakis and Xekalaki (1999) in the context of ARCH models, is used to forecast volatility. According to this criterion, the ARCH model with the lowest sum of squared standardized one step ahead prediction errors is selected for forecasting future volatility. A comparative study is made in order to examine which ARCH volatility estimation method yields the highest profits and whether there is any gain in using the PEC model selection algorithm for speculating with financial derivatives. Among a set of model selection algorithms, even marginally, the PEC algorithm appears to achieve the highest rate of return.

Robust adaptive filtering using recursive weighted least squares with combined scale and variable forgetting factors.

In this paper, a new adaptive robustified filter algorithm of recursive weighted least squares with combined scale and variable forgetting factors for time-varying parameters estimation in non-stationary and impulsive noise environments has been proposed. To reduce the effect of impulsive noise, whether this situation is stationary or not, the proposed adaptive robustified approach extends the concept of approximate maximum likelihood robust estimation, the so-called M robust estimation, to the estimation of both filter parameters and noise variance simultaneously. The application of variable forgetting factor, calculated adaptively with respect to the robustified prediction error criterion, provides the estimation of time-varying filter parameters under a stochastic environment with possible impulsive noise. The feasibility of the proposed approach is analysed in a system identification scenario using finite impulse response (FIR) filter applications.

An agricultural price forecasting model under nonstationarity using functional coefficient autoregression

In this globalized world, management of food security in the developing countries like India where agriculture is dominated needs efficient and reliable price forecasting models more than ever. Forecasts of agricultural prices are handy to the policymakers, agribusiness industries and farmers. In the present study, Functional Coefficient Autoregression (FCAR) has been applied for modeling and forecasting the monthly wholesale price of clean coffee seeds in Hyderabad coffee consuming center using the data from Jan, 2001 to Sep, 2014. FCAR (2,2) model was found suitable based on the minimum Average Prediction Error (APE) criterion. The FCAR model thus obtained was compared with the Autoregressive Integrated Moving Average (ARIMA) model. Since the original series was found to be nonstationary from Augmented Dickey-Fuller test (ADF statistic=-2.84, p=0.22), the differenced series (ADF statistic=-4.20, p<0.01) was used and ARIMA (12,1,0) was found suitable. The FCAR model obtained was compared with the ARIMA model with respect to forecast accuracy measures viz., Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE). The RMSE and MAPE for the FCAR (2,2) were found to be 17.16 and 4.41%, respectively, whereas for the ARIMA (12,1,0) models, 62.64 and 26.15%, respectively. The results indicated that the FCAR model was efficient than the ARIMA model in forecasting the future prices.

Medical Image Diagnosis of Lung Cancer by Deep Feedback GMDH-Type Neural Network

The deep feedback Group Method of Data Handling (GMDH)-type neural network is applied to the medical image diagnosis of lung cancer. The deep feedback GMDH-type neural network can identified very complex nonlinear systems using heuristic self-organization method which is a type of evolutionary computation. The deep neural network architectures are organized so as to minimize the prediction error criterion defined as Akaike’s Information Criterion (AIC) or Prediction Sum of Squares (PSS). In this algorithm, the principal component-regression analysis is used for the learning calculation of the neural network. It is shown that the deep feedback GMDH-type neural network algorithm is useful for the medical image diagnosis of lung cancer because deep neural network architectures are automatically organized using only input and output data.

Fuzzy Aggregation Based Multiple Models Explicit Multi Parametric MPC Design for a Quadruple Tank Process

Abstract In this study, design of fuzzy aggregated multi parametric model predictive controller (mpMPC) for multivariable systems is proposed. Using first principles model (FPM) of the process, a steady state map (SSM) of input output is generated. A minimum number of linearized models are obtained from the FPM in different nominal operating regions to satisfy prediction error criterion. From gap metric measure, these models are clustered by k-means algorithm, followed by cluster representatives (CR) selection and fuzzy weights (to represent each model using aggregated CR's) calculation. For a given operating point, fuzzy weights are determined by a supervisory structure. Using these weights, the estimation model and control output (from mpMPC's designed for each CR) are aggregated. A real time quadruple tank (QT) is controlled using the proposed strategy, which is implemented on an embedded platform. Performance metrics indicate a 20% improvement in prediction and 20% improvement in control under closed loop using proposed strategy.

Medical Image Analysis of Brain X-ray CT Images By Deep GMDH-Type Neural Network

The deep Group Method of Data Handling (GMDH)-type neural network is applied to the medical image analysis of brain X-ray CT image. In this algorithm, the deep neural network architectures which have many hidden layers and fit the complexity of the nonlinear systems, are automatically organized using the heuristic self-organization method so as to minimize the prediction error criterion defined as Akaike’s Information Criterion (AIC) or Prediction Sum of Squares (PSS). The learning algorithm is the principal component-regression analysis and the accurate and stable predicted values are obtained. The recognition results show that the deep GMDH-type neural network algorithm is useful for the medical image analysis of brain X-ray CT images.

Kinetics of Methane Production from Swine Manure and Buffalo Manure.

The degradation kinetics of swine and buffalo manure for methane production was investigated. Six kinetic models were employed to describe the corresponding experimental data. These models were evaluated by two statistical measurements, which were root mean square prediction error (RMSPE) and Akaike's information criterion (AIC). The results showed that the logistic and Fitzhugh models could predict the experimental data very well for the digestion of swine and buffalo manure, respectively. The predicted methane yield potential for swine and buffalo manure was 487.9 and 340.4 mL CH4/g volatile solid (VS), respectively, which was close to experimental values, when the digestion temperature was 36 ± 1 °C in the biochemical methane potential assays. Besides, the rate constant revealed that swine manure had a much faster methane production rate than buffalo manure.

Medical image diagnosis of liver cancer by hybrid feedback GMDH-type neural network using principal component-regression analysis

The hybrid feedback group method of data handling (GMDH)-type neural network is proposed and applied to the medical image diagnosis of liver cancer. In this algorithm, the principal component-regression analysis is used for the learning calculation of the neural network, and the accurate and stable predicted values are obtained. Furthermore, this neural network has the feedback loop and the complexity of neural network architecture is increased using the feedback loop calculations. The neural network architecture is automatically organized so as to fit the complexity of the nonlinear system using the prediction error criterion defined as Akaike's information criterion (AIC) or prediction sum of squares (PSS). The recognition results show that the hybrid feedback GMDH-type neural network algorithm is useful for the medical image diagnosis of liver cancer since the optimum neural network architecture is automatically organized.

Logistic GMDH-type neural network using principal component-regression analysis and its application to medical image diagnosis of lung cancer

The logistic group method of data handling (GMDH)-type neural network is proposed and applied to the medical image diagnosis of lung cancer. In this logistic GMDH-type neural network algorithm, the principal component-regression analysis is used to estimate the parameters of the neural network, and the multi-colinearity, which is generated in the conventional GMDH algorithm, is protected. Therefore, accurate and stable predicted values are obtained in the logistic GMDH-type neural network. Furthermore, the polynomial and logistic neurons are used, and the neural network architectures are automatically organized so as to minimize the prediction error criterion defined as Akaike's information criterion or prediction sum of squares. The identification results show that the logistic GMDH-type neural network algorithm is useful for the medical image diagnosis of lung cancer since the optimum neural network architecture is automatically organized so as to fit the complexity of the medical images.