The Matrix Ridge Approximation: Algorithms and Applications

We are concerned with an approximation problem for a symmetric positive semidefinite matrix due to motivation from a class of nonlinear machine learning methods. We discuss an approximation approach that we call {matrix ridge approximation}. In particular, we define the matrix ridge approximation as an incomplete matrix factorization plus a ridge term. Moreover, we present probabilistic interpretations using a normal latent variable model and a Wishart model for this approximation approach. The idea behind the latent variable model in turn leads us to an efficient EM iterative method for handling the matrix ridge approximation problem. Finally, we illustrate the applications of the approximation approach in multivariate data analysis. Empirical studies in spectral clustering and Gaussian process regression show that the matrix ridge approximation with the EM iteration is potentially useful

Facts, Values and Quanta

Quantum mechanics is a fundamentally probabilistic theory (at least so far as the empirical predictions are concerned). It follows that, if one wants to properly understand quantum mechanics, it is essential to clearly understand the meaning of probability statements. The interpretation of probability has excited nearly as much philosophical controversy as the interpretation of quantum mechanics. 20th century physicists have mostly adopted a frequentist conception. In this paper it is argued that we ought, instead, to adopt a logical or Bayesian conception. The paper includes a comparison of the orthodox and Bayesian theories of statistical inference. It concludes with a few remarks concerning the implications for the concept of physical reality.Comment: 30 pages, AMS Late

Reliability based robust design optimization based on sensitivity and elasticity factors analysis

In this paper, a Reliability Based Robust Design Optimization (RBRDO) based on sensitivity and elasticity factors analysis is presented. In the first step, a reliability assessment is performed using the First-and Second Order Reliability Method (FORM)/ (SORM), and Monte Carlo Simulation. Furthermore, FORM method is used for reliability elasticity factors assessment, which can be carried out to determine the most influential parameters, these factors can be help to reduce the size of design variables vector in RBRDO process. The main objective of the RBRDO is to improve both reliability and design of a cylindrical gear pair under uncertainties. This approach is achieved by integration of two objectives which minimize the variance and mean values of performance function. To solve this problem a decoupled approach of Sequential Optimization and Reliability Assessment (SORA) method is implemented. The results obtained shown that a desired reliability with a robust design is progressively achieved

High redshift galaxies in the ALHAMBRA survey: I. selection method and number counts based on redshift PDFs

Context. Most observational results on the high redshift restframe UV-bright galaxies are based on samples pinpointed using the so called dropout technique or Ly-alpha selection. However, the availability of multifilter data allows now replacing the dropout selections by direct methods based on photometric redshifts. In this paper we present the methodology to select and study the population of high redshift galaxies in the ALHAMBRA survey data. Aims. Our aim is to develop a less biased methodology than the traditional dropout technique to study the high redshift galaxies in ALHAMBRA and other multifilter data. Thanks to the wide area ALHAMBRA covers, we especially aim at contributing in the study of the brightest, less frequent, high redshift galaxies. Methods. The methodology is based on redshift probability distribution functions (zPDFs). It is shown how a clean galaxy sample can be obtained by selecting the galaxies with high integrated probability of being within a given redshift interval. However, reaching both a complete and clean sample with this method is challenging. Hence, a method to derive statistical properties by summing the zPDFs of all the galaxies in the redshift bin of interest is introduced. Results. Using this methodology we derive the galaxy rest frame UV number counts in five redshift bins centred at z=2.5, 3.0, 3.5, 4.0, and 4.5, being complete up to the limiting magnitude at m_UV(AB)=24. With the wide field ALHAMBRA data we especially contribute in the study of the brightest ends of these counts, sampling well the surface densities down to m_UV(AB)=21-22. Conclusions. We show that using the zPDFs it is easy to select a clean sample of high redshift galaxies. We also show that statistical analysis of the properties of galaxies is better done using a probabilistic approach, which takes into account both the incompleteness and contamination in a natural way.Comment: 16 pages, 11 figures; Accepted for A&A; language correcte

Methodology for evaluating the safety level of current accepted design solutions for limiting fire spread between buildings

External fire spread between buildings is internationally considered as a major concern for buildings in dense urban environments. While design guidelines differ between countries, the fundamental methods currently used for limiting the risk of fire spread between buildings are generally limited to specifying the minimum required separation distance for a given unprotected façade area, or conversely, limiting the maximum allowable unprotected façade area for a given separation distance. The safety level associated with the current design guidelines is however unknown, making the implementation of innovative, safer and more cost-effective design solutions difficult. In order to assess the safety target implicitly incorporated in currently accepted design solutions, a methodology is developed for evaluating the annual probability of reaching unacceptable radiation intensities at the opposite façade. As a case study, the methodology is applied to a design which is in agreement with the current UK requirements specified in BR 187. This case study exposes inconsistencies in the current design guidelines, indicating the need for developing explicit safety targets

From conformal to probabilistic prediction

This paper proposes a new method of probabilistic prediction, which is based on conformal prediction. The method is applied to the standard USPS data set and gives encouraging results.Comment: 12 pages, 2 table