A martingale approach to estimating confidence band with censored data

2014 ◽  
Vol 20 (4) ◽  
Author(s):  
Seung-Hwan Lee ◽  
Eun-Joo Lee
Keyword(s):  
Gaussian Process ◽  
Survival Function ◽  
Confidence Bands ◽  
Computer Assisted ◽  
Finite Sample ◽  
Real World Data ◽  
Data Set ◽  
Simulation Techniques ◽  
Simultaneous Confidence Bands ◽  
The Right

AbstractThis paper develops some non-parametric simultaneous confidence bands for survival function when data are randomly censored on the right. To construct the confidence bands, a computer-assisted method is utilized and this approach requires no distributional assumptions, so the confidence bands can be easily estimated. The procedures are based on the integrated martingale whose distribution is approximated by a Gaussian process. The supremum distribution of the Gaussian process generated by simulation techniques leads to the construction of the confidence bands. To improve the estimation procedures for the finite sample sizes, the log-minus-log transformation is employed. The proposed confidence bands are assessed using numerical simulations and applied to a real-world data set regarding leukemia.

A Research on Gaussian Process Based Feature Extraction

2013 ◽  
Vol 300-301 ◽  
pp. 848-852
Author(s):  
Zong Hai Sun ◽  
Osman Osman
Keyword(s):  
Feature Extraction ◽  
Gaussian Process ◽  
Latent Variable ◽  
Original Data ◽  
Data Sets ◽  
Real World Data ◽  
Cancer Treatments ◽  
Variable Model ◽  
Data Set ◽  
Comparison Of The Results

Data sets of high–dimensional spaces are problematic when it comes to classification, compression, and visualization. The main issue is to find a reduced dimensionality representation that corresponds to the intrinsic dimensionality of the original data. In this paper we try to investigate a practical Bayesian method for feature extracting problem, in particular we will apply Gaussian Process Latent Variable Model (GPLVM) to a real world data set. Feature extraction experiments were performed on a cancer treatments’ components data set using GPLVM, then we used PCA on the same data set for comparison of the results.

scholarly journals Simultaneous Confidence Bands for the Estimation of Expected Discounted Warranty Costs for Coherent Systems under Minimal Repair

2018 ◽  
Vol 41 (1) ◽  
pp. 1-30
Author(s):  
Carlos Mario Lopera Gómez ◽  
Nelfi Gertrudis Gónzalez Álvarez
Keyword(s):  
Central Limit ◽  
Confidence Bands ◽  
Finite Sample ◽  
Minimal Repair ◽  
Coherent Systems ◽  
Coverage Probabilities ◽  
Simultaneous Confidence Bands ◽  
Relevant Variables ◽  
Warranty Cost ◽  
Warranty Costs

This paper develops simultaneous confidence bands using computer intensive methods based on resampling, for the expected discounted warranty costs in coherent systems under physical minimal repair, that is, when the system is observed at its components level and only the component that causes the fault is minimally repaired. For this purpose, it is shown that, under the framework of the Martingale processes and the central limit resampling theorem (CLRT) over stochastic processes, the discounted warranty cost processes satisfy the conditions set by the central limit resampling theorem (CLRT). Additionally, a simulation study is performed on the most relevant variables, such that the finite sample features of the proposed bands may be assessed, based on their actual coverage probabilities. The results in the considered scenarios show that resampling-based simultaneous confidence bands have coverage probabilities that are close to the nominal coverage. In particular, the agreement is good when there are 100 systems or more where a large number of resamples are used for the approximation.

Exchange Spin Coupling from Gaussian Process Regression

2020 ◽  
Author(s):  
Marc Philipp Bahlke ◽  
Natnael Mogos ◽  
Jonny Proppe ◽  
Carmen Herrmann
Keyword(s):  
Machine Learning ◽  
Gaussian Process ◽  
Gaussian Process Regression ◽  
Molecular Magnets ◽  
Molecular Structures ◽  
Spin Coupling ◽  
Structure Property ◽  
Data Set ◽  
Uncertainty Estimates

Heisenberg exchange spin coupling between metal centers is essential for describing and understanding the electronic structure of many molecular catalysts, metalloenzymes, and molecular magnets for potential application in information technology. We explore the machine-learnability of exchange spin coupling, which has not been studied yet. We employ Gaussian process regression since it can potentially deal with small training sets (as likely associated with the rather complex molecular structures required for exploring spin coupling) and since it provides uncertainty estimates (“error bars”) along with predicted values. We compare a range of descriptors and kernels for 257 small dicopper complexes and find that a simple descriptor based on chemical intuition, consisting only of copper-bridge angles and copper-copper distances, clearly outperforms several more sophisticated descriptors when it comes to extrapolating towards larger experimentally relevant complexes. Exchange spin coupling is similarly easy to learn as the polarizability, while learning dipole moments is much harder. The strength of the sophisticated descriptors lies in their ability to linearize structure-property relationships, to the point that a simple linear ridge regression performs just as well as the kernel-based machine-learning model for our small dicopper data set. The superior extrapolation performance of the simple descriptor is unique to exchange spin coupling, reinforcing the crucial role of choosing a suitable descriptor, and highlighting the interesting question of the role of chemical intuition vs. systematic or automated selection of features for machine learning in chemistry and material science.

A Critical Look into the Deviation of Full Scale Performance from Design Expectations

1989 ◽  
Vol 21 (10-11) ◽  
pp. 1389-1402 ◽  
Author(s):  
R. Zaloum
Keyword(s):  
Expert Systems ◽  
Waste Treatment ◽  
Full Scale ◽  
Operating Conditions ◽  
Organic Load ◽  
Computer Assisted ◽  
Uniform Load ◽  
Effluent Quality ◽  
Simulation Techniques ◽  
Steady Level

Deviations from design expectations appear to stem from views which assume that a unique response should result from a given set of operating conditions. The results of this study showed that two systems operating at equal organic loads or F/M ratios and at the same SRT do not necessarily give equal responses. This deviation was linked to the manner in which the HRT and influent COD are manipulated to obtain a constant or uniform load, and to subtle interactions between influent COD, HRT and SRT on the biomass and effluent responses. Increases of up to 200% in influent COD from one steady level to the next did not significantly influence the effluent VSS concentration while an effect on filtered COD was observed for increases as low as 20%. Effluent TKN and filtered COD correlated strongly with the operating MLVSS while phosphorus residual depended on the operating SRT and the organic load removed. These results point to the inadequacy of traditional models to predict effluent quality and point to the need to consider these effects when developing simulation techniques or computer assisted expert systems for the control of waste treatment plants.

Auto-sharing parameters for transfer learning based on multi-objective optimization

2021 ◽  
pp. 1-13
Author(s):  
Hailin Liu ◽  
Fangqing Gu ◽  
Zixian Lin
Keyword(s):  
Transfer Learning ◽  
Optimization Problem ◽  
Data Sets ◽  
Multi Objective Optimization ◽  
Particle Swarm Optimizer ◽  
Real World Data ◽  
Data Set ◽  
Target Task ◽  
Main Research ◽  
Multi Objective

Transfer learning methods exploit similarities between different datasets to improve the performance of the target task by transferring knowledge from source tasks to the target task. “What to transfer” is a main research issue in transfer learning. The existing transfer learning method generally needs to acquire the shared parameters by integrating human knowledge. However, in many real applications, an understanding of which parameters can be shared is unknown beforehand. Transfer learning model is essentially a special multi-objective optimization problem. Consequently, this paper proposes a novel auto-sharing parameter technique for transfer learning based on multi-objective optimization and solves the optimization problem by using a multi-swarm particle swarm optimizer. Each task objective is simultaneously optimized by a sub-swarm. The current best particle from the sub-swarm of the target task is used to guide the search of particles of the source tasks and vice versa. The target task and source task are jointly solved by sharing the information of the best particle, which works as an inductive bias. Experiments are carried out to evaluate the proposed algorithm on several synthetic data sets and two real-world data sets of a school data set and a landmine data set, which show that the proposed algorithm is effective.

Assessing bias, precision, and agreement in method comparison studies

2019 ◽  
Vol 29 (3) ◽  
pp. 778-796 ◽  
Author(s):  
Patrick Taffé
Keyword(s):  
Measurement Method ◽  
Method Comparison ◽  
Estimation Procedure ◽  
Measurement Methods ◽  
Repeated Measurements ◽  
Confidence Bands ◽  
The Other ◽  
Reference Standard ◽  
Simultaneous Confidence Bands ◽  
Index Of Agreement

Recently, a new estimation procedure has been developed to assess bias and precision of a new measurement method, relative to a reference standard. However, the author did not develop confidence bands around the bias and standard deviation curves. Therefore, the goal in this paper is to extend this methodology in several important directions. First, by developing simultaneous confidence bands for the various parameters estimated to allow formal comparisons between different measurement methods. Second, by proposing a new index of agreement. Third, by providing a series of new graphs to help the investigator to assess bias, precision, and agreement between the two measurement methods. The methodology requires repeated measurements on each individual for at least one of the two measurement methods. It works very well to estimate the differential and proportional biases, even with as few as two to three measurements by one of the two methods and only one by the other. The repeated measurements need not come from the reference standard but from either measurement methods. This is a great advantage as it may sometimes be more feasible to gather repeated measurements with the new measurement method.

Broadband Combustion Noise Prediction With the Fast Random Particle Method

2014 ◽  
Author(s):  
Felix Grimm ◽  
Roland Ewert ◽  
Jürgen Dierke ◽  
Berthold Noll ◽  
Manfred Aigner
Keyword(s):  
Scaling Law ◽  
Particle Method ◽  
Reconstruction Algorithm ◽  
Combustion Noise ◽  
Frequency Noise ◽  
Noise Prediction ◽  
Data Set ◽  
Jet Flame ◽  
The Right ◽  
Random Particle

A new highly efficient, hybrid CFD/CAA approach for broadband combustion noise modeling is introduced. The inherent sound source generation mechanism is based on turbulent flow field statistics, which are determined from reacting RANS calculations. The generated sources form the right-hand side of the linearized Euler equations for the calculation of sound fields. The stochastic time-domain source reconstruction algorithm is briefly described with emphasis on two different ways of spatial discretization, RPM (Random Particle Method) and the newly developed FRPM (Fast RPM). The application of mainly the latter technique to combustion noise (CN) prediction and several methodical progressions are presented in the paper. (F)RPM-CN is verified in terms of its ability to accurately reproduce prescribed turbulence-induced one- and two-point statistics for a generic test and the DLR-A jet flame validation case. Former works on RPM-CN have been revised and as a consequence methodical improvements are introduced along with the progression to FRPM-CN: A canonical CAA setup for the applications DLR-A, -B and H3 flame is used. Furthermore, a second order Langevin decorrelation model is introduced for FRPM-CN, to avoid spurious high frequency noise. A new calibration parameter set for reacting jet noise prediction with (F)RPM-CN is proposed. The analysis shows the universality of the data set for 2D jet flame applications and furthermore the method’s accountance for Reynolds scalability. In this context, a Mach number scaling law is used to conserve Strouhal similarity of the jet flame spectra. Finally, the numerical results are compared to suitable similarity spectra.

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