Bregman primal–dual first-order method and application to sparse semidefinite programming

We present a new variant of the Chambolle–Pock primal–dual algorithm with Bregman distances, analyze its convergence, and apply it to the centering problem in sparse semidefinite programming. The novelty in the method is a line search procedure for selecting suitable step sizes. The line search obviates the need for estimating the norm of the constraint matrix and the strong convexity constant of the Bregman kernel. As an application, we discuss the centering problem in large-scale semidefinite programming with sparse coefficient matrices. The logarithmic barrier function for the cone of positive semidefinite completable sparse matrices is used as the distance-generating kernel. For this distance, the complexity of evaluating the Bregman proximal operator is shown to be roughly proportional to the cost of a sparse Cholesky factorization. This is much cheaper than the standard proximal operator with Euclidean distances, which requires an eigenvalue decomposition.

An EM Algorithm for Target Tracking with an Unknown Correlation Coefficient of Measurement Noise

In this paper, an expectation maximization based sequential modified unbiased converted measurement Kalman filter is proposed for target tracking with an unknown correlation coefficient of measurement noise between the range and the range rate. Firstly, a pseudo measurement is constructed by multiplying the range and the range rate to reduce the strong nonlinearity between the measurement and the target state. The mean and covariance of converted errors are subsequentlsubsequently derived by modified unbiased converted measurement to weaken the error caused by the linearization of the measurement equation, which is effectively to improve the dynamic accuracy of target tracking. Then, the converted errors of the position and the pseudo measurement are decorrelated by the Cholesky factorization and thus to obtain the posterior probability distribution of the state by using the sequential filtering in the Bayesian framework. Finally, the expectation maximization is introduced in the updating procedure of the pseudo measurement to jointly estimate the target state and the correlation coefficient. The target tracking scenario with an unknown correlation coefficient is built to demonstrate the validness and feasibility of the proposed algorithm. Simultaneously, the results of the normalized error squared validate the consistency of the modified unbiased converted measurement.

Oil price shock in the US and the euro area – evidence from the shadow rate and the term premium

The aim of this article is to investigate the consequences of oil price changes for the economy of the US and the euro area. Oil price transmission channel is assessed using Granger causalities and structural vector autoregressive (VAR) specifications (applying the Cholesky factorization and the restrictions following the method of Blanchard and Quah). The conventional oil price transmission channel is extended by a shadow policy rate and term premium, as the importance of both indicators has been growing rapidly in recent years. The results confirm that the oil price shock is not negligible in the aftermath of the Global Financial Crisis and in the subsequent period of monetary policy normalization. The findings are confirmed by the outcomes of the Bayesian VAR specification with sign restrictions. The consequences of changes in oil prices have significantly grown since the introduction of unconventional monetary instruments. The magnitude of the response of industrial production, price level and shadow interest rate to the oil price shock is strongest in the period corresponding to the unconventional monetary policy. In many cases, however, the reaction is short-lived. The conventional instrument (policy rate) in the euro area has still not been sufficient to stabilize the economy in the recent period of monetary policy normalization in the US.

Cholesky Factorization Based Online Sequential Multiple Kernel Extreme Learning Machine Algorithm for a Cement Clinker Free Lime Content Prediction Model

Aiming at the difficulty in real-time measuring and the long offline measurement cycle for the content of cement clinker free lime (fCaO), it is very important to build an online prediction model for fCaO content. In this work, on the basis of Cholesky factorization, the online sequential multiple kernel extreme learning machine algorithm (COS-MKELM) is proposed. The LDLT form Cholesky factorization of the matrix is introduced to avoid the large operation amount of inverse matrix calculation. In addition, the stored initial information is utilized to realize online model identification. Then, three regression datasets are used to test the performance of the COS-MKELM algorithm. Finally, an online prediction model for fCaO content is built based on COS-MKELM. Experimental results demonstrate that the fCaO content model improves the performance in terms of learning efficiency, regression accuracy, and generalization ability. In addition, the online prediction model can be corrected in real-time when the production conditions of cement clinker change.

THE EFFECTS OF FISCAL POLICY SHOCKS ON THE BUSINESS ENVIRONMENT

Fiscal policy influences economic conditions through public spending and taxes, generating positive or negative impulses, both on short and long term. The present research focuses on analysing the effects of the discretionary changes in the fiscal policy in seven post-communist countries of the European Union during the period 2000–2018. The autoregressive distributed lag model (ARDL) has been applied in order to obtain the convergence rates to equilibrium with a clear analysis of the periods needed to achieve the long-run fiscal sustainability. Also, the error correction vector model (VECM), which is based on the autoregressive vector (VAR) model, has been used in the second part of the analysis focusing on the Cholesky factorization of innovations. Impulse-response functions aiming to estimate the response of government expenditures to the shock produced by three macroeconomic variables have been identified.

Pruning Multilayered ELM Using Cholesky Factorization and Givens Rotation Transformation

Extreme learning machine is originally proposed for the learning of the single hidden layer feedforward neural network to overcome the challenges faced by the backpropagation (BP) learning algorithm and its variants. Recent studies show that ELM can be extended to the multilayered feedforward neural network in which the hidden node could be a subnetwork of nodes or a combination of other hidden nodes. Although the ELM algorithm with multiple hidden layers shows stronger nonlinear expression ability and stability in both theoretical and experimental results than the ELM algorithm with the single hidden layer, with the deepening of the network structure, the problem of parameter optimization is also highlighted, which usually requires more time for model selection and increases the computational complexity. This paper uses Cholesky factorization strategy and Givens rotation transformation to choose the hidden nodes of MELM and obtains the number of nodes more suitable for the network. First, the initial network has a large number of hidden nodes and then uses the idea of ridge regression to prune the nodes. Finally, a complete neural network can be obtained. Therefore, the ELM algorithm eliminates the need to manually set nodes and achieves complete automation. By using information from the previous generation’s connection weight matrix, it can be evitable to re-calculate the weight matrix in the network simplification process. As in the matrix factorization methods, the Cholesky factorization factor is calculated by Givens rotation transform to achieve the fast decreasing update of the current connection weight matrix, thus ensuring the numerical stability and high efficiency of the pruning process. Empirical studies on several commonly used classification benchmark problems and the real datasets collected from coal industry show that compared with the traditional ELM algorithm, the pruning multilayered ELM algorithm proposed in this paper can find the optimal number of hidden nodes automatically and has better generalization performance.