Local tests for consistency of support hyperplane data

Caption title.Includes bibliographical references (p. 32-33).Supported by the U.S. Army Research Office. DAAL03-92-G-0115 DAAL03-92-G-0320 Supported by the Office of Naval Research. N00014-91-J-1004 Supported by the National Science Foundation. MIP-9015281 IRI-9209577William C. Karl ... [et al.]

Bayesian nonparametric multivariate convex regression

In many applications, such as economics, operations research and reinforcement learning, one often needs to estimate a multivariate regression function f subject to a convexity constraint. For example, in sequential decision processes the value of a state under optimal subsequent decisions may be known to be convex or concave. We propose a new Bayesian nonparametric multivariate approach based on characterizing the unknown regression function as the max of a random collection of unknown hyperplanes. This specification induces a prior with large support in a Kullback-Leibler sense on the space of convex functions, while also leading to strong posterior consistency. Although we assume that f is defined over R^p, we show that this model has a convergence rate of log(n)^{-1} n^{-1/(d+2)} under the empirical L2 norm when f actually maps a d dimensional linear subspace to R. We design an efficient reversible jump MCMC algorithm for posterior computation and demonstrate the methods through application to value function approximation

A robust morphological classification of high-redshift galaxies using support vector machines on seeing limited images. I Method description

We present a new non-parametric method to quantify morphologies of galaxies based on a particular family of learning machines called support vector machines. The method, that can be seen as a generalization of the classical CAS classification but with an unlimited number of dimensions and non-linear boundaries between decision regions, is fully automated and thus particularly well adapted to large cosmological surveys. The source code is available for download at http://www.lesia.obspm.fr/~huertas/galsvm.html To test the method, we use a seeing limited near-infrared ($K_s$ band, $2,16\mu m$) sample observed with WIRCam at CFHT at a median redshift of $z\sim0.8$. The machine is trained with a simulated sample built from a local visually classified sample from the SDSS chosen in the high-redshift sample's rest-frame (i band, $0.77\mu m$) and artificially redshifted to match the observing conditions. We use a 12-dimensional volume, including 5 morphological parameters and other caracteristics of galaxies such as luminosity and redshift. We show that a qualitative separation in two main morphological types (late type and early type) can be obtained with an error lower than 20% up to the completeness limit of the sample ($KAB\sim 22$) which is more than 2 times better that what would be obtained with a classical C/A classification on the same sample and indeed comparable to space data. The method is optimized to solve a specific problem, offering an objective and automated estimate of errors that enables a straightforward comparison with other surveys.Comment: 11 pages, 7 figures, 3 tables. Submitted to A&A. High resolution images are available on reques

Operators for transforming kernels into quasi-local kernels that improve SVM accuracy

Motivated by the crucial role that locality plays in various learning approaches, we present, in the framework of kernel machines for classification, a novel family of operators on kernels able to integrate local information into any kernel obtaining quasi-local kernels. The quasi-local kernels maintain the possibly global properties of the input kernel and they increase the kernel value as the points get closer in the feature space of the input kernel, mixing the effect of the input kernel with a kernel which is local in the feature space of the input one. If applied on a local kernel the operators introduce an additional level of locality equivalent to use a local kernel with non-stationary kernel width. The operators accept two parameters that regulate the width of the exponential influence of points in the locality-dependent component and the balancing between the feature-space local component and the input kernel. We address the choice of these parameters with a data-dependent strategy. Experiments carried out with SVM applying the operators on traditional kernel functions on a total of 43 datasets with di®erent characteristics and application domains, achieve very good results supported by statistical significance

Becker random behavior and the as-if defense of rational choice theory in demand analysis

In discussing rational choice theory (RCT) as an explanation of demand behavior, Becker (1962, Journal of Political Economy, 70, 1–13) proposed a model of random choice in which consumers pick a bundle on their budget line according to a uniform distribution. This model has then been used in various ways to assess the validity of RCT and to support as-if arguments in defense of it. This paper makes both historical and methodological contributions. Historically, it investigates how the interpretation of Becker random behavior evolved between the original 1962 article and the modern experimental literature on individual demand, and surveys six experiments in which it has been used as an alternative hypothesis to RCT. Methodologically, this paper conducts an assessment of the as-if defense of RCT from the standpoint of Becker’s model. It argues that this defense is ‘weak’ in a number of senses, and that it has negatively influenced the design of experiments about RCT