48,514 research outputs found
Variable selection with Random Forests for missing data
Variable selection has been suggested for Random Forests to improve their efficiency of data prediction and interpretation. However, its basic element, i.e. variable importance measures, can not be computed straightforward when there is missing data. Therefore an extensive simulation study has been conducted to explore possible solutions, i.e. multiple imputation, complete case analysis and a newly suggested importance measure for several missing data generating processes. The ability to distinguish relevant from non-relevant variables has been investigated for these procedures in combination with two popular variable selection methods. Findings and recommendations: Complete case analysis should not be applied as it lead to inaccurate variable selection and models with the worst prediction accuracy. Multiple imputation is a good means to select variables that would be of relevance in fully observed data. It produced the best prediction accuracy. By contrast, the application of the new importance measure causes a selection of variables that reflects the actual data situation, i.e. that takes the occurrence of missing values into account. It's error was only negligible worse compared to imputation
The arboreal gas and the supersphere sigma model
We discuss the relationship between the phase diagram of the Q=0 state Potts
model, the arboreal gas model, and the supersphere sigma model S^{0,2} =
OSP(1/2) / OSP(0/2). We identify the Potts antiferromagnetic critical point
with the critical point of the arboreal gas (at negative tree fugacity), and
with a critical point of the sigma model. We show that the corresponding
conformal theory on the square lattice has a non-linearly realized OSP(2/2) =
SL(1/2) symmetry, and involves non-compact degrees of freedom, with a
continuous spectrum of critical exponents. The role of global topological
properties in the sigma model transition is discussed in terms of a generalized
arboreal gas model.Comment: 23 pages, 4 figure
Ward identities and combinatorics of rainbow tensor models
We discuss the notion of renormalization group (RG) completion of
non-Gaussian Lagrangians and its treatment within the framework of
Bogoliubov-Zimmermann theory in application to the matrix and tensor models.
With the example of the simplest non-trivial RGB tensor theory (Aristotelian
rainbow), we introduce a few methods, which allow one to connect calculations
in the tensor models to those in the matrix models. As a byproduct, we obtain
some new factorization formulas and sum rules for the Gaussian correlators in
the Hermitian and complex matrix theories, square and rectangular. These sum
rules describe correlators as solutions to finite linear systems, which are
much simpler than the bilinear Hirota equations and the infinite Virasoro
recursion. Search for such relations can be a way to solving the tensor models,
where an explicit integrability is still obscure.Comment: 48 page
Perturbative Quantum Field Theory on Random Trees
In this paper we start a systematic study of quantum field theory on random
trees. Using precise probability estimates on their Galton-Watson branches and
a multiscale analysis, we establish the general power counting of averaged
Feynman amplitudes and check that they behave indeed as living on an effective
space of dimension 4/3, the spectral dimension of random trees. In the `just
renormalizable' case we prove convergence of the averaged amplitude of any
completely convergent graph, and establish the basic localization and
subtraction estimates required for perturbative renormalization. Possible
consequences for an SYK-like model on random trees are briefly discussed.Comment: 44 page
Constructive Tensor Field Theory
We provide an up-to-date review of the recent constructive program for field
theories of the vector, matrix and tensor type, focusing not on the models
themselves but on the mathematical tools used.Comment: arXiv admin note: text overlap with arXiv:1401.500
Random Tensors and Quantum Gravity
We provide an informal introduction to tensor field theories and to their
associated renormalization group. We focus more on the general motivations
coming from quantum gravity than on the technical details. In particular we
discuss how asymptotic freedom of such tensor field theories gives a concrete
example of a natural "quantum relativity" postulate: physics in the deep
ultraviolet regime becomes asymptotically more and more independent of any
particular choice of Hilbert basis in the space of states of the universe.Comment: Section 6 is essentially reproduced from author's arXiv:1507.04190
for self-contained purpose of the revie
On the Invariance of Residues of Feynman Graphs
We use simple iterated one-loop graphs in massless Yukawa theory and QED to
pose the following question: what are the symmetries of the residues of a graph
under a permutation of places to insert subdivergences. The investigation
confirms partial invariance of the residue under such permutations: the highest
weight transcendental is invariant under such a permutation. For QED this
result is gauge invariant, ie the permutation invariance holds for any gauge.
Computations are done making use of the Hopf algebra structure of graphs and
employing GiNaC to automate the calculations.Comment: 24 pages, latex generated figures. Minor changes in revised versio
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