1,377 research outputs found
Measures with zeros in the inverse of their moment matrix
We investigate and discuss when the inverse of a multivariate truncated
moment matrix of a measure has zeros in some prescribed entries. We
describe precisely which pattern of these zeroes corresponds to independence,
namely, the measure having a product structure. A more refined finding is that
the key factor forcing a zero entry in this inverse matrix is a certain
conditional triangularity property of the orthogonal polynomials associated
with .Comment: Published in at http://dx.doi.org/10.1214/07-AOP365 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Predicting the outcome of renal transplantation
ObjectiveRenal transplantation has dramatically improved the survival rate of hemodialysis patients. However, with a growing proportion of marginal organs and improved immunosuppression, it is necessary to verify that the established allocation system, mostly based on human leukocyte antigen matching, still meets today's needs. The authors turn to machine-learning techniques to predict, from donor-recipient data, the estimated glomerular filtration rate (eGFR) of the recipient 1 year after transplantation.DesignThe patient's eGFR was predicted using donor-recipient characteristics available at the time of transplantation. Donors' data were obtained from Eurotransplant's database, while recipients' details were retrieved from Charite Campus Virchow-Klinikum's database. A total of 707 renal transplantations from cadaveric donors were included.MeasurementsTwo separate datasets were created, taking features with <10% missing values for one and <50% missing values for the other. Four established regressors were run on both datasets, with and without feature selection.ResultsThe authors obtained a Pearson correlation coefficient between predicted and real eGFR (COR) of 0.48. The best model for the dataset was a Gaussian support vector machine with recursive feature elimination on the more inclusive dataset. All results are available at http://transplant.molgen.mpg.de/.LimitationsFor now, missing values in the data must be predicted and filled in. The performance is not as high as hoped, but the dataset seems to be the main cause.ConclusionsPredicting the outcome is possible with the dataset at hand (COR=0.48). Valuable features include age and creatinine levels of the donor, as well as sex and weight of the recipient
Computation with Polynomial Equations and Inequalities arising in Combinatorial Optimization
The purpose of this note is to survey a methodology to solve systems of
polynomial equations and inequalities. The techniques we discuss use the
algebra of multivariate polynomials with coefficients over a field to create
large-scale linear algebra or semidefinite programming relaxations of many
kinds of feasibility or optimization questions. We are particularly interested
in problems arising in combinatorial optimization.Comment: 28 pages, survey pape
The Distance Precision Matrix: computing networks from non-linear relationships
Motivation: Full-order partial correlation, a fundamental approach for network reconstruction, e.g. in the context of gene regulation, relies on the precision matrix (the inverse of the covariance matrix) as an indicator of which variables are directly associated. The precision matrix assumes Gaussian linear data and its entries are zero for pairs of variables that are independent given all other variables. However, there is still very little theory on network reconstruction under the assumption of non-linear interactions among variables. Results: We propose Distance Precision Matrix, a network reconstruction method aimed at both linear and non-linear data. Like partial distance correlation, it builds on distance covariance, a measure of possibly non-linear association, and on the idea of full-order partial correlation, which allows to discard indirect associations. We provide evidence that the Distance Precision Matrix method can successfully compute networks from linear and non-linear data, and consistently so across different datasets, even if sample size is low. The method is fast enough to compute networks on hundreds of nodes. Availability: An R package DPM is available at https://github.molgen.mpg.de/ghanbari/DPM. Supplementary information: Supplementary data are available at Bioinformatics online
Exploiting symmetries in SDP-relaxations for polynomial optimization
In this paper we study various approaches for exploiting symmetries in
polynomial optimization problems within the framework of semi definite
programming relaxations. Our special focus is on constrained problems
especially when the symmetric group is acting on the variables. In particular,
we investigate the concept of block decomposition within the framework of
constrained polynomial optimization problems, show how the degree principle for
the symmetric group can be computationally exploited and also propose some
methods to efficiently compute in the geometric quotient.Comment: (v3) Minor revision. To appear in Math. of Operations Researc
Semidefinite approximations of projections and polynomial images of semialgebraic sets
Given a compact semialgebraic set S of R^n and a polynomial map f from R^n to R^m, we consider the problem of approximating the image set F = f(S) in R^m. This includes in particular the projection of S on R^m for n greater than m. Assuming that F is included in a set B which is simple (e.g. a box or a ball), we provide two methods to compute certified outer approximations of F. Method 1 exploits the fact that F can be defined with an existential quantifier, while Method 2 computes approximations of the support of image measures.The two methods output a sequence of superlevel sets defined with a single polynomial that yield explicit outer approximations of F. Finding the coefficients of this polynomial boils down to computing an optimal solution of a convex semidefinite program. We provide guarantees of strong convergence to F in L^1 norm on B, when the degree of the polynomial approximation tends to infinity. Several examples of applications are provided, together with numerical experiments
A Proper Motion Survey for White Dwarfs with the Wide Field Planetary Camera 2
We have performed a search for halo white dwarfs as high proper motion
objects in a second epoch WFPC2 image of the Groth-Westphal strip. We identify
24 high proper motion objects with mu > 0.014 ''/yr. Five of these high proper
motion objects are identified as strong white dwarf candidates on the basis of
their position in a reduced proper motion diagram. We create a model of the
Milky Way thin disk, thick disk and stellar halo and find that this sample of
white dwarfs is clearly an excess above the < 2 detections expected from these
known stellar populations. The origin of the excess signal is less clear.
Possibly, the excess cannot be explained without invoking a fourth galactic
component: a white dwarf dark halo. We present a statistical separation of our
sample into the four components and estimate the corresponding local white
dwarf densities using only the directly observable variables, V, V-I, and mu.
For all Galactic models explored, our sample separates into about 3 disk white
dwarfs and 2 halo white dwarfs. However, the further subdivision into the thin
and thick disk and the stellar and dark halo, and the subsequent calculation of
the local densities are sensitive to the input parameters of our model for each
Galactic component. Using the lowest mean mass model for the dark halo we find
a 7% white dwarf halo and six times the canonical value for the thin disk white
dwarf density (at marginal statistical significance), but possible systematic
errors due to uncertainty in the model parameters likely dominate these
statistical error bars. The white dwarf halo can be reduced to around 1.5% of
the halo dark matter by changing the initial mass function slightly. The local
thin disk white dwarf density in our solution can be made consistent with the
canonical value by assuming a larger thin disk scaleheight of 500 pc.Comment: revised version, accepted by ApJ, results unchanged, discussion
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