301,445 research outputs found
CP Violations in Lepton Number Violation Processes and Neutrino Oscillations
We examine the constraints on the MNS lepton mixing matrix from the present
and future experimental data of the neutrino oscillation and lepton number
violation processes. We introduce a graphical representation of the CP
violation phases which appear in the lepton number violation processes such as
neutrinoless double beta decay, the conversion, and the K decay,
Using this graphical representation, we derive the
constraints on the CP violation phases in the lepton sector.Comment: 21pp, REVTeX, 9 Figure
Graphical methods for inequality constraints in marginalized DAGs
We present a graphical approach to deriving inequality constraints for
directed acyclic graph (DAG) models, where some variables are unobserved. In
particular we show that the observed distribution of a discrete model is always
restricted if any two observed variables are neither adjacent in the graph, nor
share a latent parent; this generalizes the well known instrumental inequality.
The method also provides inequalities on interventional distributions, which
can be used to bound causal effects. All these constraints are characterized in
terms of a new graphical separation criterion, providing an easy and intuitive
method for their derivation.Comment: A final version will appear in the proceedings of the 22nd Workshop
on Machine Learning and Signal Processing, 201
Algebraic Aspects of Conditional Independence and Graphical Models
This chapter of the forthcoming Handbook of Graphical Models contains an
overview of basic theorems and techniques from algebraic geometry and how they
can be applied to the study of conditional independence and graphical models.
It also introduces binomial ideals and some ideas from real algebraic geometry.
When random variables are discrete or Gaussian, tools from computational
algebraic geometry can be used to understand implications between conditional
independence statements. This is accomplished by computing primary
decompositions of conditional independence ideals. As examples the chapter
presents in detail the graphical model of a four cycle and the intersection
axiom, a certain implication of conditional independence statements. Another
important problem in the area is to determine all constraints on a graphical
model, for example, equations determined by trek separation. The full set of
equality constraints can be determined by computing the model's vanishing
ideal. The chapter illustrates these techniques and ideas with examples from
the literature and provides references for further reading.Comment: 20 pages, 1 figur
Sparse Nested Markov models with Log-linear Parameters
Hidden variables are ubiquitous in practical data analysis, and therefore
modeling marginal densities and doing inference with the resulting models is an
important problem in statistics, machine learning, and causal inference.
Recently, a new type of graphical model, called the nested Markov model, was
developed which captures equality constraints found in marginals of directed
acyclic graph (DAG) models. Some of these constraints, such as the so called
`Verma constraint', strictly generalize conditional independence. To make
modeling and inference with nested Markov models practical, it is necessary to
limit the number of parameters in the model, while still correctly capturing
the constraints in the marginal of a DAG model. Placing such limits is similar
in spirit to sparsity methods for undirected graphical models, and regression
models. In this paper, we give a log-linear parameterization which allows
sparse modeling with nested Markov models. We illustrate the advantages of this
parameterization with a simulation study.Comment: Appears in Proceedings of the Twenty-Ninth Conference on Uncertainty
in Artificial Intelligence (UAI2013
Collaborative Training in Sensor Networks: A graphical model approach
Graphical models have been widely applied in solving distributed inference
problems in sensor networks. In this paper, the problem of coordinating a
network of sensors to train a unique ensemble estimator under communication
constraints is discussed. The information structure of graphical models with
specific potential functions is employed, and this thus converts the
collaborative training task into a problem of local training plus global
inference. Two important classes of algorithms of graphical model inference,
message-passing algorithm and sampling algorithm, are employed to tackle
low-dimensional, parametrized and high-dimensional, non-parametrized problems
respectively. The efficacy of this approach is demonstrated by concrete
examples
Nested Markov Properties for Acyclic Directed Mixed Graphs
Directed acyclic graph (DAG) models may be characterized in at least four
different ways: via a factorization, the d-separation criterion, the
moralization criterion, and the local Markov property. As pointed out by Robins
(1986, 1999), Verma and Pearl (1990), and Tian and Pearl (2002b), marginals of
DAG models also imply equality constraints that are not conditional
independences. The well-known `Verma constraint' is an example. Constraints of
this type were used for testing edges (Shpitser et al., 2009), and an efficient
marginalization scheme via variable elimination (Shpitser et al., 2011).
We show that equality constraints like the `Verma constraint' can be viewed
as conditional independences in kernel objects obtained from joint
distributions via a fixing operation that generalizes conditioning and
marginalization. We use these constraints to define, via Markov properties and
a factorization, a graphical model associated with acyclic directed mixed
graphs (ADMGs). We show that marginal distributions of DAG models lie in this
model, prove that a characterization of these constraints given in (Tian and
Pearl, 2002b) gives an alternative definition of the model, and finally show
that the fixing operation we used to define the model can be used to give a
particularly simple characterization of identifiable causal effects in hidden
variable graphical causal models.Comment: 67 pages (not including appendix and references), 8 figure
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