Backward Algorithm Research Articles

Ramp sparse support matrix machine and its application in roller bearing fault diagnosis

As an efficient matrix classifier, support matrix machine (SMM) can make full use of the spatial structure of the input matrix and show superior diagnostic performance. However, the input feature matrix may be contaminated by noise to form some outliers, which will affect the classification accuracy due to excessive loss. Therefore, this paper proposes a new matrix classification method, called Ramp sparse support matrix machine (RSSMM). In RSSMM, it compulsorily limits a loss threshold under the Ramp loss function, which solves the problem of model generalization performance degradation caused by excessive loss. Meanwhile, the generalized forward–backward algorithm (GFB) is introduced into RSSMM as a solver, and a generalized smooth Ramp loss function is designed to solve the problem that the Ramp loss function itself does not have a continuous gradient. Two roller bearing fault data sets are used to prove the effectiveness of the RSSMM method, and the analysis results show the superiority of the proposed RSSMM method in the classification of roller bearing fault signal.

Novel bleeding prediction model in atrial fibrillation patients on new oral anticoagulants

ObjectiveClinical models such as the HAS-BLED (standing for Hypertension, Abnormal liver/renal function, Stroke history, Bleeding history or predisposition, Labile INR, Elderly, Drug/alcohol usage) were developed to predict risk of major...

Nowcasting GDP Using Dynamic Factor Model with Unknown Number of Factors and Stochastic Volatility: A Bayesian Approach

Real-time nowcasting is an assessment of current economic conditions from timely released economic series (such as monthly macroeconomic data) before the direct measure (such as quarterly GDP figure) is disseminated. Dynamic factor models (DFMs) are widely used in econometrics to bridge series with different frequencies and achieve a reduction in dimensionality. However, most of the research using DFMs often assumes the number of factors is known. A Bayesian approach is developed to identify the unknown number of factors and estimate the latent dynamic factors of DFMs accurately in a real-time nowcasting framework. The proposed method can deal with unbalanced data, which is typical of a real-time nowcasting analysis. Furthermore, the particle Gibbs with backward simulation algorithm is considered to obtain estimated stochastic volatility (SV) in monthly series efficiently. The validity of the method is demonstrated through simulation studies and an empirical study of nowcasting US’s quarterly GDP growth using monthly data series of several categories in the US market. Both the simulation and empirical studies indicate that the proposed Bayesian approach is a viable option to conduct real-time nowcasting for the US’s quarterly GDP.

System identification of hammerstein models by using backward shift algorithm

In this paper, a new identification method for discrete-time Hammerstein systems is proposed. The method is a joint use of discrete Fourier transform, backward shift method, and the least squares method. The frequency responses are obtained with sampled input and output data in the time domain through discrete Fourier transform. It is followed by the backward shift algorithm that was originally developed for estimating poles of linear time-invariant systems. After poles of linear subsystem are estimated, coefficients of linear and nonlinear subsystems are respectively determined by using the least squares (LS) method. The robustness of the backward shift algorithm guarantees the effectiveness of the proposed algorithm. Simulation results show that the poles of linear subsystem are well located. Thus, it is practical to identify discrete Hammerstein systems.

RETRACTED ARTICLE: Machine learning based identification and classification of disorders in human knee joint – computational approach

Earlier identification of knee joint pathology helps the therapist to provide the appropriate clinical procedures to control the deteriorating process of arthritis. Beyond usual medical investigations, computational techniques have been used for the diagnosis of knee joint disorder. Among different methodologies, vibroarthrographic technique is employed to identify knee joint disorder. Machine learning contains number of classification methods for the given data. A novel technique called greedy sequential backward feature selection-based radial kernelized least square support vector classification (GSBFS-RKLSSVC) is introduced for accurate detection of knee joint pathology with minimum time. The proposed GSBFS-RKLSSVC technique consists of three processes, namely feature selection, feature evaluation, and classification. Initially, number of VAG signal images is taken from the dataset for detection of knee joint disorder. The relevant feature is selected through the greedy mutual informative regressed sequential backward selection algorithm to reduce an initial dimensional feature space into a low-dimensional feature subspace. Following this, the dichotomous logit regression is applied to select the best features and discard others. Therefore, the feature selection process of the proposed GSBFS-RKLSSVC minimizes the time consumption of the knee joint pathology detection. Once the signal features are extracted, RKLSSVC is applied to detect the normal and abnormal VAG signal. Decision boundary is utilized by the classifier to categorize the samples based on the similarity between the training features and testing features. As a result, the accurate classification is obtained with a minimum error rate. The observed result indicates that GSBFS-RKLSSVC achieves higher accuracy, sensitivity, and specificity and reduces time than the conventional methods.

Application of neural networks in predictions of brake wear particulate matter emission

According to the World Health Organization, air pollution with PM10 and PM2.5 (PM-particulate matter) is a significant problem that can have serious consequences for human health. Vehicles, as one of the main sources of PM10 and PM2.5 emissions, pollute the air and the environment both by creating particles by burning fuel in the engine, and by wearing of various elements in some vehicle systems. In this paper, the authors conducted the prediction of the formation of PM10 and PM2.5 particles generated by the wear of the braking system using a neural network (Artificial Neural Networks (ANN)). In this case, the neural network model was created based on the generated particles that were measured experimentally, while the validity of the created neural network was checked by means of a comparative analysis of the experimentally measured amount of particles and the prediction results. The experimental results were obtained by testing on an inertial braking dynamometer, where braking was performed in several modes, that is under different braking parameters (simulated vehicle speed, brake system pressure, temperature, braking time, braking torque). During braking, the concentration of PM10 and PM2.5 particles was measured simultaneously. The total of 196 measurements were performed and these data were used for training, validation, and verification of the neural network. When it comes to simulation, a comparison of two types of neural networks was performed with one output and with two outputs. For each type, network training was conducted using three different algorithms of backpropagation methods. For each neural network, a comparison of the obtained experimental and simulation results was performed. More accurate prediction results were obtained by the single-output neural network for both particulate sizes, while the smallest error was found in the case of a trained neural network using the Levenberg-Marquardt backward propagation algorithm. The aim of creating such a prediction model is to prove that by using neural networks it is possible to predict the emission of particles generated by brake wear, which can be further used for modern traffic systems such as traffic control. In addition, this wear algorithm could be applied on other vehicle systems, such as a clutch or tires.

A novel heterogeneous ensemble approach to variable selection for gas-liquid two-phase CO2 flow metering

Variable selection is an important preprocessing step in the development of effective data-driven models for CO2 flow measurement in carbon capture and storage systems. In order to effectively quantify the importance of potential input variables to the desired output, ensemble learning is proposed and incorporated into variable selection methodology. This paper presents a tree-based heterogeneous ensemble approach to variable selection and its application to gas-liquid two-phase CO2 flow measurement. The importance of each variable is determined through combining the importance scores from four tree-based algorithms, including decision tree regression, bootstrap aggregating of regression trees, gradient boosting decision tree and gradient boosting random forest. Then the backward elimination algorithm is applied to remove the relatively less important variables and hence a small set of input variables for data-driven models. The selection results demonstrate that the significant variables for CO2 mass flow measurement include apparent mass flow rate, time shift, differential pressure and pressure drop while observed density, density drop, observed flow velocity and outlet temperature for prediction of gas volume fraction. To assess the validity of the selected variables, data-driven models based on gradient boosting random forest are developed. Results suggest that the relative error of the model output is mostly within 1% for CO2 mass flowrate measurement and 5% for gas volume fraction prediction by taking the selected variables as model inputs.

Conical averagedness and convergence analysis of fixed point algorithms

We study a conical extension of averaged nonexpansive operators and the role it plays in convergence analysis of fixed point algorithms. Various properties of conically averaged operators are systematically investigated, in particular, the stability under relaxations, convex combinations and compositions. We derive conical averagedness properties of resolvents of generalized monotone operators. These properties are then utilized in order to analyze the convergence of the proximal point algorithm, the forward–backward algorithm, and the adaptive Douglas–Rachford algorithm. Our study unifies, improves and casts new light on recent studies of these topics.

Security investment of interdependent and identical CPSs: Stochastic games with asymmetric information

This paper considers remote state estimation in cyber-physical systems (CPSs) with multiple sensors, where measurements of each sensor are transmitted to the corresponding remote estimator over a shared communication network with interdependent security. A stochastic non-cooperative game framework with asymmetric information is provided, in which each sensor is in pursuit of minimizing the security investment cost on the first stage associated with the expected error covariance as small as possible at the corresponding remote estimator on the second stage. The asymmetry of information among sensors poses a challenge to characterize or compute the Nash equilibria (NE). To overcome the challenge, based on the common information among sensors, the game with asymmetric information is transformed into another game with symmetric information such that a subclass of NE refer to common information based Markov perfect equilibria of the original game can be achieved by using a backward induction algorithm. Finally, a numerical example is presented to verify the obtained results.

A new spatial count data model with time-varying parameters

Recent crash frequency studies incorporate spatiotemporal correlations, but these studies have two key limitations – i) none of these studies accounts for temporal variation in model parameters; and ii) Gibbs sampler suffers from convergence issues due to non-conjugacy. To address the first limitation, we propose a new count data model that identifies the underlying temporal patterns of the regression parameters while simultaneously allowing for time-varying spatial correlation. The model is also extended to incorporate heterogeneity in non-temporal parameters across spatial units. We tackle the second shortcoming by deriving a Gibbs sampler that ensures conditionally conjugate posterior updates for all model parameters. To this end, we take the advantages of Pólya-Gamma data augmentation and forward filtering backward sampling algorithm. After validating the properties of the Gibbs sampler in a Monte Carlo study, the advantages of the proposed specification are demonstrated in an empirical application to uncover relationships between crash frequency spanning across nine years and pavement characteristics. Model parameters exhibit practically significant temporal patterns (i.e., temporal instability). For example, the safety benefits of better pavement ride quality are estimated to increase over time.

Stochastic security-constrained optimal power flow for a microgrid considering tie-line switching

With the rapid development of microgrid, its tie-line switching from grid-connected to islanded mode is a topic worth discussing for considering both main grid resilience and microgrid security. In this paper, a stochastic security-constrained optimal power flow (OPF) method is proposed to deal with these conditions under high uncertainties. Firstly, a linear load flow model and a backward forward sweep algorithm are applied to present microgrid power flow with reduced computing burdens. Secondly, with consideration of tie-line switching from grid-connected to islanded operation mode, a security-constrained OPF problem for a microgrid is proposed to minimize operating cost and by optimizing microturbine setpoints and load shedding coefficient. To promise stable islanded operation after disconnection from the main grid, a Benders decomposition method is developed to decouple the OPF problem into a grid-connected master problem and an islanded sub-problem and then solve them iteratively with Benders cuts to guarantee microgrid security after tie-line switching. Last, a stochastic optimization method with probabilistic modelling is adopted to address the uncertainty issue caused by renewable energy sources and loads. The proposed stochastic security-constrained OPF method has been verified with high computing efficiency and robust security via comprehensive numerical simulations.

On the Relationship between Uhlig Extended and beta‐Bartlett Processes

Stochastic volatility processes are used in multi‐variate time series analysis to track time‐varying patterns in covariance matrices. Uhlig extended (UE) and beta‐Bartlett (BB) processes are especially convenient for analyzing high‐dimensional time series because they are conjugate with Wishart likelihoods. In this article, we show that UE and BB are closely related, but not equivalent: their hyperparameters can be matched so that they have the same forward‐filtered posteriors and one‐step ahead forecasts, but different joint (smoothed) posterior distributions. Under this circumstance, Bayes factors cannot discriminate the models and alternative approaches to model comparison are needed. We illustrate these issues in a retrospective analysis of volatilities of returns of foreign exchange rates. Additionally, we provide a backward sampling algorithm for the BB process, for which retrospective analysis had not been developed.

Stock Market Prediction on High-Frequency Data Using ANN

A stock market is a place where company shares are traded to the stockbrokers. Stock price prediction is one of the most challenging problems as a high level of accuracy is the key factor in predicting a stock market. Many methods are used to predict the price in the stock market but none of those methods are proved as a consistently acceptable prediction tool due to its volatile nature. In this paper, we proposed Artificial Neural Network (ANN) technique because ANN can generalize and predict data after learning and analyzing from the initial inputs and their relationships. We used feed forward network and backward propagation algorithm to predict stock prices. In this paper, we introduced a method that can find out the future value of stock prices in a particular day based on some input using ANN back propagation algorithm.

A New Forward–Backward Algorithm with Line Searchand Inertial Techniques for Convex Minimization Problems with Applications

For the past few decades, various algorithms have been proposed to solve convex minimization problems in the form of the sum of two lower semicontinuous and convex functions. The convergence of these algorithms was guaranteed under the L-Lipschitz condition on the gradient of the objective function. In recent years, an inertial technique has been widely used to accelerate the convergence behavior of an algorithm. In this work, we introduce a new forward–backward splitting algorithm using a new line search and inertial technique to solve convex minimization problems in the form of the sum of two lower semicontinuous and convex functions. A weak convergence of our proposed method is established without assuming the L-Lipschitz continuity of the gradient of the objective function. Moreover, a complexity theorem is also given. As applications, we employed our algorithm to solve data classification and image restoration by conducting some experiments on these problems. The performance of our algorithm was evaluated using various evaluation tools. Furthermore, we compared its performance with other algorithms. Based on the experiments, we found that the proposed algorithm performed better than other algorithms mentioned in the literature.

Iterative Design for the Common Solution of Monotone Inclusions and Variational Inequalities

Some new forward–backward multi-choice iterative algorithms with superposition perturbations are presented in a real Hilbert space for approximating common solution of monotone inclusions and variational inequalities. Some new ideas of constructing iterative elements can be found and strong convergence theorems are proved under mild restrictions, which extend and complement some already existing work.

Modified Inertial Forward–Backward Algorithm in Banach Spaces and Its Application

In this paper, we present a new modified inertial forward–backward algorithm for finding a common solution of the quasi-variational inclusion problem and the variational inequality problem in a q-uniformly smooth Banach space. The proposed algorithm is based on descent, splitting and inertial ideas. Under suitable assumptions, we prove that the sequence generated by the iterative algorithm converges strongly to the unique solution of the abovementioned problems. Numerical examples are also given to demonstrate our results.

Numerical simulation and experimental verification studies on a unified strength theory-based elastoplastic damage constitutive model of shale

The purpose of this study is to establish an elastic–plastic damage constitutive model of shale and simulate the elastic–plastic damage characteristics of shale under stress. Based on the unified strength theory and the mechanics of shale rock samples characterized in laboratory tests, a new elastic–plastic damage constitutive model for shale is established by introducing compression factors and damage variables. The main considerations include the compressibility of primary fractures and pores in the shale core, and the formation of secondary cracks in the rock matrix under stress. A fully implicit backward Euler regression mapping algorithm has been used to solve the model, and the numerical simulation results are in good agreement with the experimental results. The results show that the model established in this paper can accurately simulate the elastic–plastic damage characteristics of shale under stress, and that it provides a new numerical simulation method for describing the elastic–plastic damage in shale.

Line spectrum extraction method based on hidden Markov model

To solve the difficult problem of line spectrum detection with a low signal-to-noise ratio, a line spectrum extraction algorithm based on a hidden Markov model (HMM) is proposed. The forward–backward algorithm was used to track single and multiple spectral lines in a lofargram, and a new algorithm for the state transition probability matrix was proposed to handle the large amount of HMM calculation and the uncertainty difficulty in processing real signals. Finally, a median fitting algorithm was used to correct the few outlier points in the line spectrum estimation process. Simulation and sea trial data showed that the algorithm had good line spectrum tracking ability for a low signal-to-noise ratio.

An Interpretable Denoising Layer for Neural Networks Based on Reproducing Kernel Hilbert Space and its Application in Machine Fault Diagnosis

Deep learning algorithms based on neural networks make remarkable achievements in machine fault diagnosis, while the noise mixed in measured signals harms the prediction accuracy of networks. Existing denoising methods in neural networks, such as using complex network architectures and introducing sparse techniques, always suffer from the difficulty of estimating hyperparameters and the lack of physical interpretability. To address this issue, this paper proposes a novel interpretable denoising layer based on reproducing kernel Hilbert space (RKHS) as the first layer for standard neural networks, with the aim to combine the advantages of both traditional signal processing technology with physical interpretation and network modeling strategy with parameter adaption. By investigating the influencing mechanism of parameters on the regularization procedure in RKHS, the key parameter that dynamically controls the signal smoothness with low computational cost is selected as the only trainable parameter of the proposed layer. Besides, the forward and backward propagation algorithms of the designed layer are formulated to ensure that the selected parameter can be automatically updated together with other parameters in the neural network. Moreover, exponential and piecewise functions are introduced in the weight updating process to keep the trainable weight within a reasonable range and avoid the ill-conditioned problem. Experiment studies verify the effectiveness and compatibility of the proposed layer design method in intelligent fault diagnosis of machinery in noisy environments.

A Note on Least-Squares Method For Pricing American Options

The ultimate goal of this note is to provide a background for, and describe, the Longstaff-Schwartz LSM (Least-Squares Monte Carlo) algorithm for evaluating derivatives with early (American/Bermudan) exercise. The reason for writing yet another paper on the matter is that this method is often presented in a complicated context, which makes the reading difficult, and obfuscates the rather simple idea of the algorithm. For example, the presentation in (Longstaff & Schwartz, 2001) comprises of a little example, and applications of the algorithm to more complex derivatives, without actually spelling out the algorithm. Indeed, Section 2.2, promisingly entitled “LSM algorithm”, elaborates more on which regression method should be used for approximating the expected value from continuation rather than the actual algorithm. An informal description of the method is arguably given in a short paragraph, which nevertheless fails to lay down the steps used in the backward traversal algorithm. Perhaps the authors thought that the actual steps of the algorithm are too simple, but wouldn’t that be a compelling reason to write them down? In addition to introducing unnecessary regression details, the presentation in (Brigo & Mercurio, 2006) brings in another complication: the algorithm is formalized in the context of a path-dependent payoff function, leading to a formalism arguably hard to follow. This paper aims at revealing that neither the regression method used for approximating the value from continuation, nor the path dependence (or not) of the derivative payoff are relevant to the method, from the algorithmic and conceptual prospective. They are implementation details that should be left at the latitude of the quant developer. Besides the presentation of the LSM algorithm, this note has a hidden agenda: to provide an introduction to the basic notions and concepts that can be heard in any discussion about derivatives with an early exercise provision. In Section 1 we introduced stopping times and stopped processes, optimal exercise strategies and exercise boundaries. Many statements are left without proof, or even justification at times, to allow the attention stay focused on the intuition behind these notions rather than be distracted by an exhaustive presentation of the framework in all its complexity. In the course of this section, we hope to have simplified even further the rather clear presentation in (Shreve, 2004), source which we recommend to be kept at hand. Incidentally, we hope to have clarified a rather ambiguous construct, which can be found in Shreve’s first book, Chapter 4 (page 98), in the definition of stopped process: the lattice operator ∧ (min) is rather ambiguously used over time steps and stopping times, despite of the fact that the stopping times are random variables over a tree’s paths (or equivalently, leaves) and not on the internal tree nodes. This remark will be mentioned in Section 2.2 in more detail. In addition, an equivalent definition of stopping times, in filtration terms and with a rather non-trivial justification, is presented in the second part of Section 2.1. Section 3 fulfills the mandate of this note: we revisit the example in (Longstaff & Schwartz, 2001) with additional details and hopefully in a more organized manner, and we spell out the mere one-page-short LSM algorithm.