469 research outputs found
Variations on undirected graphical models and their relationships
No full textsummary:We compare alternative definitions of undirected graphical models for discrete, finite variables. Lauritzen [7] provides several definitions of such models and describes their relationships. He shows that the definitions agree only when joint distributions represented by the models are limited to strictly positive distributions. Heckerman et al. [6], in their paper on dependency networks, describe another definition of undirected graphical models for strictly positive distributions. They show that this definition agrees with those of Lauritzen [7] again when distributions are strictly positive. In this paper, we extend the definition of Heckerman et al. [6] to arbitrary distributions and show how this definition relates to those of Lauritzen [7] in the general case
Coauthor prediction for junior researchers
No full textResearch collaboration can bring in different perspectives and generate more productive results. However, finding an appropriate collaborator can be difficult due to the lacking of sufficient information. Link prediction is a related technique for collaborator discovery; but its focus has been mostly on the core authors who have relatively more publications. We argue that junior researchers actually need more help in finding collaborators. Thus, in this paper, we focus on coauthor prediction for junior researchers. Most of the previous works on coauthor prediction considered global network feature and local network feature separately, or tried to combine local network feature and content feature. But we found a significant improvement by simply combing local network feature and global network feature. We further developed a regularization based approach to incorporate multiple features simultaneously. Experimental results demonstrated that this approach outperformed the simple linear combination of multiple features. We further showed that content features, which were proved to be useful in link prediction, can be easily integrated into our regularization approach. © 2013 Springer-Verlag
Compatible Priors for Causal Bayesian Networks
No full textWe consider discrete causal DAG-models (or Bayesian Networks) wherein the ordering
of the variables is fixed across model structures. Given a prior on the parameter space of
a model we describe a method for deriving a compatible prior on the parameter space of
a submodel. This allows to generate automatically compatible priors for model parameters
starting from a single prior relative to the largest entertained model. Our method makes
use of a general procedure for constructing compatible priors for causal DAG-models, named
reference conditioning, which is invariant within a suitable class of re-parameterisations and is
model intrinsic. We show that if the generating prior satisfies global parameter independence,
so does the compatible prior; in addition, prior modularity holds. Further results are obtained
when the starting prior is product Dirichlet. A simple illustration of the methodology, and
comparisons with alternative methods, are presented
Exploiting knowledge of immune selection in HIV-1 to detect HIV-specific CD8 T-cell responses
No full textSince HLA-restricted cytotoxic T-cell responses select specific polymorphisms in HIV-1 sequences and HLA diversity is relatively static in human populations, we investigated the use of peptide epitopes based on sites of HLA-associated adaptation in HIV-1 sequences to stimulate and detect T-cell responses ex vivo. These "HLA-optimised" peptides captured more HIV-1 Nef-specific responses compared with overlapping peptides of a single consensus sequence, in interferon-γ enzyme linked immunospot assays. Sites of immune selection can reveal more immunogenic epitopes in HLA-diverse populations and offer insights into the nature of HLA-epitope targeting, which could be applied in vaccine design
Leveraging hierarchical population structure in discrete association studies
No full textPopulation structure can confound the identification of correlations in biological data. Such confounding has been recognized in multiple biological disciplines, resulting in a disparate collection of proposed solutions. We examine several methods that correct for confounding on discrete data with hierarchical population structure and identify two distinct confounding processes, which we call coevolution and conditional influence. We describe these processes in terms of generative models and show that these generative models can be used to correct for the confounding effects. Finally, we apply the models to three applications: identification of escape mutations in HIV-1 in response to specific HLA-mediated immune pressure, prediction of coevolving residues in an HIV-1 peptide, and a search for genotypes that are associated with bacterial resistance traits in Arabidopsis thaliana. We show that coevolution is a better description of confounding in some applications and conditional influence is better in others. That is, we show that no single method is best for addressing all forms of confounding. Analysis tools based on these models are available on the internet as both web based applications and downloadable source code at http://atom.research.microsoft.com/bio/phylod.asp
New tools for consistency in Bayesian Nonparametrics (with discussion)
No full textPosterior consistency and the parallel behaviour of consistency of maximum likelihood estimators is analyzed
in nonparametric statistical problems. The framework is the hypo-Strong Law of Large Numbers,
a form of “one-sided” Uniform Law of Large Numbers
Moment priors for Bayesian model choice with applications to directed acyclic graphs
No full textWe propose a new method for the objective comparison of two nested models based on non-local priors. More specifically, starting with a default prior under each of the two models, we construct a moment prior under the larger model, and then use the fractional Bayes factor for a comparison. Non-local priors
have been recently introduced to obtain a better separation between nested
models, thus accelerating the learning behaviour, relative to currently used
local priors, when the smaller model holds. Although the argument showing
the superior performance of non-local priors is asymptotic, the improvement
they produce is already apparent for small to moderate samples sizes, which
makes them a useful and practical tool. As a by-product, it turns out that routinely used objective methods, such as ordinary fractional Bayes factors, are alarmingly slow in learning that the smaller model holds. On the downside, when the larger model holds, non-local priors exhibit a weaker discriminatory power against sampling distributions close to the smaller model. However, this drawback becomes rapidly negligible as the sample size grows, because the learning rate of the Bayes factor under the larger model is exponentially fast, whether one uses local or non-local priors. We apply our methodology to directed acyclic graph models having a Gaussian distribution. Because of the recursive nature of the joint density, and the assumption of global parameter independence embodied in our prior, calculations need only be performed for individual vertices admitting a distinct parent structure under the two graphs; additionally we obtain closed-form expressions as in the ordinary conjugate case. We provide illustrations of our method for a simple three-variable case, as well as for a more elaborate seven-variable situation. Although we concentrate on pairwise comparisons of nested models, our procedure can be implemented to carry-out a search over the space of all models
Estimation in causal graphical models
No full textPearl (2000), Spirtes et al (1993) and Lauritzen (2001) set up a new framework to encode the causal relationships between the random variables by a causal Bayesian network. The estimation of the conditional probabilities in a Bayesian network has received considerable attention by several investigators (e. g., Jordan (1998), Geiger and Heckerman (1997), Ileckerman et al (1995)), but, this issue has not been studied in a causal Bayesian network.
In this thesis, we define the multicausal essential graph on the equivalence class of Bayesian networks in which each member of this class manifests a sort of strong type of invariance under (causal) manipulation called hypercausality. We then characterise the families of prior distributions on the parameters of the Bayesian networks which are consistent with hypercausality and show that their unmanipulated uncertain Bayesian networks must demonstrate the independence assumptions. As a result, such prior distributions satisfy a generalisation of the Geiger and lieckerman condition. In particular, when the corresponding essential graph is undirected, the mentioned class of prior distributions will reduce to the Hyper-Dirichlet family (see Chapter 6).
In tile second part of this thesis, we will calculate certain local sensitivity measures and through them we are able to provide the solutions for the following questions: Is the network structure that is learned from data robust with respect to changes of the directionality of some specific arrows? Is the local conditional distributions associated with the specified node robust with respect to the changes to its prior distribution or with respect to the changes to the local conditional distribution of another node? Most importantly, is the posterior distribution associated with the parameters of any node robust with respect to the changes to the prior distribution associated with the parameters of one specific node? Finally, are the quantities mentioned above robust with respect to the changes in the independence assumptions described in Chapter 3?
Most of the local sensitivity measures (particularly, local measures of the overall posteriors sensitivity), developed in the last decade, tend to diverge to infinity as the sample size becomes very large (Gustafson (1994) and Gustafson et al (1996)). This is in contrast to our knowledge that, starting from different priors, posteriors tend to agree as the data accumulate. Here we define a now class of metrics with more satisfactory asymptotic behaviour. The advantage of the corresponding local sensitivity measures is boundedness for large sample size
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