Gaussian Process training with input noise

In standard Gaussian Process regression input locations are assumed to be noise free. We present a simple yet effective GP model for training on input points corrupted by i.i.d. Gaussian noise. To make computations tractable we use a local linear expansion about each input point. This allows the input noise to be recast as output noise proportional to the squared gradient of the GP posterior mean. The input noise variances are inferred from the data as extra hyperparameters. They are trained alongside other hyperparameters by the usual method of maximisation of the marginal likelihood. Training uses an iterative scheme, which alternates between optimising the hyperparameters and calculating the posterior gradient. Analytic predictive moments can then be found for Gaussian distributed test points. We compare our model to others over a range of different regression problems and show that it improves over current methods.

Spoken Dialog Challenge 2010: Comparison of live and control test results

The Spoken Dialog Challenge 2010 was an exercise to investigate how different spoken dialog systems perform on the same task. The existing Let's Go Pittsburgh Bus Information System was used as a task and four teams provided systems that were first tested in controlled conditions with speech researchers as users. The three most stable systems were then deployed to real callers. This paper presents the results of the live tests, and compares them with the control test results. Results show considerable variation both between systems and between the control and live tests. Interestingly, relatively high task completion for controlled tests did not always predict relatively high task completion for live tests. Moreover, even though the systems were quite different in their designs, we saw very similar correlations between word error rate and task completion for all the systems. The dialog data collected is available to the research community. © 2011 Association for Computational Linguistics.

Stiffness of sands through a laboratory test database

Deformations of sandy soils around geotechnical structures generally involve strains in the range small (0·01%) to medium (0·5%). In this strain range the soil exhibits non-linear stress-strain behaviour, which should be incorporated in any deformation analysis. In order to capture the possible variability in the non-linear behaviour of various sands, a database was constructed including the secant shear modulus degradation curves of 454 tests from the literature. By obtaining a unique S-shaped curve of shear modulus degradation, a modified hyperbolic relationship was fitted. The three curve-fitting parameters are: an elastic threshold strain γe, up to which the elastic shear modulus is effectively constant at G0; a reference strain γr, defined as the shear strain at which the secant modulus has reduced to 0·5G0; and a curvature parameter a, which controls the rate of modulus reduction. The two characteristic strains γe and γr were found to vary with sand type (i.e. uniformity coefficient), soil state (i.e. void ratio, relative density) and mean effective stress. The new empirical expression for shear modulus reduction G/G0 is shown to make predictions that are accurate within a factor of 1·13 for one standard deviation of random error, as determined from 3860 data points. The initial elastic shear modulus, G0, should always be measured if possible, but a new empirical relation is shown to provide estimates within a factor of 1·6 for one standard deviation of random error, as determined from 379 tests. The new expressions for non-linear deformation are easy to apply in practice, and should be useful in the analysis of geotechnical structures under static loading.

Control of a shock-wave/boundary-layer interaction and subsequent subsonic diffuser using a combination of vortex generators and bleed

An experimental investigation has been undertaken in which vortex generators (VGs) have been employed to inhibit boundary-layer separation produced by the combined adversepressure- gradient of a terminal shock-wave and subsonic diffuser. This setup has been developed as part of a program to produce a more inlet relevant flow-field using a small-scale wind tunnel than previous studies. The resulting flow is dominated by large-scale separation, and as such, is thought to be a good test-bed for flow control. In this investigation, VGs have been added to determine their potential for shock-induced separation mitigation. In line with previous studies, it was observed that the application of VGs alone was not able to significantly alleviate separation overall, because enlarged corner separations was observed. Only when control of the corner separations using corner bleed was employed alongside centre-span control using VGs was a significant improvement in both wall pressure recovery (6% increase) and stagnation pressure recovery (2.4% increase) observed. Copyright © 2012 by the American Institute of Aeronautics and Astronautics, Inc.

Generalized power method for sparse principal component analysis

In this paper we develop a new approach to sparse principal component analysis (sparse PCA). We propose two single-unit and two block optimization formulations of the sparse PCA problem, aimed at extracting a single sparse dominant principal component of a data matrix, or more components at once, respectively. While the initial formulations involve nonconvex functions, and are therefore computationally intractable, we rewrite them into the form of an optimization program involving maximization of a convex function on a compact set. The dimension of the search space is decreased enormously if the data matrix has many more columns (variables) than rows. We then propose and analyze a simple gradient method suited for the task. It appears that our algorithm has best convergence properties in the case when either the objective function or the feasible set are strongly convex, which is the case with our single-unit formulations and can be enforced in the block case. Finally, we demonstrate numerically on a set of random and gene expression test problems that our approach outperforms existing algorithms both in quality of the obtained solution and in computational speed. © 2010 Michel Journée, Yurii Nesterov, Peter Richtárik and Rodolphe Sepulchre.