Robust mixtures in the presence of measurement errors

We develop a mixture-based approach to robust density modeling and outlier detection for experimental multivariate data that includes measurement error information. Our model is designed to infer atypical measurements that are not due to errors, aiming to retrieve potentially interesting peculiar objects. Since exact inference is not possible in this model, we develop a tree-structured variational EM solution. This compares favorably against a fully factorial approximation scheme, approaching the accuracy of a Markov-Chain-EM, while maintaining computational simplicity. We demonstrate the benefits of including measurement errors in the model, in terms of improved outlier detection rates in varying measurement uncertainty conditions. We then use this approach in detecting peculiar quasars from an astrophysical survey, given photometric measurements with errors.Comment: (Refereed) Proceedings of the 24-th Annual International Conference on Machine Learning 2007 (ICML07), (Ed.) Z. Ghahramani. June 20-24, 2007, Oregon State University, Corvallis, OR, USA, pp. 847-854; Omnipress. ISBN 978-1-59593-793-3; 8 pages, 6 figure

Broadband boundary effects on Brownian motion

Brownian motion of particles in confined fluids is important for many applications, yet the effects of the boundary over a wide range of time scales are still not well understood. We report high-bandwidth, comprehensive measurements of Brownian motion of an optically trapped micrometer-sized silica sphere in water near an approximately flat wall. At short distances we observe anisotropic Brownian motion with respect to the wall. We find that surface confinement not only occurs in the long time scale diffusive regime but also in the short time scale ballistic regime, and the velocity autocorrelation function of the Brownian particle decays faster than that of a particle in bulk fluid. Furthermore, at low frequencies the thermal force loses its color due to the reflected flow from the no-slip boundary. The power spectrum of the thermal force on the particle near a no-slip boundary becomes flat at low frequencies. This detailed understanding of boundary effects on Brownian motion opens a door to developing a 3D microscope using particles as remote sensors.Sid W. Richardson FoundationR. A. Welch Foundation F-1258Physic