The Complexity of Reasoning with FODD and GFODD

Recent work introduced Generalized First Order Decision Diagrams (GFODD) as a knowledge representation that is useful in mechanizing decision theoretic planning in relational domains. GFODDs generalize function-free first order logic and include numerical values and numerical generalizations of existential and universal quantification. Previous work presented heuristic inference algorithms for GFODDs and implemented these heuristics in systems for decision theoretic planning. In this paper, we study the complexity of the computational problems addressed by such implementations. In particular, we study the evaluation problem, the satisfiability problem, and the equivalence problem for GFODDs under the assumption that the size of the intended model is given with the problem, a restriction that guarantees decidability. Our results provide a complete characterization placing these problems within the polynomial hierarchy. The same characterization applies to the corresponding restriction of problems in first order logic, giving an interesting new avenue for efficient inference when the number of objects is bounded. Our results show that for $\Sigma_k$ formulas, and for corresponding GFODDs, evaluation and satisfiability are $\Sigma_k^p$ complete, and equivalence is $\Pi_{k+1}^p$ complete. For $\Pi_k$ formulas evaluation is $\Pi_k^p$ complete, satisfiability is one level higher and is $\Sigma_{k+1}^p$ complete, and equivalence is $\Pi_{k+1}^p$ complete.Comment: A short version of this paper appears in AAAI 2014. Version 2 includes a reorganization and some expanded proof

Going the distance for protein function prediction: a new distance metric for protein interaction networks

Due to an error introduced in the production process, the x-axes in the first panels of Figure 1 and Figure 7 are not formatted correctly. The correct Figure 1 can be viewed here: http://dx.doi.org/10.1371/annotation/343bf260-f6ff-48a2-93b2-3cc79af518a9In protein-protein interaction (PPI) networks, functional similarity is often inferred based on the function of directly interacting proteins, or more generally, some notion of interaction network proximity among proteins in a local neighborhood. Prior methods typically measure proximity as the shortest-path distance in the network, but this has only a limited ability to capture fine-grained neighborhood distinctions, because most proteins are close to each other, and there are many ties in proximity. We introduce diffusion state distance (DSD), a new metric based on a graph diffusion property, designed to capture finer-grained distinctions in proximity for transfer of functional annotation in PPI networks. We present a tool that, when input a PPI network, will output the DSD distances between every pair of proteins. We show that replacing the shortest-path metric by DSD improves the performance of classical function prediction methods across the board.MC, HZ, NMD and LJC were supported in part by National Institutes of Health (NIH) R01 grant GM080330. JP was supported in part by NIH grant R01 HD058880. This material is based upon work supported by the National Science Foundation under grant numbers CNS-0905565, CNS-1018266, CNS-1012910, and CNS-1117039, and supported by the Army Research Office under grant W911NF-11-1-0227 (to MEC). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Assessment of network module identification across complex diseases

Many bioinformatics methods have been proposed for reducing the complexity of large gene or protein networks into relevant subnetworks or modules. Yet, how such methods compare to each other in terms of their ability to identify disease-relevant modules in different types of network remains poorly understood. We launched the 'Disease Module Identification DREAM Challenge', an open competition to comprehensively assess module identification methods across diverse protein-protein interaction, signaling, gene co-expression, homology and cancer-gene networks. Predicted network modules were tested for association with complex traits and diseases using a unique collection of 180 genome-wide association studies. Our robust assessment of 75 module identification methods reveals top-performing algorithms, which recover complementary trait-associated modules. We find that most of these modules correspond to core disease-relevant pathways, which often comprise therapeutic targets. This community challenge establishes biologically interpretable benchmarks, tools and guidelines for molecular network analysis to study human disease biology

Towards a more molecular taxonomy of disease

Abstract Background Disease taxonomies have been designed for many applications, but they tend not to fully incorporate the growing amount of molecular-level knowledge of disease processes, inhibiting research efforts. Understanding the degree to which we can infer disease relationships from molecular data alone may yield insights into how to ultimately construct more modern taxonomies that integrate both physiological and molecular information. Results We introduce a new technique we call Parent Promotion to infer hierarchical relationships between disease terms using disease-gene data. We compare this technique with both an established ontology inference method (CliXO) and a minimum weight spanning tree approach. Because there is no gold standard molecular disease taxonomy available, we compare our inferred hierarchies to both the Medical Subject Headings (MeSH) category C forest of diseases and to subnetworks of the Disease Ontology (DO). This comparison provides insights about the inference algorithms, choices of evaluation metrics, and the existing molecular content of various subnetworks of MeSH and the DO. Our results suggest that the Parent Promotion method performs well in most cases. Performance across MeSH trees is also correlated between inference methods. Specifically, inferred relationships are more consistent with those in smaller MeSH disease trees than larger ones, but there are some notable exceptions that may correlate with higher molecular content in MeSH. Conclusions Our experiments provide insights about learning relationships between diseases from disease genes alone. Future work should explore the prospect of disease term discovery from molecular data and how best to integrate molecular data with anatomical and clinical knowledge. This study nonetheless suggests that disease gene information has the potential to form an important part of the foundation for future representations of the disease landscape

Inferring Mechanisms of Compensation from E-MAP and SGA Data Using Local Search Algorithms for Max Cut

A new method based on a mathematically natural local search framework for max cut is developed to uncover functionally coherent module and BPM motifs in high-throughput genetic interaction data. Unlike previous methods, which also consider physical protein-protein interaction data, our method utilizes genetic interaction data only; this becomes increasingly important as high-throughput genetic interaction data is becoming available in settings where less is known about physical interaction data. We compare modules and BPMs obtained to previous methods and across different datasets. Despite needing no physical interaction information, the BPMs produced by our method are competitive with previous methods. Biological findings include a suggested global role for the prefoldin complex and a SWR subcomplex in pathway buffering in the budding yeast interactome

An example of functional annotation with DSD.

<p>The correct functional annotation for GLR1, on the third level of the MIPS hierarchy, 32.01.01 (oxidative stress response) is found among none of its direct neighbors, but with the node that is closest in DSD, MXR2. MXR2 is closest in DSD because it has the most similar neighborhood to GLR1.</p