Over-Fitting in Model Selection with Gaussian Process Regression

Model selection in Gaussian Process Regression (GPR) seeks to determine the optimal values of the hyper-parameters governing the covariance function, which allows flexible customization of the GP to the problem at hand. An oft-overlooked issue that is often encountered in the model process is over-fitting the model selection criterion, typically the marginal likelihood. The over-fitting in machine learning refers to the fitting of random noise present in the model selection criterion in addition to features improving the generalisation performance of the statistical model. In this paper, we construct several Gaussian process regression models for a range of high-dimensional datasets from the UCI machine learning repository. Afterwards, we compare both MSE on the test dataset and the negative log marginal likelihood (nlZ), used as the model selection criteria, to find whether the problem of overfitting in model selection also affects GPR. We found that the squared exponential covariance function with Automatic Relevance Determination (SEard) is better than other kernels including squared exponential covariance function with isotropic distance measure (SEiso) according to the nLZ, but it is clearly not the best according to MSE on the test data, and this is an indication of over-fitting problem in model selection

Locating very high energy gamma ray sources with arc minute accuracy

The angular accuracy of gamma-ray detectors is intrinsically limited by the physical processes involved in photon detection. Although a number of point-like sources were detected by the COS-B satellite, only two were unambiguously identified by time signature with counterparts at longer wavelengths. By taking advantage of the extended longitudinal structure of Very High Energy gamma-ray showers, measurements in the TeV energy range can pinpoint source coordinates to arc minute accuracy. This was demonstrated using Cerenkov air shower imaging techniques. With two telescopes in coincidence, the individual event circular probable error will be 0.13 deg. The half-cone angle of the field of view is effectively 1 deg

Observations of TeV gamma rays from Markarian 501 at large zenith angles

TeV gamma rays from the blazar Markarian 501 have been detected with the University of Durham Mark 6 atmospheric Cerenkov telescope using the imaging technique at large zenith angles. Observations were made at zenith angles in the range 70 - 73 deg during 1997 July and August when Markarian 501 was undergoing a prolonged and strong flare.Comment: 7 pages, 2 figures, accepted for publication in J. Phys. G.: Nucl. Part. Phy

Status of the Whipple Observatory Cerenkov air shower imaging telescope array

Recently the power of the Cerenkov imaging technique in Very High Energy gamma-ray astronomy was demonstrated by the detection of the Crab nebula at high statistical significance. In order to further develop this technique to allow the detection of weaker or more distant sources a second 10 m class reflector was constructed about 120 m from the original instrument. The addition of the second reflector will allow both a reduction in the energy threshold and an improvement in the rejection of the hadronic background. The design and construction of the second reflector, Gamma Ray Astrophysics New Imaging TElescope (GRANITE) is described

Application of imaging to the atmospheric Cherenkov technique

Turver and Weekes proposed using a system of phototubes in the focal plane of a large reflector to give an air Cherenkov camera for gamma ray astronomy. Preliminary results with a 19 element camera have been reported previously. In 1983 the camera was increased to 37 pixels; it has now been routinely operated for two years. A brief physical description of the camera, its mode of operation, and the data reduction procedures are presented. The Monte Carlo simultations on which these are based on also reviewed

Oxidation of Carbon/Carbon through Coating Cracks

Reinforced carbon/carbon (RCC) is used to protect the wing leading edge and nose cap of the Space Shuttle Orbiter on re-entry. It is composed of a lay-up of carbon/carbon fabric protected by a SiC conversion coating. Due to the thermal expansion mismatch of the carbon/carbon and the SiC, the SiC cracks on cool-down from the processing temperature. The cracks act as pathways for oxidation of the carbon/carbon. A model for the diffusion controlled oxidation of carbon/carbon through machined slots and cracks is developed and compared to laboratory experiments. A symmetric cylindrical oxidation cavity develops under the slots, confirming diffusion control. Comparison of cross sectional dimensions as a function of oxidation time shows good agreement with the model. A second set of oxidation experiments was done with samples with only the natural craze cracks, using weight loss as an index of oxidation. The agreement of these rates with the model is quite reasona

Variability in the high energy gamma ray emission from Cyg X-3 over a two-year period (1983 - 1984) at E 4 x 10(11) eV

Cygnus X-3 is observed to emit gamma rays with energies in excess of 4 x 10 to the 11th power eV during two out of 9 observational categories over an 18 month time span. The emissions are observed at the 0.6 phase of the characteristic 4.8 hr light curve for this binary system. We estimate a peak flux at phase 0.6 of 5 x 10 to the minus 10th power photons cm-2s-1 at a software threshold of 8 x 10 to the 11th power eV for Oct/Nov 1983. A flux for the June 84 effect cannot be reliably calculated at present due to lack of Monte Carlo simulations for the energy range and spectral region. For the other 7 observational categories the observations are consistent with zero source emission. The light curve would appear to be variable on a time scale of a couple of weeks at these categories. Selection of compact images in accordance with Monte Carlo simulations combined with empirical optimization techniques have led to an enriched gamma ray light curve for the Oct/Nov 1983 data. Selection on the basis of shower orientation, however, has not led to any notable enhancement of the gamma ray content. Individual Cherenko images can be reliably sorted on an event by event basis into either proton-induced or photon-induced showers

Search for gamma-rays from M31 and other extragalactic objects

Although the existence of fluxes of gamma-rays of energies 10 to the 12th power eV is now established for galactic sources, the detection of such gamma-rays from extragalactic sources has yet to be independently confirmed in any case. The detection and confirmation of such energetic photons is of great astrophysical importance in the study of production mechanisms for cosmic rays, and other high energy processes in extragalactic objects. Observations of m31 are discussed. It is reported as a 10 to the 12th power eV gamma-ray source. Flux limits on a number of other extragalactic objects chosen for study are given