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## A scoring function for learning Bayesian networks based on mutual information and conditional independence tests

Fonte: MIT Press
Publicador: MIT Press

Tipo: Artigo de Revista Científica

Português

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We propose a new scoring function for learning Bayesian networks from data using score+search algorithms. This is based on the concept of mutual information and exploits some well-known properties of this measure in a novel way. Essentially, a statistical independence test based on the
chi-square distribution, associated with the mutual information measure, together with a property of additive decomposition of this measure, are combined in order to measure the degree of interaction between each variable and its parent variables in the network. The result is a non-Bayesian
scoring function called MIT (mutual information tests) which belongs to the family of scores based on information theory. The MIT score also represents a penalization of the Kullback-Leibler divergence between the joint probability distributions associated with a candidate network and with the available data set. Detailed results of a complete experimental evaluation of the proposed scoring
function and its comparison with the well-known K2, BDeu and BIC/MDL scores are also presented.

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## A nonparametric copula based test for conditional independence with applications to granger causality

Fonte: Universidade Carlos III de Madrid
Publicador: Universidade Carlos III de Madrid

Tipo: Trabalho em Andamento
Formato: application/pdf

Publicado em /06/2009
Português

Relevância na Pesquisa

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#Nonparametric tests#Conditional independence#Granger non-causality#Bernstein density copula#Bootstrap#Finance#Volatility asymmetry#Leverage effect#Volatility feedback effect#Macroeconomics#C12

This paper proposes a new nonparametric test for conditional independence, which is
based on the comparison of Bernstein copula densities using the Hellinger distance.
The test is easy to implement because it does not involve a weighting function in the
test statistic, and it can be applied in general settings since there is no restriction on the
dimension of the data. In fact, to apply the test, only a bandwidth is needed for the
nonparametric copula. We prove that the test statistic is asymptotically pivotal under
the null hypothesis, establish local power properties, and motivate the validity of the
bootstrap technique that we use in finite sample settings. A simulation study illustrates
the good size and power properties of the test. We illustrate the empirical relevance of
our test by focusing on Granger causality using financial time series data to test for
nonlinear leverage versus volatility feedback effects and to test for causality between
stock returns and trading volume. In a third application, we investigate Granger
causality between macroeconomic variables

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## Nonparametric tests for conditional independence using conditional distributions

Fonte: Universidade Carlos III de Madrid
Publicador: Universidade Carlos III de Madrid

Tipo: info:eu-repo/semantics/draft; info:eu-repo/semantics/workingPaper
Formato: text/plain; application/pdf

Publicado em 06/01/2012
Português

Relevância na Pesquisa

66.56%

#Nonparametric tests#Time series#Conditional independence#Granger non-causality#Nadaraya-Watson estimator#Conditional distribution function#VIX volatility index#S&P500 index#C12#C14#C15

The concept of causality is naturally defined in terms of conditional distribution, however almost all the empirical works focus on causality in mean. This paper aim to propose a nonparametric statistic to test the conditional independence and Granger non-causality between two variables conditionally on another one. The test statistic is based on the comparison of conditional distribution functions using an L2 metric. We use Nadaraya-Watson method to estimate the conditional distribution functions. We establish the asymptotic size and power properties of the test statistic and we motivate the validity of the local bootstrap. Further, we ran a simulation experiment to investigate the finite sample properties of the test and we illustrate its practical relevance by examining the Granger non-causality between S&P 500 Index returns and VIX volatility index. Contrary to the conventional t-test, which is based on a linear mean-regression model, we find that VIX index predicts excess returns both at short and long horizons.; Financial support from the Natural Sciences and Engineering Research
Council of Canada and from the Spanish Ministry of Education through grants SEJ 2007-63098 are also acknowledged

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## Minimum Distance Estimation in Categorical Conditional Independence Models

Fonte: Universidade Rice
Publicador: Universidade Rice

Tipo: Thesis; Text
Formato: 185 p.; application/pdf

Português

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#Pure sciences#Minimum distance estimation#Categorical independence#Conditional independence#Discrete multivariate analysis#Contingency table#Statistics

One of the oldest and most fundamental problems in statistics is the analysis of cross-classified data called contingency tables. Analyzing contingency tables is typically a question of association - do the variables represented in the table exhibit special dependencies or lack thereof? The statistical models which best capture these experimental notions of dependence are the categorical conditional independence models; however, until recent discoveries concerning the strongly algebraic nature of the conditional independence models surfaced, the models were widely overlooked due to their unwieldy implicit description. Apart from the inferential question above, this thesis asks the more basic question - suppose such an experimental model of association is known, how can one incorporate this information into the estimation of the joint distribution of the table? In the traditional parametric setting several estimation paradigms have been developed over the past century; however, traditional results are not applicable to arbitrary categorical conditional independence models due to their implicit nature. After laying out the framework for conditional independence and algebraic statistical models, we consider three aspects of estimation in the models using the minimum Euclidean (L2E)...

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## Technical Note : assessing predictive capacity and conditional independence of landslide predisposing factors for shallow landslide susceptibility models

Fonte: Universidade do Porto
Publicador: Universidade do Porto

Tipo: Artigo de Revista Científica

Português

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The aim of this study is to identify the landslide predisposing factors' combination using a bivariate statistical model that best predicts landslide susceptibility. The best model is one that has simultaneously good performance in terms of suitability and predictive power and has been developed using variables that are conditionally independent. The study area is the Santa Marta de Penaguião council (70 km2) located in the Northern Portugal. In order to identify the best combination of landslide predisposing factors, all possible combinations using up to seven predisposing factors were performed, which resulted in 120 predictions that were assessed with a landside inventory containing 767 shallow translational slides. The best landslide susceptibility model was selected according to the model degree of fitness and on the basis of a conditional independence criterion. The best model was developed with only three landslide predisposing factors (slope angle, inverse wetness index, and land use) and was compared with a model developed using all seven landslide predisposing factors. Results showed that it is possible to produce a reliable landslide susceptibility model using fewer landslide predisposing factors, which contributes towards higher conditional independence.

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## Conditional independence relations among biological markers may improve clinical decision as in the case of triple negative breast cancers

Fonte: BioMed Central
Publicador: BioMed Central

Tipo: Artigo de Revista Científica

Publicado em 15/10/2009
Português

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The associations existing among different biomarkers are important in clinical settings because they contribute to the characterisation of specific pathways related to the natural history of the disease, genetic and environmental determinants. Despite the availability of binary/linear (or at least monotonic) correlation indices, the full exploitation of molecular information depends on the knowledge of direct/indirect conditional independence (and eventually causal) relationships among biomarkers, and with target variables in the population of interest. In other words, that depends on inferences which are performed on the joint multivariate distribution of markers and target variables. Graphical models, such as Bayesian Networks, are well suited to this purpose. Therefore, we reconsidered a previously published case study on classical biomarkers in breast cancer, namely estrogen receptor (ER), progesterone receptor (PR), a proliferative index (Ki67/MIB-1) and to protein HER2/neu (NEU) and p53, to infer conditional independence relations existing in the joint distribution by inferring (learning) the structure of graphs entailing those relations of independence. We also examined the conditional distribution of a special molecular phenotype...

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## Gaussian conditional independence relations have no finite complete characterization

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 21/04/2007
Português

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We show that there can be no finite list of conditional independence
relations which can be used to deduce all conditional independence implications
among Gaussian random variables. To do this, we construct, for each $n> 3$ a
family of $n$ conditional independence statements on $n$ random variables which
together imply that $X_1 \ind X_2$, and such that no subset have this same
implication. The proof relies on binomial primary decomposition.; Comment: 6 pages

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## A Scalable Conditional Independence Test for Nonlinear, Non-Gaussian Data

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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Many relations of scientific interest are nonlinear, and even in linear
systems distributions are often non-Gaussian, for example in fMRI BOLD data. A
class of search procedures for causal relations in high dimensional data relies
on sample derived conditional independence decisions. The most common
applications rely on Gaussian tests that can be systematically erroneous in
nonlinear non-Gaussian cases. Recent work (Gretton et al. (2009), Tillman et
al. (2009), Zhang et al. (2011)) has proposed conditional independence tests
using Reproducing Kernel Hilbert Spaces (RKHS). Among these, perhaps the most
efficient has been KCI (Kernel Conditional Independence, Zhang et al. (2011)),
with computational requirements that grow effectively at least as O(N3),
placing it out of range of large sample size analysis, and restricting its
applicability to high dimensional data sets. We propose a class of O(N2) tests
using conditional correlation independence (CCI) that require a few seconds on
a standard workstation for tests that require tens of minutes to hours for the
KCI method, depending on degree of parallelization, with similar accuracy. For
accuracy on difficult nonlinear, non-Gaussian data sets, we also compare a
recent test due to Harris & Drton (2012)...

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## Robustness and Conditional Independence Ideals

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 06/10/2011
Português

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We study notions of robustness of Markov kernels and probability distribution
of a system that is described by $n$ input random variables and one output
random variable. Markov kernels can be expanded in a series of potentials that
allow to describe the system's behaviour after knockouts. Robustness imposes
structural constraints on these potentials. Robustness of probability
distributions is defined via conditional independence statements. These
statements can be studied algebraically. The corresponding conditional
independence ideals are related to binary edge ideals. The set of robust
probability distributions lies on an algebraic variety. We compute a Gr\"obner
basis of this ideal and study the irreducible decomposition of the variety.
These algebraic results allow to parametrize the set of all robust probability
distributions.; Comment: 16 pages

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## Extended Conditional Independence and Applications in Causal Inference

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 01/12/2015
Português

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The goal of this paper is to integrate the notions of stochastic conditional
independence and variation conditional independence under a more general notion
of extended conditional independence. We show that under appropriate
assumptions the calculus that applies for the two cases separately (axioms of a
separoid) still applies for the extended case. These results provide a rigorous
basis for a wide range of statistical concepts, including ancillarity and
sufficiency, and, in particular, the Decision Theoretic framework for
statistical causality, which uses the language and calculus of conditional
independence in order to express causal properties and make causal inferences.

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## Conditional Independence and Markov Properties in Possibility Theory

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 16/01/2013
Português

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Conditional independence and Markov properties are powerful tools allowing
expression of multidimensional probability distributions by means of
low-dimensional ones. As multidimensional possibilistic models have been
studied for several years, the demand for analogous tools in possibility theory
seems to be quite natural. This paper is intended to be a promotion of de
Cooman's measure-theoretic approcah to possibility theory, as this approach
allows us to find analogies to many important results obtained in probabilistic
framework. First, we recall semi-graphoid properties of conditional
possibilistic independence, parameterized by a continuous t-norm, and find
sufficient conditions for a class of Archimedean t-norms to have the graphoid
property. Then we introduce Markov properties and factorization of possibility
distrubtions (again parameterized by a continuous t-norm) and find the
relationships between them. These results are accompanied by a number of
conterexamples, which show that the assumptions of specific theorems are
substantial.; Comment: Appears in Proceedings of the Sixteenth Conference on Uncertainty in
Artificial Intelligence (UAI2000)

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## Kernel-based Conditional Independence Test and Application in Causal Discovery

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 14/02/2012
Português

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46.59%

Conditional independence testing is an important problem, especially in
Bayesian network learning and causal discovery. Due to the curse of
dimensionality, testing for conditional independence of continuous variables is
particularly challenging. We propose a Kernel-based Conditional Independence
test (KCI-test), by constructing an appropriate test statistic and deriving its
asymptotic distribution under the null hypothesis of conditional independence.
The proposed method is computationally efficient and easy to implement.
Experimental results show that it outperforms other methods, especially when
the conditioning set is large or the sample size is not very large, in which
case other methods encounter difficulties.

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## Bayesian test of significance for conditional independence: The multinomial model

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 16/06/2013
Português

Relevância na Pesquisa

46.41%

Conditional independence tests (CI tests) have received special attention
lately in Machine Learning and Computational Intelligence related literature as
an important indicator of the relationship among the variables used by their
models. In the field of Probabilistic Graphical Models (PGM)--which includes
Bayesian Networks (BN) models--CI tests are especially important for the task
of learning the PGM structure from data. In this paper, we propose the Full
Bayesian Significance Test (FBST) for tests of conditional independence for
discrete datasets. FBST is a powerful Bayesian test for precise hypothesis, as
an alternative to frequentist's significance tests (characterized by the
calculation of the \emph{p-value}).; Comment: 24 pages, 33 figures

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## Smoothness of Gaussian conditional independence models

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 28/10/2009
Português

Relevância na Pesquisa

46.52%

Conditional independence in a multivariate normal (or Gaussian) distribution
is characterized by the vanishing of subdeterminants of the distribution's
covariance matrix. Gaussian conditional independence models thus correspond to
algebraic subsets of the cone of positive definite matrices. For statistical
inference in such models it is important to know whether or not the model
contains singularities. We study this issue in models involving up to four
random variables. In particular, we give examples of conditional independence
relations which, despite being probabilistically representable, yield models
that non-trivially decompose into a finite union of several smooth submodels.

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## Conditional Independence in Uncertainty Theories

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 13/03/2013
Português

Relevância na Pesquisa

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This paper introduces the notions of independence and conditional
independence in valuation-based systems (VBS). VBS is an axiomatic framework
capable of representing many different uncertainty calculi. We define
independence and conditional independence in terms of factorization of the
joint valuation. The definitions of independence and conditional independence
in VBS generalize the corresponding definitions in probability theory. Our
definitions apply not only to probability theory, but also to Dempster-Shafer's
belief-function theory, Spohn's epistemic-belief theory, and Zadeh's
possibility theory. In fact, they apply to any uncertainty calculi that fit in
the framework of valuation-based systems.; Comment: Appears in Proceedings of the Eighth Conference on Uncertainty in
Artificial Intelligence (UAI1992)

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## A Graph-Based Inference Method for Conditional Independence

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 20/03/2013
Português

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The graphoid axioms for conditional independence, originally described by
Dawid [1979], are fundamental to probabilistic reasoning [Pearl, 19881. Such
axioms provide a mechanism for manipulating conditional independence assertions
without resorting to their numerical definition. This paper explores a
representation for independence statements using multiple undirected graphs and
some simple graphical transformations. The independence statements derivable in
this system are equivalent to those obtainable by the graphoid axioms.
Therefore, this is a purely graphical proof technique for conditional
independence.; Comment: Appears in Proceedings of the Seventh Conference on Uncertainty in
Artificial Intelligence (UAI1991)

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## Conditional independence relations and log-linear models for random permutations

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 16/11/2007
Português

Relevância na Pesquisa

46.41%

We propose a new class of models for random permutations, which we call
log-linear models, by the analogy with log-linear models used in the analysis
of contingency tables. As a special case, we study the family of all
Luce-decomposable distributions, and the family of those random permutations,
for which the distribution of both the permutation and its inverse is
Luce-decomposable. We show that these latter models can be described by
conditional independence relations. We calculate the number of free parameters
in these models, and describe an iterative algorithm for maximum likelihood
estimation, which enables us to test if a set of data satisfies the conditional
independence relations or not.; Comment: 25 pages

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## Conditions Under Which Conditional Independence and Scoring Methods Lead to Identical Selection of Bayesian Network Models

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 10/01/2013
Português

Relevância na Pesquisa

46.41%

#Computer Science - Artificial Intelligence#Computer Science - Learning#Statistics - Machine Learning

It is often stated in papers tackling the task of inferring Bayesian network
structures from data that there are these two distinct approaches: (i) Apply
conditional independence tests when testing for the presence or otherwise of
edges; (ii) Search the model space using a scoring metric. Here I argue that
for complete data and a given node ordering this division is a myth, by showing
that cross entropy methods for checking conditional independence are
mathematically identical to methods based upon discriminating between models by
their overall goodness-of-fit logarithmic scores.; Comment: Appears in Proceedings of the Seventeenth Conference on Uncertainty
in Artificial Intelligence (UAI2001)

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## Nonparametric testing of conditional independence by means of the partial copula

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 24/01/2011
Português

Relevância na Pesquisa

46.64%

We propose a new method to test conditional independence of two real random
variables $Y$ and $Z$ conditionally on an arbitrary third random variable $X$.
%with $F_{.|.}$ representing conditional distribution functions, The partial
copula is introduced, defined as the joint distribution of $U=F_{Y|X}(Y|X)$ and
$V=F_{Z|X}(Z|X)$. We call this transformation of $(Y,Z)$ into $(U,V)$ the
partial copula transform. It is easy to show that if $Y$ and $Z$ are continuous
for any given value of $X$, then $Y\ind Z|X$ implies $U\ind V$. Conditional
independence can then be tested by (i) applying the partial copula transform to
the data points and (ii) applying a test of ordinary independence to the
transformed data. In practice, $F_{Y|X}$ and $F_{Z|X}$ will need to be
estimated, which can be done by, e.g., standard kernel methods. We show that
under easily satisfied conditions, and for a very large class of test
statistics for independence which includes the covariance, Kendall's tau, and
Hoeffding's test statistic, the effect of this estimation vanishes
asymptotically. Thus, for large samples, the estimation can be ignored and we
have a simple method which can be used to apply a wide range of tests of
independence, including ones with consistency for arbitrary alternatives...

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## Testing conditional independence using maximal nonlinear conditional correlation

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 19/10/2010
Português

Relevância na Pesquisa

46.52%

In this paper, the maximal nonlinear conditional correlation of two random
vectors $X$ and $Y$ given another random vector $Z$, denoted by
$\rho_1(X,Y|Z)$, is defined as a measure of conditional association, which
satisfies certain desirable properties. When $Z$ is continuous, a test for
testing the conditional independence of $X$ and $Y$ given $Z$ is constructed
based on the estimator of a weighted average of the form
$\sum_{k=1}^{n_Z}f_Z(z_k)\rho^2_1(X,Y|Z=z_k)$, where $f_Z$ is the probability
density function of $Z$ and the $z_k$'s are some points in the range of $Z$.
Under some conditions, it is shown that the test statistic is asymptotically
normal under conditional independence, and the test is consistent.; Comment: Published in at http://dx.doi.org/10.1214/09-AOS770 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org)

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