Bayesian Gaussian Copula Factor Models for Mixed Data.

Gaussian factor models have proven widely useful for parsimoniously characterizing dependence in multivariate data. There is a rich literature on their extension to mixed categorical and continuous variables, using latent Gaussian variables or through generalized latent trait models acommodating measurements in the exponential family. However, when generalizing to non-Gaussian measured variables the latent variables typically influence both the dependence structure and the form of the marginal distributions, complicating interpretation and introducing artifacts. To address this problem we propose a novel class of Bayesian Gaussian copula factor models which decouple the latent factors from the marginal distributions. A semiparametric specification for the marginals based on the extended rank likelihood yields straightforward implementation and substantial computational gains. We provide new theoretical and empirical justifications for using this likelihood in Bayesian inference. We propose new default priors for the factor loadings and develop efficient parameter-expanded Gibbs sampling for posterior computation. The methods are evaluated through simulations and applied to a dataset in political science. The models in this paper are implemented in the R package bfa.

Task-driven adaptive statistical compressive sensing of gaussian mixture models

A framework for adaptive and non-adaptive statistical compressive sensing is developed, where a statistical model replaces the standard sparsity model of classical compressive sensing. We propose within this framework optimal task-specific sensing protocols specifically and jointly designed for classification and reconstruction. A two-step adaptive sensing paradigm is developed, where online sensing is applied to detect the signal class in the first step, followed by a reconstruction step adapted to the detected class and the observed samples. The approach is based on information theory, here tailored for Gaussian mixture models (GMMs), where an information-theoretic objective relationship between the sensed signals and a representation of the specific task of interest is maximized. Experimental results using synthetic signals, Landsat satellite attributes, and natural images of different sizes and with different noise levels show the improvements achieved using the proposed framework when compared to more standard sensing protocols. The underlying formulation can be applied beyond GMMs, at the price of higher mathematical and computational complexity. © 1991-2012 IEEE.

Sticky central limit theorems on open books

Given a probability distribution on an open book (a metric space obtained by gluing a disjoint union of copies of a half-space along their boundary hyperplanes), we define a precise concept of when the Fréchet mean (barycenter) is sticky. This nonclassical phenomenon is quantified by a law of large numbers (LLN) stating that the empirical mean eventually almost surely lies on the (codimension 1 and hence measure 0) spine that is the glued hyperplane, and a central limit theorem (CLT) stating that the limiting distribution is Gaussian and supported on the spine.We also state versions of the LLN and CLT for the cases where the mean is nonsticky (i.e., not lying on the spine) and partly sticky (i.e., is, on the spine but not sticky). © Institute of Mathematical Statistics, 2013.

Geodesically reversible Finsler 2-spheres of constant curvature

A Finsler space is said to be geodesically reversible if each oriented geodesic can be reparametrized as a geodesic with the reverse orientation. A reversible Finsler space is geodesically reversible, but the converse need not be true. In this note, building on recent work of LeBrun and Mason, it is shown that a geodesically reversible Finsler metric of constant flag curvature on the 2-sphere is necessarily projectively flat. As a corollary, using a previous result of the author, it is shown that a reversible Finsler metric of constant flag curvature on the 2-sphere is necessarily a Riemannian metric of constant Gauss curvature, thus settling a long- standing problem in Finsler geometry.

Gaussian Process Kernels for Cross-Spectrum Analysis in Electrophysiological Time Series

Multi-output Gaussian processes provide a convenient framework for multi-task problems. An illustrative and motivating example of a multi-task problem is multi-region electrophysiological time-series data, where experimentalists are interested in both power and phase coherence between channels. Recently, the spectral mixture (SM) kernel was proposed to model the spectral density of a single task in a Gaussian process framework. This work develops a novel covariance kernel for multiple outputs, called the cross-spectral mixture (CSM) kernel. This new, flexible kernel represents both the power and phase relationship between multiple observation channels. The expressive capabilities of the CSM kernel are demonstrated through implementation of 1) a Bayesian hidden Markov model, where the emission distribution is a multi-output Gaussian process with a CSM covariance kernel, and 2) a Gaussian process factor analysis model, where factor scores represent the utilization of cross-spectral neural circuits. Results are presented for measured multi-region electrophysiological data.

FtsZ Protofilament Curvature is the Opposite of Tubulin Rings

Bacterial tubulin homolog FtsZ assembles straight protofilaments (pfs) that form the scaffold of the cytokinetic Z ring. These pfs can adopt a curved conformation forming a miniring or spiral tube 24 nm in diameter. Tubulin pfs also have a curved conformation, forming 42 nm tubulin rings. We have previously provided evidence that FtsZ generates a constriction force by switching from straight pfs to the curved conformation, generating a bending force on the membrane. In the simplest model the membrane tether, which exits from the C terminus of the globular FtsZ, would have to be on the outside of the curved pf. However, it is well established that tubulin rings have the C terminus on the inside of the ring. Could FtsZ and tubulin rings have the opposite curvature? In the present study we explored the direction of curvature of FtsZ rings by fusing large protein tags to the N or C terminus of the FtsZ globular domain. FtsZ with a protein tag on the N terminus did not assemble tubes. This was expected if the N terminus is on the inside, because the protein tags are too big to fit in the interior of the tube. FtsZ with C-terminal tags assembled normal tubes, consistent with the C terminus on the outside. The FN extension was not visible in negative stain, but thin section EM gave definitive evidence that the C-terminal tag was on the outside of the tubes. This has interesting implications for the evolution of tubulin. It seems likely that tubulin began with the curvature of FtsZ, which would have resulted in pfs curving toward the interior of a disassembling MT. Evolution not only eliminated this undesirable curvature, but managed to reverse direction to produce the outward curving rings, which is useful for pulling chromosomes.