24,780 research outputs found
Structure estimation for discrete graphical models: Generalized covariance matrices and their inverses
We investigate the relationship between the structure of a discrete graphical
model and the support of the inverse of a generalized covariance matrix. We
show that for certain graph structures, the support of the inverse covariance
matrix of indicator variables on the vertices of a graph reflects the
conditional independence structure of the graph. Our work extends results that
have previously been established only in the context of multivariate Gaussian
graphical models, thereby addressing an open question about the significance of
the inverse covariance matrix of a non-Gaussian distribution. The proof
exploits a combination of ideas from the geometry of exponential families,
junction tree theory and convex analysis. These population-level results have
various consequences for graph selection methods, both known and novel,
including a novel method for structure estimation for missing or corrupted
observations. We provide nonasymptotic guarantees for such methods and
illustrate the sharpness of these predictions via simulations.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1162 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Low-shot learning with large-scale diffusion
This paper considers the problem of inferring image labels from images when
only a few annotated examples are available at training time. This setup is
often referred to as low-shot learning, where a standard approach is to
re-train the last few layers of a convolutional neural network learned on
separate classes for which training examples are abundant. We consider a
semi-supervised setting based on a large collection of images to support label
propagation. This is possible by leveraging the recent advances on large-scale
similarity graph construction.
We show that despite its conceptual simplicity, scaling label propagation up
to hundred millions of images leads to state of the art accuracy in the
low-shot learning regime
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