Accuracy estimation for supervised learning algorithms

This paper illustrates the relative merits of three methods - k-fold Cross Validation, Error Bounds, and Incremental Halting Test - to estimate the accuracy of a supervised learning algorithm. For each of the three methods we point out the problem they address, some of the important assumptions that are based on, and illustrate them through an example. Finally, we discuss the relative advantages and disadvantages of each method

Recurrence Plot Based Measures of Complexity and its Application to Heart Rate Variability Data

The knowledge of transitions between regular, laminar or chaotic behavior is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there are several nonlinear methods which however require rather long time observations. To overcome these difficulties, we propose measures of complexity based on vertical structures in recurrence plots and apply them to the logistic map as well as to heart rate variability data. For the logistic map these measures enable us not only to detect transitions between chaotic and periodic states, but also to identify laminar states, i.e. chaos-chaos transitions. The traditional recurrence quantification analysis fails to detect the latter transitions. Applying our new measures to the heart rate variability data, we are able to detect and quantify the laminar phases before a life-threatening cardiac arrhythmia occurs thereby facilitating a prediction of such an event. Our findings could be of importance for the therapy of malignant cardiac arrhythmias

N-learners problem: Fusion of concepts

We are given N learners each capable of learning concepts (subsets) of a domain set X in the sense of Valiant, i.e. for any c {element of} C {improper subset} 2{sup X}, given a finite set of examples of the form ; ;...; generated according to an unknown probability distribution P{sub X} on X, each learner produces a close approximation to c with a high probability. We are interested in combining the N learners using a single fuser or consolidator. We consider the paradigm of passive fusion, where each learner is first trained with the sample without the influence of the consolidator. The composite system is constituted by the fuser and the individual learners. We consider two cases: open and closed fusion. In open fusion the fuser is given the sample and the hypotheses of the individual learners; we show that the fusion rule can be obtained by formulating this problem as another learning problem. For the case all individual learners are trained with the same sample, we show sufficiency conditions that ensure the composite system to be better than the best of the individual: the hypothesis space of the consolidator (a) satisfies the isolation property of degree at least N, and (b) has Vapnik-Chervonenkis dimension less than or equal to that of every individual learner. If individual learners are trained by independently generated samples, we obtain a much weaker bound on the VC-dimension of the hypothesis space of the fuser. Second, in closed fusion the fuser does not have an access to either the training sample or the hypotheses of the individual learners. By suitable designing a linear threshold function of the outputs of individual learners, we show that the composite system can be made better than the best of the learners

Sensitivity theory for reactor thermal-hydraulics problems

A sensitivity theory based on reactor physics experience was successfully developed for a reactor thermal-hydraulics problem. The new theory is derived for the case of non-linear, transient heat and mass transfer in a typical reactor subassembly. Suitable adjoint equations for heat and fluid flow are presented along with methods for deriving the sources and boundary and final conditions for these equations. Expressions for the sensitivity of any integral temperature response to problem input data are also presented. The theory is applied to a sample problem describing the steady-state thermal-hydraulic conditions in a CRBR fuel channel. For this case, sensitivity coefficients are derived for several thermal response functions (i.e., peak clad and peak fuel temperature) for all physical input data (i.e., the heat transfer coefficient, thermal conductivities, etc.). A typical uncertainty analysis for peak clad and peak fuel temperature was also performed using uncertainty information about the physical data. Conclusions are drawn about the applicability of this approach to more general problems and the procedures for its implementation in conjunction with large safety or thermal-hydraulics codes are outlined. The method is also compared with currently used response surface techniques

Analysis of a neutron scattering and gamma-ray production integral and experiment on silicon dioxide for neutron energies from 1 to 15 MeV

Monte Carlo calculations were made to analyze the results of an integral experiment with a sample of SiO/sub 2/ to determine the adequacy of ENDF/B-IV neutron scattering and gamma-ray production cross-section data for silicon and oxygen. The experimental results analyzed included energy-dependent NE-213 detector neutron and gamma-ray count rates at a scattering angle of 90 deg and pulse-height spectra for scattered neutrons and gamma rays. The experiments were carried out with the ORELA 1- to 20-MeV pulsed neutron source. The pulse-height data were unfolded to generate secondary neutron and gamma-ray spectra at 90 deg as a function of incident neutron energy. Multigroup Monte Carlo calculations using the MORSE code and ENDF/B-IV cross sections were made to analyze all reported results. No outstanding discrepancies between calculated and measured responses were found on the neutron data below 12 MeV. Possible discrepancies in the inelastic scattering data above 12 MeV are indicated. This is consistent with a previous analysis of an oxygen experiment. A more detailed analysis will have to be performed before any definite conclusions can be drawn from these comparisons

Analysis of a neutron scattering and gamma-ray production integral experiment on aluminum for neutron energies from 1 to 15 MeV

Monte Carlo calculations were made to analyze the results of an integral experiment with an aluminum sample to determine the adequacy of ENDF/B-IV neutron scattering and gamma-ray production cross-section data for aluminum. The experimental results analyzed included energy-dependent NE-213 detector neutron and gamma-ray count rates at a scattering angle of 125 deg and pulse-height spectra for scattered neutrons and gamma-rays. The experiments were carried out with the ORELA 1- to 20-MeV pulsed neutron source. The pulse-height data were unfolded to generate secondary neutron and gamma-ray spectra at 125 deg as a function of incident neutron energy. Multigroup Monte Carlo calculations using the MORSE code and ENDF/B-IV cross sections were made to analyze all reported results. Discrepancies between calculated and measured responses were found for secondary neutron scattering data above 10 MeV and for gamma-rays produced at energies between 4 and 7 MeV. A detailed analysis has not yet been performed to determine the reasons for these discrepancies