6,142 research outputs found
Penalized Estimation of Directed Acyclic Graphs From Discrete Data
Bayesian networks, with structure given by a directed acyclic graph (DAG),
are a popular class of graphical models. However, learning Bayesian networks
from discrete or categorical data is particularly challenging, due to the large
parameter space and the difficulty in searching for a sparse structure. In this
article, we develop a maximum penalized likelihood method to tackle this
problem. Instead of the commonly used multinomial distribution, we model the
conditional distribution of a node given its parents by multi-logit regression,
in which an edge is parameterized by a set of coefficient vectors with dummy
variables encoding the levels of a node. To obtain a sparse DAG, a group norm
penalty is employed, and a blockwise coordinate descent algorithm is developed
to maximize the penalized likelihood subject to the acyclicity constraint of a
DAG. When interventional data are available, our method constructs a causal
network, in which a directed edge represents a causal relation. We apply our
method to various simulated and real data sets. The results show that our
method is very competitive, compared to many existing methods, in DAG
estimation from both interventional and high-dimensional observational data.Comment: To appear in Statistics and Computin
Mott-Hubbard transition in infinite dimensions
We analyze the unanalytical structure of metal-insulator transition (MIT) in
infinite dimensions. By introducing a simple transformation into the dynamical
mean-field equation of Hubbard model, a multiple-valued structure in Green's
function and other thermodynamical quantities with respect to the interaction
strength are found at low temperatures. A unified description of stable,
metastable and unstable phases is obtained in the regime
, and the Maxwell construction is performed to evaluate
the MIT line . We show how the first-order MIT at
for evolves into second-order one at for . The phase
diagram near MIT is presented.Comment: 5 pages with 3 figures, text and figures revise
Disorder effect of resonant spin Hall effect in a tilted magnetic field
We study the disorder effect of resonant spin Hall effect in a two-dimension
electron system with Rashba coupling in the presence of a tilted magnetic
field. The competition between the Rashba coupling and the Zeeman coupling
leads to the energy crossing of the Landau levels, which gives rise to the
resonant spin Hall effect. Utilizing the Streda's formula within the
self-consistent Born approximation, we find that the impurity scattering
broadens the energy levels, and the resonant spin Hall conductance exhibits a
double peak around the resonant point, which is recovered in an applied titled
magnetic field.Comment: 6 pages, 4 figure
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