8,312 research outputs found
The Magnetic Topology of the Weak-Lined T Tauri Star V410 - A Simultaneous Temperature and Magnetic Field Inversion
We present a detailed temperature and magnetic investigation of the T Tauri
star V410 Tau by means of a simultaneous Doppler- and Zeeman-Doppler Imaging.
Moreover we introduce a new line profile reconstruction method based on a
singular value decomposition (SVD) to extract the weak polarized line profiles.
One of the key features of the line profile reconstruction is that the SVD line
profiles are amenable to radiative transfer modeling within our Zeeman-Doppler
Imaging code iMap. The code also utilizes a new iterative regularization scheme
which is independent of any additional surface constraints. To provide more
stability a vital part of our inversion strategy is the inversion of both
Stokes I and Stokes V profiles to simultaneously reconstruct the temperature
and magnetic field surface distribution of V410 Tau. A new image-shear analysis
is also implemented to allow the search for image and line profile distortions
induced by a differential rotation of the star. The magnetic field structure we
obtain for V410 Tau shows a good spatial correlation with the surface
temperature and is dominated by a strong field within the cool polar spot. The
Zeeman-Doppler maps exhibit a large-scale organization of both polarities
around the polar cap in the form of a twisted bipolar structure. The magnetic
field reaches a value of almost 2 kG within the polar region but smaller fields
are also present down to lower latitudes. The pronounced non-axisymmetric field
structure and the non-detection of a differential rotation for V410 Tau
supports the idea of an underlying -type dynamo, which is predicted
for weak-lined T Tauri stars.Comment: Accepted for A&A, 18 pages, 10 figure
Bayesian Sparse Factor Analysis of Genetic Covariance Matrices
Quantitative genetic studies that model complex, multivariate phenotypes are
important for both evolutionary prediction and artificial selection. For
example, changes in gene expression can provide insight into developmental and
physiological mechanisms that link genotype and phenotype. However, classical
analytical techniques are poorly suited to quantitative genetic studies of gene
expression where the number of traits assayed per individual can reach many
thousand. Here, we derive a Bayesian genetic sparse factor model for estimating
the genetic covariance matrix (G-matrix) of high-dimensional traits, such as
gene expression, in a mixed effects model. The key idea of our model is that we
need only consider G-matrices that are biologically plausible. An organism's
entire phenotype is the result of processes that are modular and have limited
complexity. This implies that the G-matrix will be highly structured. In
particular, we assume that a limited number of intermediate traits (or factors,
e.g., variations in development or physiology) control the variation in the
high-dimensional phenotype, and that each of these intermediate traits is
sparse -- affecting only a few observed traits. The advantages of this approach
are two-fold. First, sparse factors are interpretable and provide biological
insight into mechanisms underlying the genetic architecture. Second, enforcing
sparsity helps prevent sampling errors from swamping out the true signal in
high-dimensional data. We demonstrate the advantages of our model on simulated
data and in an analysis of a published Drosophila melanogaster gene expression
data set.Comment: 35 pages, 7 figure
Tensor Graphical Lasso (TeraLasso)
This paper introduces a multi-way tensor generalization of the Bigraphical
Lasso (BiGLasso), which uses a two-way sparse Kronecker-sum multivariate-normal
model for the precision matrix to parsimoniously model conditional dependence
relationships of matrix-variate data based on the Cartesian product of graphs.
We call this generalization the {\bf Te}nsor g{\bf ra}phical Lasso (TeraLasso).
We demonstrate using theory and examples that the TeraLasso model can be
accurately and scalably estimated from very limited data samples of high
dimensional variables with multiway coordinates such as space, time and
replicates. Statistical consistency and statistical rates of convergence are
established for both the BiGLasso and TeraLasso estimators of the precision
matrix and estimators of its support (non-sparsity) set, respectively. We
propose a scalable composite gradient descent algorithm and analyze the
computational convergence rate, showing that the composite gradient descent
algorithm is guaranteed to converge at a geometric rate to the global minimizer
of the TeraLasso objective function. Finally, we illustrate the TeraLasso using
both simulation and experimental data from a meteorological dataset, showing
that we can accurately estimate precision matrices and recover meaningful
conditional dependency graphs from high dimensional complex datasets.Comment: accepted to JRSS-
Dissecting high-dimensional phenotypes with bayesian sparse factor analysis of genetic covariance matrices.
Quantitative genetic studies that model complex, multivariate phenotypes are important for both evolutionary prediction and artificial selection. For example, changes in gene expression can provide insight into developmental and physiological mechanisms that link genotype and phenotype. However, classical analytical techniques are poorly suited to quantitative genetic studies of gene expression where the number of traits assayed per individual can reach many thousand. Here, we derive a Bayesian genetic sparse factor model for estimating the genetic covariance matrix (G-matrix) of high-dimensional traits, such as gene expression, in a mixed-effects model. The key idea of our model is that we need consider only G-matrices that are biologically plausible. An organism's entire phenotype is the result of processes that are modular and have limited complexity. This implies that the G-matrix will be highly structured. In particular, we assume that a limited number of intermediate traits (or factors, e.g., variations in development or physiology) control the variation in the high-dimensional phenotype, and that each of these intermediate traits is sparse - affecting only a few observed traits. The advantages of this approach are twofold. First, sparse factors are interpretable and provide biological insight into mechanisms underlying the genetic architecture. Second, enforcing sparsity helps prevent sampling errors from swamping out the true signal in high-dimensional data. We demonstrate the advantages of our model on simulated data and in an analysis of a published Drosophila melanogaster gene expression data set
Automatic Differentiation Variational Inference
Probabilistic modeling is iterative. A scientist posits a simple model, fits
it to her data, refines it according to her analysis, and repeats. However,
fitting complex models to large data is a bottleneck in this process. Deriving
algorithms for new models can be both mathematically and computationally
challenging, which makes it difficult to efficiently cycle through the steps.
To this end, we develop automatic differentiation variational inference (ADVI).
Using our method, the scientist only provides a probabilistic model and a
dataset, nothing else. ADVI automatically derives an efficient variational
inference algorithm, freeing the scientist to refine and explore many models.
ADVI supports a broad class of models-no conjugacy assumptions are required. We
study ADVI across ten different models and apply it to a dataset with millions
of observations. ADVI is integrated into Stan, a probabilistic programming
system; it is available for immediate use
Decomposable Principal Component Analysis
We consider principal component analysis (PCA) in decomposable Gaussian
graphical models. We exploit the prior information in these models in order to
distribute its computation. For this purpose, we reformulate the problem in the
sparse inverse covariance (concentration) domain and solve the global
eigenvalue problem using a sequence of local eigenvalue problems in each of the
cliques of the decomposable graph. We demonstrate the application of our
methodology in the context of decentralized anomaly detection in the Abilene
backbone network. Based on the topology of the network, we propose an
approximate statistical graphical model and distribute the computation of PCA
Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches
Imaging spectrometers measure electromagnetic energy scattered in their
instantaneous field view in hundreds or thousands of spectral channels with
higher spectral resolution than multispectral cameras. Imaging spectrometers
are therefore often referred to as hyperspectral cameras (HSCs). Higher
spectral resolution enables material identification via spectroscopic analysis,
which facilitates countless applications that require identifying materials in
scenarios unsuitable for classical spectroscopic analysis. Due to low spatial
resolution of HSCs, microscopic material mixing, and multiple scattering,
spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus,
accurate estimation requires unmixing. Pixels are assumed to be mixtures of a
few materials, called endmembers. Unmixing involves estimating all or some of:
the number of endmembers, their spectral signatures, and their abundances at
each pixel. Unmixing is a challenging, ill-posed inverse problem because of
model inaccuracies, observation noise, environmental conditions, endmember
variability, and data set size. Researchers have devised and investigated many
models searching for robust, stable, tractable, and accurate unmixing
algorithms. This paper presents an overview of unmixing methods from the time
of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models
are first discussed. Signal-subspace, geometrical, statistical, sparsity-based,
and spatial-contextual unmixing algorithms are described. Mathematical problems
and potential solutions are described. Algorithm characteristics are
illustrated experimentally.Comment: This work has been accepted for publication in IEEE Journal of
Selected Topics in Applied Earth Observations and Remote Sensin
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