6,500 research outputs found
Structure Learning in Graphical Modeling
A graphical model is a statistical model that is associated to a graph whose
nodes correspond to variables of interest. The edges of the graph reflect
allowed conditional dependencies among the variables. Graphical models admit
computationally convenient factorization properties and have long been a
valuable tool for tractable modeling of multivariate distributions. More
recently, applications such as reconstructing gene regulatory networks from
gene expression data have driven major advances in structure learning, that is,
estimating the graph underlying a model. We review some of these advances and
discuss methods such as the graphical lasso and neighborhood selection for
undirected graphical models (or Markov random fields), and the PC algorithm and
score-based search methods for directed graphical models (or Bayesian
networks). We further review extensions that account for effects of latent
variables and heterogeneous data sources
algcomparison: Comparing the Performance of Graphical Structure Learning Algorithms with TETRAD
In this report we describe a tool for comparing the performance of graphical
causal structure learning algorithms implemented in the TETRAD freeware suite
of causal analysis methods. Currently the tool is available as package in the
TETRAD source code (written in Java). Simulations can be done varying the
number of runs, sample sizes, and data modalities. Performance on this
simulated data can then be compared for a number of algorithms, with parameters
varied and with performance statistics as selected, producing a publishable
report. The package presented here may also be used to compare structure
learning methods across platforms and programming languages, i.e., to compare
algorithms implemented in TETRAD with those implemented in MATLAB, Python, or
R
Causal Structure Learning
Graphical models can represent a multivariate distribution in a convenient
and accessible form as a graph. Causal models can be viewed as a special class
of graphical models that not only represent the distribution of the observed
system but also the distributions under external interventions. They hence
enable predictions under hypothetical interventions, which is important for
decision making. The challenging task of learning causal models from data
always relies on some underlying assumptions. We discuss several recently
proposed structure learning algorithms and their assumptions, and compare their
empirical performance under various scenarios.Comment: to appear in `Annual Review of Statistics and Its Application', 30
page
Latent Variable Discovery Using Dependency Patterns
The causal discovery of Bayesian networks is an active and important research
area, and it is based upon searching the space of causal models for those which
can best explain a pattern of probabilistic dependencies shown in the data.
However, some of those dependencies are generated by causal structures
involving variables which have not been measured, i.e., latent variables. Some
such patterns of dependency "reveal" themselves, in that no model based solely
upon the observed variables can explain them as well as a model using a latent
variable. That is what latent variable discovery is based upon. Here we did a
search for finding them systematically, so that they may be applied in latent
variable discovery in a more rigorous fashion
Robust causal structure learning with some hidden variables
We introduce a new method to estimate the Markov equivalence class of a
directed acyclic graph (DAG) in the presence of hidden variables, in settings
where the underlying DAG among the observed variables is sparse, and there are
a few hidden variables that have a direct effect on many of the observed ones.
Building on the so-called low rank plus sparse framework, we suggest a
two-stage approach which first removes the effect of the hidden variables, and
then estimates the Markov equivalence class of the underlying DAG under the
assumption that there are no remaining hidden variables. This approach is
consistent in certain high-dimensional regimes and performs favourably when
compared to the state of the art, both in terms of graphical structure recovery
and total causal effect estimation
Permutation-based Causal Inference Algorithms with Interventions
Learning directed acyclic graphs using both observational and interventional
data is now a fundamentally important problem due to recent technological
developments in genomics that generate such single-cell gene expression data at
a very large scale. In order to utilize this data for learning gene regulatory
networks, efficient and reliable causal inference algorithms are needed that
can make use of both observational and interventional data. In this paper, we
present two algorithms of this type and prove that both are consistent under
the faithfulness assumption. These algorithms are interventional adaptations of
the Greedy SP algorithm and are the first algorithms using both observational
and interventional data with consistency guarantees. Moreover, these algorithms
have the advantage that they are nonparametric, which makes them useful also
for analyzing non-Gaussian data. In this paper, we present these two algorithms
and their consistency guarantees, and we analyze their performance on simulated
data, protein signaling data, and single-cell gene expression data
Combining Linear Non-Gaussian Acyclic Model with Logistic Regression Model for Estimating Causal Structure from Mixed Continuous and Discrete Data
Estimating causal models from observational data is a crucial task in data
analysis. For continuous-valued data, Shimizu et al. have proposed a linear
acyclic non-Gaussian model to understand the data generating process, and have
shown that their model is identifiable when the number of data is sufficiently
large. However, situations in which continuous and discrete variables coexist
in the same problem are common in practice. Most existing causal discovery
methods either ignore the discrete data and apply a continuous-valued algorithm
or discretize all the continuous data and then apply a discrete Bayesian
network approach. These methods possibly loss important information when we
ignore discrete data or introduce the approximation error due to
discretization. In this paper, we define a novel hybrid causal model which
consists of both continuous and discrete variables. The model assumes: (1) the
value of a continuous variable is a linear function of its parent variables
plus a non-Gaussian noise, and (2) each discrete variable is a logistic
variable whose distribution parameters depend on the values of its parent
variables. In addition, we derive the BIC scoring function for model selection.
The new discovery algorithm can learn causal structures from mixed continuous
and discrete data without discretization. We empirically demonstrate the power
of our method through thorough simulations
Detecting Causal Relations in the Presence of Unmeasured Variables
The presence of latent variables can greatly complicate inferences about
causal relations between measured variables from statistical data. In many
cases, the presence of latent variables makes it impossible to determine for
two measured variables A and B, whether A causes B, B causes A, or there is
some common cause. In this paper I present several theorems that state
conditions under which it is possible to reliably infer the causal relation
between two measured variables, regardless of whether latent variables are
acting or not.Comment: Appears in Proceedings of the Seventh Conference on Uncertainty in
Artificial Intelligence (UAI1991
A Robust Independence Test for Constraint-Based Learning of Causal Structure
Constraint-based (CB) learning is a formalism for learning a causal network
with a database D by performing a series of conditional-independence tests to
infer structural information. This paper considers a new test of independence
that combines ideas from Bayesian learning, Bayesian network inference, and
classical hypothesis testing to produce a more reliable and robust test. The
new test can be calculated in the same asymptotic time and space required for
the standard tests such as the chi-squared test, but it allows the
specification of a prior distribution over parameters and can be used when the
database is incomplete. We prove that the test is correct, and we demonstrate
empirically that, when used with a CB causal discovery algorithm with
noninformative priors, it recovers structural features more reliably and it
produces networks with smaller KL-Divergence, especially as the number of nodes
increases or the number of records decreases. Another benefit is the dramatic
reduction in the probability that a CB algorithm will stall during the search,
providing a remedy for an annoying problem plaguing CB learning when the
database is small.Comment: Appears in Proceedings of the Nineteenth Conference on Uncertainty in
Artificial Intelligence (UAI2003
A Survey on Social Media Anomaly Detection
Social media anomaly detection is of critical importance to prevent malicious
activities such as bullying, terrorist attack planning, and fraud information
dissemination. With the recent popularity of social media, new types of
anomalous behaviors arise, causing concerns from various parties. While a large
amount of work have been dedicated to traditional anomaly detection problems,
we observe a surge of research interests in the new realm of social media
anomaly detection. In this paper, we present a survey on existing approaches to
address this problem. We focus on the new type of anomalous phenomena in the
social media and review the recent developed techniques to detect those special
types of anomalies. We provide a general overview of the problem domain, common
formulations, existing methodologies and potential directions. With this work,
we hope to call out the attention from the research community on this
challenging problem and open up new directions that we can contribute in the
future.Comment: 23 page
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