254,538 research outputs found
A contribution to the second neighborhood problem
Seymour's Second Neighborhood Conjecture asserts that every digraph (without
digons) has a vertex whose first out-neighborhood is at most as large as its
second out-neighborhood. It is proved for tournaments, tournaments missing a
matching and tournaments missing a generalized star. We prove this conjecture
for classes of digraphs whose missing graph is a comb, a complete graph minus 2
independent edges, or a complete graph minus the edges of a cycle of length 5
High-dimensional Sparse Inverse Covariance Estimation using Greedy Methods
In this paper we consider the task of estimating the non-zero pattern of the
sparse inverse covariance matrix of a zero-mean Gaussian random vector from a
set of iid samples. Note that this is also equivalent to recovering the
underlying graph structure of a sparse Gaussian Markov Random Field (GMRF). We
present two novel greedy approaches to solving this problem. The first
estimates the non-zero covariates of the overall inverse covariance matrix
using a series of global forward and backward greedy steps. The second
estimates the neighborhood of each node in the graph separately, again using
greedy forward and backward steps, and combines the intermediate neighborhoods
to form an overall estimate. The principal contribution of this paper is a
rigorous analysis of the sparsistency, or consistency in recovering the
sparsity pattern of the inverse covariance matrix. Surprisingly, we show that
both the local and global greedy methods learn the full structure of the model
with high probability given just samples, which is a
\emph{significant} improvement over state of the art -regularized
Gaussian MLE (Graphical Lasso) that requires samples. Moreover,
the restricted eigenvalue and smoothness conditions imposed by our greedy
methods are much weaker than the strong irrepresentable conditions required by
the -regularization based methods. We corroborate our results with
extensive simulations and examples, comparing our local and global greedy
methods to the -regularized Gaussian MLE as well as the Neighborhood
Greedy method to that of nodewise -regularized linear regression
(Neighborhood Lasso).Comment: Accepted to AI STAT 2012 for Oral Presentatio
Group-Average Observables as Controls for Sorting on Unobservables When Estimating Group Treatment Effects: The Case of School and Neighborhood Effects
We consider the classic problem of estimating group treatment effects when individuals sort based on observed and unobserved characteristics. Using a standard choice model, we show that controlling for group averages of observed individual characteristics potentially absorbs all the across-group variation in unobservable individual characteristics. We use this insight to bound the treatment effect variance of school systems and associated neighborhoods for various outcomes. Across four datasets, our conservative estimates indicate that a 90th versus 10th percentile school system increases high school graduation and college enrollment probabilities by at least 0.047 and 0.11. Other applications include measurement of teacher value-added
Identification of probabilistic cellular automata
The identification of probabilistic cellular automata (PCA) is studied using a new two stage neighborhood detection algorithm. It is shown that a binary probabilistic cellular automaton (BPCA) can be described by an integer-parameterized polynomial corrupted by noise. Searching for the correct neighborhood of a BPCA is then equivalent to selecting the correct terms which constitute the polynomial model of the BPCA, from a large initial term set. It is proved that the contribution values for the correct terms can be calculated independently of the contribution values for the noise terms. This allows the neighborhood detection technique developed for deterministic rules in to be applied with a larger cutoff value to discard the majority of spurious terms and to produce an initial presearch for the BPCA neighborhood. A multiobjective genetic algorithm (GA) search with integer constraints is then evolved to refine the reduced neighborhood and to identify the polynomial rule which is equivalent to the probabilistic rule with the largest probability. A probability table representing the BPCA can then be determined based on the identified neighborhood and the deterministic rule. The new algorithm is tested over a large set of one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) BPCA rules. Simulation results demonstrate the efficiency of the new method
Neighborhood detection and rule selection from cellular automata patterns
Using genetic algorithms (GAs) to search for cellular automation (CA) rules from spatio-temporal patterns produced in CA evolution is usually complicated and time-consuming when both, the neighborhood structure and the local rule are searched simultaneously. The complexity of this problem motivates the development of a new search which separates the neighborhood detection from the GA search. In the paper, the neighborhood is determined by independently selecting terms from a large term set on the basis of the contribution each term makes to the next state of the cell to be updated. The GA search is then started with a considerably smaller set of candidate rules pre-defined by the detected neighhorhood. This approach is tested over a large set of one-dimensional (1-D) and two-dimensional (2-D) CA rules. Simulation results illustrate the efficiency of the new algorith
New constraints on data-closeness and needle map consistency for shape-from-shading
This paper makes two contributions to the problem of needle-map recovery using shape-from-shading. First, we provide a geometric update procedure which allows the image irradiance equation to be satisfied as a hard constraint. This not only improves the data closeness of the recovered needle-map, but also removes the necessity for extensive parameter tuning. Second, we exploit the improved ease of control of the new shape-from-shading process to investigate various types of needle-map consistency constraint. The first set of constraints are based on needle-map smoothness. The second avenue of investigation is to use curvature information to impose topographic constraints. Third, we explore ways in which the needle-map is recovered so as to be consistent with the image gradient field. In each case we explore a variety of robust error measures and consistency weighting schemes that can be used to impose the desired constraints on the recovered needle-map. We provide an experimental assessment of the new shape-from-shading framework on both real world images and synthetic images with known ground truth surface normals. The main conclusion drawn from our analysis is that the data-closeness constraint improves the efficiency of shape-from-shading and that both the topographic and gradient consistency constraints improve the fidelity of the recovered needle-map
Finite width effects and gauge cancellations in W- and Z-boson production in framework of modified perturbation theory
The processes of production and subsequent decay of W- and Z-bosons in collisions are considered in a recently proposed modified perturbation
theory (PT), based on a direct expansion of probabilities instead of
amplitudes. In such an approach the non-integrable singularities in the phase
space, which are intrinsic in the conventional PT, appear as singularities in
the coupling constant (with subsequent compensation by the decay factors of
unstable particles). In the present paper the systematic investigation of the
modified PT is carried out. The results are compared with the results of the
conventional approach, based on calculation of the amplitude with Dyson
resummation. A solution to the problem of the loss of one-loop PT order in the
resonance region is found. On the basis of this solution the proof of gauge
cancellations in any order of the modified PT is given. A simple generalization
of the fermion-loop scheme is proposed which provides a complete description of
W-pair production in next-to-leading order approximation.Comment: 25 pages, 2 figures; minor changes in the text, version to appear in
Eur.Phys.J.
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