Bagging statistical network inference from large-scale gene expression data.

Modern biology and medicine aim at hunting molecular and cellular causes of biological functions and diseases. Gene regulatory networks (GRN) inferred from gene expression data are considered an important aid for this research by providing a map of molecular interactions. Hence, GRNs have the potential enabling and enhancing basic as well as applied research in the life sciences. In this paper, we introduce a new method called BC3NET for inferring causal gene regulatory networks from large-scale gene expression data. BC3NET is an ensemble method that is based on bagging the C3NET algorithm, which means it corresponds to a Bayesian approach with noninformative priors. In this study we demonstrate for a variety of simulated and biological gene expression data from S. cerevisiae that BC3NET is an important enhancement over other inference methods that is capable of capturing biochemical interactions from transcription regulation and protein-protein interaction sensibly. An implementation of BC3NET is freely available as an R package from the CRAN repository. © 2012 de Matos Simoes, Emmert-Streib.

Hierarchical Bayesian models in ecology: Reconstructing species interaction networks from non-homogeneous species abundance data

The relationships among organisms and their surroundings can be of immense complexity. To describe and understand an ecosystem as a tangled bank, multiple ways of interaction and their effects have to be considered, such as predation, competition, mutualism and facilitation. Understanding the resulting interaction networks is a challenge in changing environments, e.g. to predict knock-on effects of invasive species and to understand how climate change impacts biodiversity. The elucidation of complex ecological systems with their interactions will benefit enormously from the development of new machine learning tools that aim to infer the structure of interaction networks from field data. In the present study, we propose a novel Bayesian regression and multiple changepoint model (BRAM) for reconstructing species interaction networks from observed species distributions. The model has been devised to allow robust inference in the presence of spatial autocorrelation and distributional heterogeneity. We have evaluated the model on simulated data that combines a trophic niche model with a stochastic population model on a 2-dimensional lattice, and we have compared the performance of our model with L1-penalized sparse regression (LASSO) and non-linear Bayesian networks with the BDe scoring scheme. In addition, we have applied our method to plant ground coverage data from the western shore of the Outer Hebrides with the objective to infer the ecological interactions. (C) 2012 Elsevier B.V. All rights reserved.

Effects of Gold Nanoparticle and Enzyme Precipitation on Enhancement of Surface Plasmon Resonance Immunoassay: A Super Sensitive Measurement of Anti- Glutamic Acid Decarboxylase Antibody

Introduction: In this study, colloidal gold nanoparticle and precipitation of an insoluble product formed by HRP-biocatalyzed oxidation of 3,3'-diaminobenzidine (DAB) in the presence of H2O2 were used to enhance the signal obtained from the surface plasmon resonance biosensor.

Methods: The colloidal gold nanoparticle was synthesized as described by Turkevitch et al., and their surface was firstly functionalized with HS(CH2)11(OCH2CH2)3COOH (OEG3¬-COOH) by self assembling technique. Thereafter, those OEG3-COOH functionalized nanoparticles were covalently conjugated with horseradish peroxidase (HRP) and anti-IgG antibody (specific to the Fc portion of all human IgG subclasses) to form an enzyme-immunogold complex. Characterization was performed by several methods: UV-Vis absorption, dynamic light scattering (DLS), transmission electron microscopy (TEM) and FTIR. The as-prepared enzyme-immunogold complex has been applied in enhancement of SPR immunoassay. A sensor chip used in the experiment was constructed by using 1:10 molar ratio of HS(CH2)11(OCH2CH2)6COOH and HS(CH2)11(OCH2CH2)3OH. The capture protein, GAD65 (autoantigen) which is recognized by anti-GAD antibody (autoantibody) in the sera of insulin-dependent diabetes mellitus patients, was immobilized onto the 1:10 surface via biotin-streptavidin interaction.

Results and conclusions: In the research, we reported the influences of gold nanoparticle and enzyme precipitation on the enhancement of SPR signal. Gold nanoparticle showed its enhancement as being consistent with other previous studies, while the enzyme precipitation using DAB substrate was applied for the first time and greatly amplified the SPR detection. As the results, anti-GAD antibody could be detected at pg/ml level which is far higher than that of commercial ELISA detection kit. This study indicates another way to enhance SPR measurement, and it is generally applicable to other SPR-based immunoassays.

Influence of the experimental design of gene expression studies on the inference of gene regulatory networks: environmental factors

The inference of gene regulatory networks gained within recent years a considerable interest in the biology and biomedical community. The purpose of this paper is to investigate the influence that environmental conditions can exhibit on the inference performance of network inference algorithms. Specifically, we study five network inference methods, Aracne, BC3NET, CLR, C3NET and MRNET, and compare the results for three different conditions: (I) observational gene expression data: normal environmental condition, (II) interventional gene expression data: growth in rich media, (III) interventional gene expression data: normal environmental condition interrupted by a positive spike-in stimulation. Overall, we find that different statistical inference methods lead to comparable, but condition-specific results. Further, our results suggest that non-steady-state data enhance the inferability of regulatory networks.

Using geostatistical Bayesian Updating to integrate airborne radiometrics and soil geochemistry to improve mapping for mineral exploration

Mineral exploration programmes around the world use data from remote sensing, geophysics and direct sampling. On a regional scale, the combination of airborne geophysics and ground-based geochemical sampling can aid geological mapping and economic minerals exploration. The fact that airborne geophysical and traditional soil-sampling data are generated at different spatial resolutions means that they are not immediately comparable due to their different sampling density. Several geostatistical techniques, including indicator cokriging and collocated cokriging, can be used to integrate different types of data into a geostatistical model. With increasing numbers of variables the inference of the cross-covariance model required for cokriging can be demanding in terms of effort and computational time. In this paper a Gaussian-based Bayesian updating approach is applied to integrate airborne radiometric data and ground-sampled geochemical soil data to maximise information generated from the soil survey, to enable more accurate geological interpretation for the exploration and development of natural resources. The Bayesian updating technique decomposes the collocated estimate into a production of two models: prior and likelihood models. The prior model is built from primary information and the likelihood model is built from secondary information. The prior model is then updated with the likelihood model to build the final model. The approach allows multiple secondary variables to be simultaneously integrated into the mapping of the primary variable. The Bayesian updating approach is demonstrated using a case study from Northern Ireland where the history of mineral prospecting for precious and base metals dates from the 18th century. Vein-hosted, strata-bound and volcanogenic occurrences of mineralisation are found. The geostatistical technique was used to improve the resolution of soil geochemistry, collected one sample per 2 km2, by integrating more closely measured airborne geophysical data from the GSNI Tellus Survey, measured over a footprint of 65 x 200 m. The directly measured geochemistry data were considered as primary data in the Bayesian approach and the airborne radiometric data were used as secondary data. The approach produced more detailed updated maps and in particular maximized information on mapped estimates of zinc, copper and lead. Greater delineation of an elongated northwest/southeast trending zone in the updated maps strengthened the potential to investigate stratabound base metal deposits.

Probabilistic Inference in Credal Networks: New Complexity Results

Credal networks are graph-based statistical models whose parameters take values in a set, instead of being sharply specified as in traditional statistical models (e.g., Bayesian networks). The computational complexity of inferences on such models depends on the irrelevance/independence concept adopted. In this paper, we study inferential complexity under the concepts of epistemic irrelevance and strong independence. We show that inferences under strong independence are NP-hard even in trees with binary variables except for a single ternary one. We prove that under epistemic irrelevance the polynomial-time complexity of inferences in credal trees is not likely to extend to more general models (e.g., singly connected topologies). These results clearly distinguish networks that admit efficient inferences and those where inferences are most likely hard, and settle several open questions regarding their computational complexity. We show that these results remain valid even if we disallow the use of zero probabilities. We also show that the computation of bounds on the probability of the future state in a hidden Markov model is the same whether we assume epistemic irrelevance or strong independence, and we prove an analogous result for inference in Naive Bayes structures. These inferential equivalences are important for practitioners, as hidden Markov models and Naive Bayes networks are used in real applications of imprecise probability.

Generalized loopy 2U: A new algorithm for approximate inference in credal networks

Credal networks generalize Bayesian networks by relaxing the requirement of precision of probabilities. Credal networks are considerably more expressive than Bayesian networks, but this makes belief updating NP-hard even on polytrees. We develop a new efficient algorithm for approximate belief updating in credal networks. The algorithm is based on an important representation result we prove for general credal networks: that any credal network can be equivalently reformulated as a credal network with binary variables; moreover, the transformation, which is considerably more complex than in the Bayesian case, can be implemented in polynomial time. The equivalent binary credal network is then updated by L2U, a loopy approximate algorithm for binary credal networks. Overall, we generalize L2U to non-binary credal networks, obtaining a scalable algorithm for the general case, which is approximate only because of its loopy nature. The accuracy of the inferences with respect to other state-of-the-art algorithms is evaluated by extensive numerical tests.

Generalized Loopy 2U: A New Algorithm for Approximate Inference in Credal Networks

Credal nets generalize Bayesian nets by relaxing the requirement of precision of probabilities. Credal nets are considerably more expressive than Bayesian nets, but this makes belief updating NP-hard even on polytrees. We develop a new efficient algorithm for approximate belief updating in credal nets. The algorithm is based on an important representation result we prove for general credal nets: that any credal net can be equivalently reformulated as a credal net with binary variables; moreover, the transformation, which is considerably more complex than in the Bayesian case, can be implemented in polynomial time. The equivalent binary credal net is updated by L2U, a loopy approximate algorithm for binary credal nets. Thus, we generalize L2U to non-binary credal nets, obtaining an accurate and scalable algorithm for the general case, which is approximate only because of its loopy nature. The accuracy of the inferences is evaluated by empirical tests.

Improving parameter learning of Bayesian nets from incomplete data

This paper addresses the estimation of parameters of a Bayesian network from incomplete data. The task is usually tackled by running the Expectation-Maximization (EM) algorithm several times in order to obtain a high log-likelihood estimate. We argue that choosing the maximum log-likelihood estimate (as well as the maximum penalized log-likelihood and the maximum a posteriori estimate) has severe drawbacks, being affected both by overfitting and model uncertainty. Two ideas are discussed to overcome these issues: a maximum entropy approach and a Bayesian model averaging approach. Both ideas can be easily applied on top of EM, while the entropy idea can be also implemented in a more sophisticated way, through a dedicated non-linear solver. A vast set of experiments shows that these ideas produce significantly better estimates and inferences than the traditional and widely used maximum (penalized) log-likelihood and maximum a posteriori estimates. In particular, if EM is adopted as optimization engine, the model averaging approach is the best performing one; its performance is matched by the entropy approach when implemented using the non-linear solver. The results suggest that the applicability of these ideas is immediate (they are easy to implement and to integrate in currently available inference engines) and that they constitute a better way to learn Bayesian network parameters.

Inference with multinomial data: why to weaken the prior strength

This paper considers inference from multinomial data and addresses the problem of choosing the strength of the Dirichlet prior under a mean-squared error criterion. We compare the Maxi-mum Likelihood Estimator (MLE) and the most commonly used Bayesian estimators obtained by assuming a prior Dirichlet distribution with non-informative prior parameters, that is, the parameters of the Dirichlet are equal and altogether sum up to the so called strength of the prior. Under this criterion, MLE becomes more preferable than the Bayesian estimators at the increase of the number of categories k of the multinomial, because non-informative Bayesian estimators induce a region where they are dominant that quickly shrinks with the increase of k. This can be avoided if the strength of the prior is not kept constant but decreased with the number of categories. We argue that the strength should decrease at least k times faster than usual estimators do.

Propositional and Relational Bayesian Networks Associated with Imprecise and Qualitative Probabilistic Assessments

This paper investigates a representation language with flexibility inspired by probabilistic logic and compactness inspired by relational Bayesian networks. The goal is to handle propositional and first-order constructs together with precise, imprecise, indeterminate and qualitative probabilistic assessments. The paper shows how this can be achieved through the theory of credal networks. New exact and approximate inference algorithms based on multilinear programming and iterated/loopy propagation of interval probabilities are presented; their superior performance, compared to existing ones, is shown empirically.

Inference in credal networks using multilinear programming

A credal network is a graphical tool for representation and manipulation of uncertainty, where probability values may be imprecise or indeterminate. A credal network associates a directed acyclic graph with a collection of sets of probability measures; in this context, inference is the computation of tight lower and upper bounds for conditional probabilities. In this paper we present new algorithms for inference in credal networks based on multilinear programming techniques. Experiments indicate that these new algorithms have better performance than existing ones, in the sense that they can produce more accurate results in larger networks.