13,977 research outputs found
Scalable Bayesian nonparametric measures for exploring pairwise dependence via Dirichlet Process Mixtures
In this article we propose novel Bayesian nonparametric methods using
Dirichlet Process Mixture (DPM) models for detecting pairwise dependence
between random variables while accounting for uncertainty in the form of the
underlying distributions. A key criteria is that the procedures should scale to
large data sets. In this regard we find that the formal calculation of the
Bayes factor for a dependent-vs.-independent DPM joint probability measure is
not feasible computationally. To address this we present Bayesian diagnostic
measures for characterising evidence against a "null model" of pairwise
independence. In simulation studies, as well as for a real data analysis, we
show that our approach provides a useful tool for the exploratory nonparametric
Bayesian analysis of large multivariate data sets
Bayesian factorizations of big sparse tensors
It has become routine to collect data that are structured as multiway arrays
(tensors). There is an enormous literature on low rank and sparse matrix
factorizations, but limited consideration of extensions to the tensor case in
statistics. The most common low rank tensor factorization relies on parallel
factor analysis (PARAFAC), which expresses a rank tensor as a sum of rank
one tensors. When observations are only available for a tiny subset of the
cells of a big tensor, the low rank assumption is not sufficient and PARAFAC
has poor performance. We induce an additional layer of dimension reduction by
allowing the effective rank to vary across dimensions of the table. For
concreteness, we focus on a contingency table application. Taking a Bayesian
approach, we place priors on terms in the factorization and develop an
efficient Gibbs sampler for posterior computation. Theory is provided showing
posterior concentration rates in high-dimensional settings, and the methods are
shown to have excellent performance in simulations and several real data
applications
Exploring dependence between categorical variables: benefits and limitations of using variable selection within Bayesian clustering in relation to log-linear modelling with interaction terms
This manuscript is concerned with relating two approaches that can be used to
explore complex dependence structures between categorical variables, namely
Bayesian partitioning of the covariate space incorporating a variable selection
procedure that highlights the covariates that drive the clustering, and
log-linear modelling with interaction terms. We derive theoretical results on
this relation and discuss if they can be employed to assist log-linear model
determination, demonstrating advantages and limitations with simulated and real
data sets. The main advantage concerns sparse contingency tables. Inferences
from clustering can potentially reduce the number of covariates considered and,
subsequently, the number of competing log-linear models, making the exploration
of the model space feasible. Variable selection within clustering can inform on
marginal independence in general, thus allowing for a more efficient
exploration of the log-linear model space. However, we show that the clustering
structure is not informative on the existence of interactions in a consistent
manner. This work is of interest to those who utilize log-linear models, as
well as practitioners such as epidemiologists that use clustering models to
reduce the dimensionality in the data and to reveal interesting patterns on how
covariates combine.Comment: Preprin
ProbCD: enrichment analysis accounting for categorization uncertainty
As in many other areas of science, systems biology makes extensive use of statistical association and significance estimates in contingency tables, a type of categorical data analysis known in this field as enrichment (also over-representation or enhancement) analysis. In spite of efforts to create probabilistic annotations, especially in the Gene Ontology context, or to deal with uncertainty in high throughput-based datasets, current enrichment methods largely ignore this probabilistic information since they are mainly based on variants of the Fisher Exact Test. We developed an open-source R package to deal with probabilistic categorical data analysis, ProbCD, that does not require a static contingency table. The contingency table for
the enrichment problem is built using the expectation of a Bernoulli Scheme stochastic process given the categorization probabilities. An on-line interface was created to allow usage by non-programmers and is available at: http://xerad.systemsbiology.net/ProbCD/. We present an analysis framework and software tools to address the issue of uncertainty in categorical data analysis. In particular, concerning the enrichment analysis, ProbCD can accommodate: (i) the stochastic nature of the high-throughput experimental techniques and (ii) probabilistic gene annotation
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