2,114 research outputs found
Gene Function Classification Using Bayesian Models with Hierarchy-Based Priors
We investigate the application of hierarchical classification schemes to the
annotation of gene function based on several characteristics of protein
sequences including phylogenic descriptors, sequence based attributes, and
predicted secondary structure. We discuss three Bayesian models and compare
their performance in terms of predictive accuracy. These models are the
ordinary multinomial logit (MNL) model, a hierarchical model based on a set of
nested MNL models, and a MNL model with a prior that introduces correlations
between the parameters for classes that are nearby in the hierarchy. We also
provide a new scheme for combining different sources of information. We use
these models to predict the functional class of Open Reading Frames (ORFs) from
the E. coli genome. The results from all three models show substantial
improvement over previous methods, which were based on the C5 algorithm. The
MNL model using a prior based on the hierarchy outperforms both the
non-hierarchical MNL model and the nested MNL model. In contrast to previous
attempts at combining these sources of information, our approach results in a
higher accuracy rate when compared to models that use each data source alone.
Together, these results show that gene function can be predicted with higher
accuracy than previously achieved, using Bayesian models that incorporate
suitable prior information
Improving Classification When a Class Hierarchy is Available Using a Hierarchy-Based Prior
We introduce a new method for building classification models when we have
prior knowledge of how the classes can be arranged in a hierarchy, based on how
easily they can be distinguished. The new method uses a Bayesian form of the
multinomial logit (MNL, a.k.a. ``softmax'') model, with a prior that introduces
correlations between the parameters for classes that are nearby in the tree. We
compare the performance on simulated data of the new method, the ordinary MNL
model, and a model that uses the hierarchy in different way. We also test the
new method on a document labelling problem, and find that it performs better
than the other methods, particularly when the amount of training data is small
Nonlinear Models Using Dirichlet Process Mixtures
We introduce a new nonlinear model for classification, in which we model the
joint distribution of response variable, y, and covariates, x,
non-parametrically using Dirichlet process mixtures. We keep the relationship
between y and x linear within each component of the mixture. The overall
relationship becomes nonlinear if the mixture contains more than one component.
We use simulated data to compare the performance of this new approach to a
simple multinomial logit (MNL) model, an MNL model with quadratic terms, and a
decision tree model. We also evaluate our approach on a protein fold
classification problem, and find that our model provides substantial
improvement over previous methods, which were based on Neural Networks (NN) and
Support Vector Machines (SVM). Folding classes of protein have a hierarchical
structure. We extend our method to classification problems where a class
hierarchy is available. We find that using the prior information regarding the
hierarchical structure of protein folds can result in higher predictive
accuracy
A Bayesian alternative to mutual information for the hierarchical clustering of dependent random variables
The use of mutual information as a similarity measure in agglomerative
hierarchical clustering (AHC) raises an important issue: some correction needs
to be applied for the dimensionality of variables. In this work, we formulate
the decision of merging dependent multivariate normal variables in an AHC
procedure as a Bayesian model comparison. We found that the Bayesian
formulation naturally shrinks the empirical covariance matrix towards a matrix
set a priori (e.g., the identity), provides an automated stopping rule, and
corrects for dimensionality using a term that scales up the measure as a
function of the dimensionality of the variables. Also, the resulting log Bayes
factor is asymptotically proportional to the plug-in estimate of mutual
information, with an additive correction for dimensionality in agreement with
the Bayesian information criterion. We investigated the behavior of these
Bayesian alternatives (in exact and asymptotic forms) to mutual information on
simulated and real data. An encouraging result was first derived on
simulations: the hierarchical clustering based on the log Bayes factor
outperformed off-the-shelf clustering techniques as well as raw and normalized
mutual information in terms of classification accuracy. On a toy example, we
found that the Bayesian approaches led to results that were similar to those of
mutual information clustering techniques, with the advantage of an automated
thresholding. On real functional magnetic resonance imaging (fMRI) datasets
measuring brain activity, it identified clusters consistent with the
established outcome of standard procedures. On this application, normalized
mutual information had a highly atypical behavior, in the sense that it
systematically favored very large clusters. These initial experiments suggest
that the proposed Bayesian alternatives to mutual information are a useful new
tool for hierarchical clustering
Fully Bayesian Logistic Regression with Hyper-Lasso Priors for High-dimensional Feature Selection
High-dimensional feature selection arises in many areas of modern science.
For example, in genomic research we want to find the genes that can be used to
separate tissues of different classes (e.g. cancer and normal) from tens of
thousands of genes that are active (expressed) in certain tissue cells. To this
end, we wish to fit regression and classification models with a large number of
features (also called variables, predictors). In the past decade, penalized
likelihood methods for fitting regression models based on hyper-LASSO
penalization have received increasing attention in the literature. However,
fully Bayesian methods that use Markov chain Monte Carlo (MCMC) are still in
lack of development in the literature. In this paper we introduce an MCMC
(fully Bayesian) method for learning severely multi-modal posteriors of
logistic regression models based on hyper-LASSO priors (non-convex penalties).
Our MCMC algorithm uses Hamiltonian Monte Carlo in a restricted Gibbs sampling
framework; we call our method Bayesian logistic regression with hyper-LASSO
(BLRHL) priors. We have used simulation studies and real data analysis to
demonstrate the superior performance of hyper-LASSO priors, and to investigate
the issues of choosing heaviness and scale of hyper-LASSO priors.Comment: 33 pages. arXiv admin note: substantial text overlap with
arXiv:1308.469
Latent protein trees
Unbiased, label-free proteomics is becoming a powerful technique for
measuring protein expression in almost any biological sample. The output of
these measurements after preprocessing is a collection of features and their
associated intensities for each sample. Subsets of features within the data are
from the same peptide, subsets of peptides are from the same protein, and
subsets of proteins are in the same biological pathways, therefore, there is
the potential for very complex and informative correlational structure inherent
in these data. Recent attempts to utilize this data often focus on the
identification of single features that are associated with a particular
phenotype that is relevant to the experiment. However, to date, there have been
no published approaches that directly model what we know to be multiple
different levels of correlation structure. Here we present a hierarchical
Bayesian model which is specifically designed to model such correlation
structure in unbiased, label-free proteomics. This model utilizes partial
identification information from peptide sequencing and database lookup as well
as the observed correlation in the data to appropriately compress features into
latent proteins and to estimate their correlation structure. We demonstrate the
effectiveness of the model using artificial/benchmark data and in the context
of a series of proteomics measurements of blood plasma from a collection of
volunteers who were infected with two different strains of viral influenza.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS639 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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