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A genomic strategy to refine prognosis in early-stage non-small-cell lung cancer.
TLDR
The lung metagene model provides a potential mechanism to refine the estimation of a patient's risk of disease recurrence and, in principle, to alter decisions regarding the use of adjuvant chemotherapy in early-stage NSCLC.
Probability measures on the space of persistence diagrams
This paper shows that the space of persistence diagrams has properties that allow for the definition of probability measures which support expectations, variances, percentiles and conditional
Fréchet Means for Distributions of Persistence Diagrams
TLDR
An algorithm is introduced that estimates a Fréchet mean from the set of diagrams given observations drawn iid and it is proved the algorithm converges to a local minimum and a law of large numbers result for a FrÉchet mean computed by the algorithm.
Evidence of Influence of Genomic DNA Sequence on Human X Chromosome Inactivation
TLDR
It is suggested that features of the underlying primary DNA sequence of the human X chromosome may influence the spreading and/or maintenance of X inactivation.
Persistent Homology Transform for Modeling Shapes and Surfaces
In this paper we introduce a statistic, the persistent homology transform (PHT), to model surfaces in $\mathbb{R}^3$ and shapes in $\mathbb{R}^2$. This statistic is a collection of persistence
Learning Coordinate Covariances via Gradients
We introduce an algorithm that learns gradients from samples in the supervised learning framework. An error analysis is given for the convergence of the gradient estimated by the algorithm to the
The Information Geometry of Mirror Descent
TLDR
It is proved that mirror descent induced by Bregman divergence proximity functions is equivalent to the natural gradient descent algorithm on the dual Riemannian manifold.
Characterizing the Function Space for Bayesian Kernel Models
TLDR
A coherent Bayesian kernel model based on an integral operator defined as the convolution of a kernel with a signed measure is studied, creating a function theoretic foundation for using non-parametric prior specifications in Bayesian modeling, such as Gaussian process and Dirichlet process prior distributions.
Risk bounds for mixture density estimation
TLDR
An O( 1 √ n ) bound on the estimation error which does not depend on the number of densities in the estimated combination is proved, which improves the bound of Li and Barron by removing the logn factor and also generalizes it to the base classes with converging Dudley integral.
Nonparametric Bayesian Kernel Models
TLDR
A Bayesian framework and theory for kernel methods is discussed, providing a new rationalization of kernel regression based on nonparametric Bayesian models, and augmented the model with Bayesian variable selection priors over kernel bandwidth parameters.
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