Exponential Weighting Research Articles

Metal artifact reduction algorithm based on model images and spatial information

Computed tomography (CT) has become one of the most favorable choices for diagnosis of trauma. However, high-density metal implants can induce metal artifacts in CT images, compromising image quality. In this study, we proposed a model-based metal artifact reduction (MAR) algorithm. First, we built a model image using the k-means clustering technique with spatial information and calculated the difference between the original image and the model image. Then, the projection data of these two images were combined using an exponential weighting function. At last, the corrected image was reconstructed using the filter back-projection algorithm. Two metal-artifact contaminated images were studied. For the cylindrical water phantom image, the metal artifact was effectively removed. The mean CT number of water was improved from −28.95±97.97 to −4.76±4.28. For the clinical pelvic CT image, the dark band and the metal line were removed, and the continuity and uniformity of the soft tissue were recovered as well. These results indicate that the proposed MAR algorithm is useful for reducing metal artifact and could improve the diagnostic value of metal-artifact contaminated CT images.

A modified rapid access heuristic for flowshop scheduling problem

This paper presents a modified rapid access (MRA) heuristic to solve the flowshop scheduling problems. This new heuristic follows the fundamental idea of the original rapid access approach by forming a two-machine subproblem, but the processing times are determined by using an exponential weighting modifier for the original linear weighting scheme without additional computational effort, then the subproblem is solved by using Johnson’s two-machine algorithm. The performance of MRA is tested using instances from the literature and compared with the performance of the original rapid access (RA). Results show that the MRA outperforms the original RA in large size problems by using specific value of parameter alpha. Factorial experiment and response surface methodology are applied to determine the best alpha value which is the main factor that impacts the performance of MRA and produce the best performance of the MRA heuristic.

Adaptive UKF Filtering Algorithm Based on Maximum a Posterior Estimation and Exponential Weighting

摘要: 针对传统Unscented卡尔曼滤波器(Unscented Kalman filter, UKF)在噪声先验统计未知时变情况下非线性滤波精度下降甚至发散的问题, 设计了一种带噪声统计估计器的自适应UKF滤波算法. 首先根据极大后验(Maximum a posterior, MAP)估计原理, 推导出一种次优无偏MAP常值噪声统计估计器; 接着在此基础之上, 采用指数加权的方法, 给出了时变噪声统计估计器的递推公式; 最后对自适应UKF算法进行了性能分析. 相比于传统UKF, 该自适应UKF算法在噪声统计未知时变情况下不仅滤波依然收敛, 滤波精度及稳定性显著提高, 而且其具有应对噪声变化的自适应能力. 仿真实例验证了其有效性. 关键词: 非线性 / 自适应UKF滤波算法 / 常值噪声统计估计器 / 时变噪声统计估计器 / 极大后验估计 / 指数加权

Context-kernel support vector machines (KSVM) based run-to-run control for nonlinear processes

Past studies on multi-tool and multi-product (MTMP) processes have focused on linear systems. In this paper, a novel run-to-run control (RtR) methodology designed for nonlinear semiconductor processes is presented. The proposed methodology utilizes kernel support vector machines (KSVM) to perform nonlinear modeling. In this method, the original variables are mapped using a kernel function into a feature space where linear regression is done. To eliminate the effects of unknown disturbances and drifts, the KSVM expression for the KSVM controller is modified to include constants that are updated in a manner similar to the weights used in double exponential weighting moving average method and the control law for KSVM controllers is derived. Illustrative examples are presented to demonstrate the effectiveness of KSVM and its method in process modeling and control of processes. Even if there is limited data in process modeling, KSVM still has the good capability of characterizing the nonlinear behavior. The performance of the proposed KSVM control algorithm is highly satisfactory and is superior to the other MTMP control algorithms in controlling MTMP processes.

An Efficient Estimation for Switching Regression Models: A Monte Carlo Study

This article investigates an efficient estimation method for a class of switching regressions based on the characteristic function (CF). We show that with the exponential weighting function, the CF-based estimator can be achieved from minimizing a closed form distance measure. Due to the availability of the analytical structure of the asymptotic covariance, an iterative estimation procedure is developed involving the minimization of a precision measure of the asymptotic covariance matrix. Numerical examples are illustrated via a set of Monte Carlo experiments examining the implementation, finite sample property and the efficiency of the proposed estimator.

Signal estimation with binary-valued sensors

This paper introduces several algorithms for signal estimation using binary-valued output sensing. The main idea is derived from the empirical measure approach for quantized identification, which has been shown to be convergent and asymptotically efficient when the unknown parameters are constants. Signal estimation under binary-valued observations must take into consideration of time varying variables. Typical empirical measure based algorithms are modified with exponential weighting and threshold adaptation to accommodate time-varying natures of the signals. Without any information on signal generators, the authors establish estimation algorithms, interaction between noise reduction by averaging and signal tracking, convergence rates, and asymptotic efficiency. A threshold adaptation algorithm is introduced. Its convergence and convergence rates are analyzed by using the ODE method for stochastic approximation problems.

HELP 모형과 SWAT 모형의 지하수 함양량 비교

The groundwater recharge was assessed by using both SWAT and HELP models in Bocheong-cheon watershed. The SWAT model is a comprehensive surface and subsurface model, but it lacks the physical basis for simulating a soil water percolation process. The HELP model which has a drawback in simulating subsurface lateral flow and groundwater flow component can simulate soil water percolation process by considering the unsaturated flow effect of soil layers. The SWAT model has been successfully applied for estimating groundwater recharge in a number of watersheds in Korea, while the application of HELP model has been very limited. The subsurface lateral flow parameter was proposed in order to consider the subsurface lateral flow effect in HELP model and the groundwater recharge was simulated by the modified exponential decay weighting function in HELP model. The simulation results indicate that the recharge of HELP model significantly depends on the values of lateral flow parameter. The recharge errors between SWAT and HELP are the smallest when the lateral flow parameter is about 0.6 and the recharge rates between two models are shown to be reasonably comparable for daily, monthly, and yearly time scales. The HELP model is useful for estimating groundwater recharge at watershed scale because the model structure and input parameters of HELP model are simpler than that of SWAT model. The accuracy of assessing the groundwater recharge might be improved by the concurrent application of SWAT model and HELP model.

A data-driven weighting scheme for family-based genome-wide association studies

Recently, Steen et al proposed a novel two-stage approach for family-based genome-wide association studies. In the first stage, a test based on between-family information is used to rank SNPs according to their P-values or conditional power of the test. In the second stage, the R most promising SNPs are tested using a family-based association test. We call this two-stage approach top R method. Ionita-Laza et al proposed an exponential weighting method within a two-stage framework. In the second stage of this approach, instead of testing top R SNPs, it tests all SNPs and weights the P-values of association test according to the information of the first stage. However, both of the top R and exponential weighting methods only use the information from the first stage to rank SNPs. It seems that the two methods do not use information from the first stage efficiently. Furthermore, it may be unreasonable for the exponential weighting method to use the same weight for all SNPs within a group when only one or a few SNPs are related with a disease. In this article, we propose a data-driven weighting scheme within a two-stage framework. In this method, we use the information from the first stage to determine a SNP-specific weight for each SNP. We use simulation studies to evaluate the performance of our method. The simulation results showed that our proposed method is consistently more powerful than the top R method and the exponential weighting method, regardless of the LD structure, population structure, and family structure.

A mathematical model for quantifying training

A systems modelling approach has been used to quantify the dose-response nature of training. Considerable attention has been focused on the modelling process with little work on the determination of the training impulse (TRIMP) scores. Currently, the methods employed to calculate TRIMPs are subject to various limitations including the use of generic ordinal category or exponential weighting factors for higher exercise intensities. These weightings are necessary to prevent excessively high scores from long duration, low intensity bouts of exercise. We propose a new method to calculate TRIMP scores based upon a whole body bioenergetic model. Our method is individual specific, removing many of the previous limitations. Furthermore, this model could enable a greater comparison of continuous and interval training methods. This model takes into account the length of repetition(s), concentration of the interval session and mode of recovery. This approach, while requiring further research, offers a potential improvement in the accuracy of training load calculations.

Parametric weighting functions

This paper provides preference foundations for parametric weighting functions under rank-dependent utility. This is achieved by decomposing the independence axiom of expected utility into separate meaningful properties. These conditions allow us to characterize rank-dependent utility with power and exponential weighting functions. Moreover, by allowing probabilistic risk attitudes to vary within the probability interval, a preference foundation for rank-dependent utility with parametric inverse- S shaped weighting function is obtained.

Stability of the Extended Kalman Filter When the States are Constrained

In this note, stability of the projection-based constrained discrete time extended Kalman filter (EKF) when applied to deterministic nonlinear systems has been studied. It is proved that, like the unconstrained case, under certain assumptions, the EKF with state equality constraints is an exponential observer, i.e., it keeps the dynamics of its estimation error exponentially stable. Also, it has been shown that a simple modification to the general definition of the EKF with exponential weighting increases the filter's degree of stability and convergence speed with or without state constraints.

On Exponentially Weighted Recursive Least Squares for Estimating Time-Varying Parameters and its Application to Computer Workload Forecasting

Motivated by a relationship between the exponentially weighted recursive least squares (RLS) and the Kalman filter (KF) under a special state-space model (SSM), several simple generalizations of RLS are discussed. These generalized RLS algorithms preserve the key feature of exponential weighting but provide additional flexibility for better tracking performance. They can even outperform KF in some situations when the SSM assumption does not hold. The algorithms are applied to a problem of computer workload forecasting with real data.

Phase diagram for once-reinforced random walks on trees with exponential weighting scheme

We determine the recurrence–transience phase diagram for a variant once-edge-reinforced random walk on trees of bounded degree and supercritical Galton–Watson trees.

Aggregation by exponential weighting, sharp PAC-Bayesian bounds and sparsity

We study the problem of aggregation under the squared loss in the model of regression with deterministic design. We obtain sharp PAC-Bayesian risk bounds for aggregates defined via exponential weights, under general assumptions on the distribution of errors and on the functions to aggregate. We then apply these results to derive sparsity oracle inequalities.

Sequential Procedures for Aggregating Arbitrary Estimators of a Conditional Mean

In this correspondence, a sequential procedure for aggregating linear combinations of a finite family of regression estimates is described and analyzed. Particular attention is given to linear combinations having coefficients in the generalized simplex. The procedure is based on exponential weighting, and has a computationally tractable approximation. Analysis of the procedure is based in part on techniques from the sequential prediction of nonrandom sequences. Here these techniques are applied in a stochastic setting to obtain cumulative loss bounds for the aggregation procedure. From the cumulative loss bounds we derive an oracle inequality for the aggregate estimator for an unbounded response having a suitable moment-generating function. The inequality shows that the risk of the aggregate estimator is less than the risk of the best candidate linear combination in the generalized simplex, plus a complexity term that depends on the size of the coefficient set. The inequality readily yields convergence rates for aggregation over the unit simplex that are within logarithmic factors of known minimax bounds. Some preliminary results on model selection are also presented.

The optimal MR acquisition strategy for exponential decay constants estimation

Estimating the relaxation constant of an exponentially decaying signal from experimental MR data is fundamental in diffusion tensor imaging, fractional anisotropy mapping, measurements of transverse relaxation rates and contrast agent uptake. The precision of such measurements depends on the choice of acquisition parameters made at the design stage of the experiments. In this report, chi(2) fitting of multipoint data is used to demonstrate that the most efficient acquisition strategy is a two-point scheme. We also conjecture that the smallest coefficient of variation of the decay constant achievable in any N-point experiment is 3.6 times larger than that in the image intensity obtained by averaging N acquisitions with minimal exponential weighting.

IBoost: Boosting using an instance-based exponential weighting scheme

AdaBoost is a well-recognized ensemble method to improve prediction accuracy over the base learning algorithm. However, it is prone to overfitting the training instances [18]. Freund, Mansour and Schapire [5] established that using exponential weighting scheme in combining classifiers reduces the problem of overfitting. Also, Helmbold, Kwek and Pitt [7] showed in the prediction using a pool of experts framework an instance-based weighting scheme improves performance. Motivated by these results, we propose here an instance-based exponential weighting scheme in which the weights of the base classifiers are adjusted according to the test instance x. Here, a competency classifier c_i is constructed for each base classifier h_i to predict whether the base classifier's guess of x's label can be trusted and adjust the weight of h_i accordingly. We show that this instance-based exponential weighting scheme enhances the performance of AdaBoost.

Logarithmic regret algorithms for online convex optimization

In an online convex optimization problem a decision-maker makes a sequence of decisions, i.e., chooses a sequence of points in Euclidean space, from a fixed feasible set. After each point is chosen, it encounters a sequence of (possibly unrelated) convex cost functions. Zinkevich (ICML 2003) introduced this framework, which models many natural repeated decision-making problems and generalizes many existing problems such as Prediction from Expert Advice and Cover’s Universal Portfolios. Zinkevich showed that a simple online gradient descent algorithm achieves additive regret $O(\sqrt{T})$ , for an arbitrary sequence of T convex cost functions (of bounded gradients), with respect to the best single decision in hindsight. In this paper, we give algorithms that achieve regret O(log (T)) for an arbitrary sequence of strictly convex functions (with bounded first and second derivatives). This mirrors what has been done for the special cases of prediction from expert advice by Kivinen and Warmuth (EuroCOLT 1999), and Universal Portfolios by Cover (Math. Finance 1:1–19, 1991). We propose several algorithms achieving logarithmic regret, which besides being more general are also much more efficient to implement. The main new ideas give rise to an efficient algorithm based on the Newton method for optimization, a new tool in the field. Our analysis shows a surprising connection between the natural follow-the-leader approach and the Newton method. We also analyze other algorithms, which tie together several different previous approaches including follow-the-leader, exponential weighting, Cover’s algorithm and gradient descent.

Simultaneous adaptation to the margin and to complexity in classification

We consider the problem of adaptation to the margin and to complexity in binary classification. We suggest an exponential weighting aggregation scheme. We use this aggregation procedure to construct classifiers which adapt automatically to margin and complexity. Two main examples are worked out in which adaptivity is achieved in frameworks proposed by Steinwart and Scovel [Learning Theory. Lecture Notes in Comput. Sci. 3559 (2005) 279–294. Springer, Berlin; Ann. Statist. 35 (2007) 575–607] and Tsybakov [Ann. Statist. 32 (2004) 135–166]. Adaptive schemes, like ERM or penalized ERM, usually involve a minimization step. This is not the case for our procedure.

Single and multiple channel estimation using the time-updated recursive least squares algorithm

A time-updated recursive least squares algorithm (TURLS) is presented, analyzed, and applied to the problem of estimating the time-varying impulse response in both single and multiple channel cases. The TURLS algorithm may be viewed as a least squares extension of the EM channel estimation algorithm [W. Li and J. C. Preisig, ICASSP, IV 313IV, 316 (2005)], in the sense that it jointly estimates the channel impulse response and its dynamic parameters by minimizing a least squares error instead of maximizing the likelihood function. Based on the intuition that the sequence of channel estimates contains information regarding the true channel dynamics, the algorithm estimates the parameters from the sequence of channel estimates. Analysis of the algorithm based on a first-order AR channel model shows that the resulting channel estimate is a second-order approximation whose poles converge as the parameter estimate improves. In addition, it is shown that with exponential weighting, the resulting parameter estimate may be biased at low SNR level. The algorithm is applied to experimental data and results with both single channel and multiple channels are demonstrated. [Work supported by ONR Ocean Acoustics.]