45 research outputs found
Reversible MCMC on Markov equivalence classes of sparse directed acyclic graphs
Graphical models are popular statistical tools which are used to represent
dependent or causal complex systems. Statistically equivalent causal or
directed graphical models are said to belong to a Markov equivalent class. It
is of great interest to describe and understand the space of such classes.
However, with currently known algorithms, sampling over such classes is only
feasible for graphs with fewer than approximately 20 vertices. In this paper,
we design reversible irreducible Markov chains on the space of Markov
equivalent classes by proposing a perfect set of operators that determine the
transitions of the Markov chain. The stationary distribution of a proposed
Markov chain has a closed form and can be computed easily. Specifically, we
construct a concrete perfect set of operators on sparse Markov equivalence
classes by introducing appropriate conditions on each possible operator.
Algorithms and their accelerated versions are provided to efficiently generate
Markov chains and to explore properties of Markov equivalence classes of sparse
directed acyclic graphs (DAGs) with thousands of vertices. We find
experimentally that in most Markov equivalence classes of sparse DAGs, (1) most
edges are directed, (2) most undirected subgraphs are small and (3) the number
of these undirected subgraphs grows approximately linearly with the number of
vertices. The article contains supplement arXiv:1303.0632,
http://dx.doi.org/10.1214/13-AOS1125SUPPComment: Published in at http://dx.doi.org/10.1214/13-AOS1125 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Identifying Causal Effects Using Instrumental Variables from the Auxiliary Population
Instrumental variable approaches have gained popularity for estimating causal
effects in the presence of unmeasured confounding. However, the availability of
instrumental variables in the primary population is often challenged due to
stringent and untestable assumptions. This paper presents a novel method to
identify and estimate causal effects in the primary population by utilizing
instrumental variables from the auxiliary population, incorporating a
structural equation model, even in scenarios with nonlinear treatment effects.
Our approach involves using two datasets: one from the primary population with
joint observations of treatment and outcome, and another from the auxiliary
population providing information about the instrument and treatment. Our
strategy differs from most existing methods by not depending on the
simultaneous measurements of instrument and outcome. The central idea for
identifying causal effects is to establish a valid substitute through the
auxiliary population, addressing unmeasured confounding. This is achieved by
developing a control function and projecting it onto the function space spanned
by the treatment variable. We then propose a three-step estimator for
estimating causal effects and derive its asymptotic results. We illustrate the
proposed estimator through simulation studies, and the results demonstrate
favorable performance. We also conduct a real data analysis to evaluate the
causal effect between vitamin D status and BMI.Comment: 19 page
On the Representation of Causal Background Knowledge and its Applications in Causal Inference
Causal background knowledge about the existence or the absence of causal
edges and paths is frequently encountered in observational studies. The shared
directed edges and links of a subclass of Markov equivalent DAGs refined due to
background knowledge can be represented by a causal maximally partially
directed acyclic graph (MPDAG). In this paper, we first provide a sound and
complete graphical characterization of causal MPDAGs and give a minimal
representation of a causal MPDAG. Then, we introduce a novel representation
called direct causal clause (DCC) to represent all types of causal background
knowledge in a unified form. Using DCCs, we study the consistency and
equivalency of causal background knowledge and show that any causal background
knowledge set can be equivalently decomposed into a causal MPDAG plus a minimal
residual set of DCCs. Polynomial-time algorithms are also provided for checking
the consistency, equivalency, and finding the decomposed MPDAG and residual
DCCs. Finally, with causal background knowledge, we prove a sufficient and
necessary condition to identify causal effects and surprisingly find that the
identifiability of causal effects only depends on the decomposed MPDAG. We also
develop a local IDA-type algorithm to estimate the possible values of an
unidentifiable effect. Simulations suggest that causal background knowledge can
significantly improve the identifiability of causal effects
Identification and Estimation of Causal Effects Using non-Gaussianity and Auxiliary Covariates
Assessing causal effects in the presence of unmeasured confounding is a
challenging problem. Although auxiliary variables, such as instrumental
variables, are commonly used to identify causal effects, they are often
unavailable in practice due to stringent and untestable conditions. To address
this issue, previous researches have utilized linear structural equation models
to show that the causal effect can be identifiable when noise variables of the
treatment and outcome are both non-Gaussian. In this paper, we investigate the
problem of identifying the causal effect using auxiliary covariates and
non-Gaussianity from the treatment. Our key idea is to characterize the impact
of unmeasured confounders using an observed covariate, assuming they are all
Gaussian. The auxiliary covariate can be an invalid instrument or an invalid
proxy variable. We demonstrate that the causal effect can be identified using
this measured covariate, even when the only source of non-Gaussianity comes
from the treatment. We then extend the identification results to the
multi-treatment setting and provide sufficient conditions for identification.
Based on our identification results, we propose a simple and efficient
procedure for calculating causal effects and show the -consistency of
the proposed estimator. Finally, we evaluate the performance of our estimator
through simulation studies and an application.Comment: 16 papges, 7 Figure
Low Rank Directed Acyclic Graphs and Causal Structure Learning
Despite several important advances in recent years, learning causal
structures represented by directed acyclic graphs (DAGs) remains a challenging
task in high dimensional settings when the graphs to be learned are not sparse.
In particular, the recent formulation of structure learning as a continuous
optimization problem proved to have considerable advantages over the
traditional combinatorial formulation, but the performance of the resulting
algorithms is still wanting when the target graph is relatively large and
dense. In this paper we propose a novel approach to mitigate this problem, by
exploiting a low rank assumption regarding the (weighted) adjacency matrix of a
DAG causal model. We establish several useful results relating interpretable
graphical conditions to the low rank assumption, and show how to adapt existing
methods for causal structure learning to take advantage of this assumption. We
also provide empirical evidence for the utility of our low rank algorithms,
especially on graphs that are not sparse. Not only do they outperform
state-of-the-art algorithms when the low rank condition is satisfied, the
performance on randomly generated scale-free graphs is also very competitive
even though the true ranks may not be as low as is assumed
A sensor with coating Pt/WO3 powder with an Erbium-doped fiber amplifier to detect the hydrogen concentration
A highly sensitive hydrogen sensor coated with Pt/WO3 powder with an Erbium-doped fibre amplifier (EDFA) is proposed and experimentally demonstrated. The sensing head is constructed by splicing a short section of tapered small diameter coreless fiber (TSDCF diameter of 62.5 μm, and tapered to 14.5 μm) between two single-mode fibres. The Pt/WO3 powder adheres to the surface of PDMS film coated on the TSDCF structure, which is sensitive to hydrogen. An EDFA is introduced into the sensor system to improve the quality factor of the output spectrum and thus improve the sensor’s resolution. As the hydrogen concentration varies from 0 to 1.44, the measured maximum light intensity variation and the sensor’s sensitivity are -32.41 dB and -21.25 dB/, respectively. The sensor demonstrates good stability with the light intensity fluctuation of < 1.26 dB over a 30-minute duration
Sodic Soil Swelling and Dispersion and Their Implications for Water Movement and Management
Video summarizing Ph.D. dissertation for a non-specialist audience.NRCS Conservation Innovation GrantChina Scholarship CouncilNorth Dakota Water Resources Research InstituteSoil ScienceSoil ScienceSchool of Natural Resource SciencesCollege of Agriculture, Food Systems and Natural Resource
Sodic Soil Swelling and Dispersion and Their Implications for Water Movement and Management
Video summarizing Ph.D. dissertation for a non-specialist audience.NRCS Conservation Innovation GrantChina Scholarship CouncilNorth Dakota Water Resources Research InstituteSoil ScienceSoil ScienceSchool of Natural Resource SciencesCollege of Agriculture, Food Systems and Natural Resource