Generalized Permutohedra from Probabilistic Graphical Models

A graphical model encodes conditional independence relations via the Markov properties. For an undirected graph these conditional independence relations can be represented by a simple polytope known as the graph associahedron, which can be constructed as a Minkowski sum of standard simplices. There is an analogous polytope for conditional independence relations coming from a regular Gaussian model, and it can be defined using multiinformation or relative entropy. For directed acyclic graphical models and also for mixed graphical models containing undirected, directed and bidirected edges, we give a construction of this polytope, up to equivalence of normal fans, as a Minkowski sum of matroid polytopes. Finally, we apply this geometric insight to construct a new ordering-based search algorithm for causal inference via directed acyclic graphical models.Comment: Appendix B is expanded. Final version to appear in SIAM J. Discrete Mat

The IBMAP approach for Markov networks structure learning

In this work we consider the problem of learning the structure of Markov networks from data. We present an approach for tackling this problem called IBMAP, together with an efficient instantiation of the approach: the IBMAP-HC algorithm, designed for avoiding important limitations of existing independence-based algorithms. These algorithms proceed by performing statistical independence tests on data, trusting completely the outcome of each test. In practice tests may be incorrect, resulting in potential cascading errors and the consequent reduction in the quality of the structures learned. IBMAP contemplates this uncertainty in the outcome of the tests through a probabilistic maximum-a-posteriori approach. The approach is instantiated in the IBMAP-HC algorithm, a structure selection strategy that performs a polynomial heuristic local search in the space of possible structures. We present an extensive empirical evaluation on synthetic and real data, showing that our algorithm outperforms significantly the current independence-based algorithms, in terms of data efficiency and quality of learned structures, with equivalent computational complexities. We also show the performance of IBMAP-HC in a real-world application of knowledge discovery: EDAs, which are evolutionary algorithms that use structure learning on each generation for modeling the distribution of populations. The experiments show that when IBMAP-HC is used to learn the structure, EDAs improve the convergence to the optimum

The identification of informative genes from multiple datasets with increasing complexity

Background In microarray data analysis, factors such as data quality, biological variation, and the increasingly multi-layered nature of more complex biological systems complicates the modelling of regulatory networks that can represent and capture the interactions among genes. We believe that the use of multiple datasets derived from related biological systems leads to more robust models. Therefore, we developed a novel framework for modelling regulatory networks that involves training and evaluation on independent datasets. Our approach includes the following steps: (1) ordering the datasets based on their level of noise and informativeness; (2) selection of a Bayesian classifier with an appropriate level of complexity by evaluation of predictive performance on independent data sets; (3) comparing the different gene selections and the influence of increasing the model complexity; (4) functional analysis of the informative genes. Results In this paper, we identify the most appropriate model complexity using cross-validation and independent test set validation for predicting gene expression in three published datasets related to myogenesis and muscle differentiation. Furthermore, we demonstrate that models trained on simpler datasets can be used to identify interactions among genes and select the most informative. We also show that these models can explain the myogenesis-related genes (genes of interest) significantly better than others (P < 0.004) since the improvement in their rankings is much more pronounced. Finally, after further evaluating our results on synthetic datasets, we show that our approach outperforms a concordance method by Lai et al. in identifying informative genes from multiple datasets with increasing complexity whilst additionally modelling the interaction between genes. Conclusions We show that Bayesian networks derived from simpler controlled systems have better performance than those trained on datasets from more complex biological systems. Further, we present that highly predictive and consistent genes, from the pool of differentially expressed genes, across independent datasets are more likely to be fundamentally involved in the biological process under study. We conclude that networks trained on simpler controlled systems, such as in vitro experiments, can be used to model and capture interactions among genes in more complex datasets, such as in vivo experiments, where these interactions would otherwise be concealed by a multitude of other ongoing events

A review on probabilistic graphical models in evolutionary computation

Thanks to their inherent properties, probabilistic graphical models are one of the prime candidates for machine learning and decision making tasks especially in uncertain domains. Their capabilities, like representation, inference and learning, if used effectively, can greatly help to build intelligent systems that are able to act accordingly in different problem domains. Evolutionary algorithms is one such discipline that has employed probabilistic graphical models to improve the search for optimal solutions in complex problems. This paper shows how probabilistic graphical models have been used in evolutionary algorithms to improve their performance in solving complex problems. Specifically, we give a survey of probabilistic model building-based evolutionary algorithms, called estimation of distribution algorithms, and compare different methods for probabilistic modeling in these algorithms

Learning from peer feedback on student-generated multiple choice questions: Views of introductory physics students

PeerWise is an online application where students are encouraged to generate a bank of multiple choice questions for their classmates to answer. After answering a question, students can provide feedback to the question author about the quality of the question and the question author can respond to this. Student use of, and attitudes to, this online community within PeerWise was investigated in two large first year undergraduate physics courses, across three academic years, to explore how students interact with the system and the extent to which they believe PeerWise to be useful to their learning. Most students recognized that there is value in engaging with PeerWise, and many students engaged deeply with the system, thinking critically about the quality of their submissions and reflecting on feedback provided to them. Students also valued the breadth of topics and level of difficulty offered by the questions, recognized the revision benefits afforded by the resource, and were often willing to contribute to the community by providing additional explanations and engaging in discussion

Understanding non-governmental organizations in world politics: the promise and pitfalls of the early ‘science of internationalism’

The years immediately preceding the First World War witnessed the development of a significant body of literature claiming to establish a ‘science of internationalism’. This article draws attention to the importance of this literature, especially in relation to understanding the roles of non-governmental organizations in world politics. It elaborates the ways in which this literature sheds light on issues that have become central to twenty-first century debates, including the characteristics, influence, and legitimacy of non-governmental organizations in international relations. Amongst the principal authors discussed in the article are Paul Otlet, Henri La Fontaine and Alfred Fried, whose role in the development of international theory has previously received insufficient attention. The article concludes with evaluation of potential lessons to be drawn from the experience of the early twentieth century ‘science of internationalism’

A genetic algorithm-Bayesian network approach for the analysis of metabolomics and spectroscopic data: application to the rapid detection of Bacillus spores and identification of Bacillus species

Background The rapid identification of Bacillus spores and bacterial identification are paramount because of their implications in food poisoning, pathogenesis and their use as potential biowarfare agents. Many automated analytical techniques such as Curie-point pyrolysis mass spectrometry (Py-MS) have been used to identify bacterial spores giving use to large amounts of analytical data. This high number of features makes interpretation of the data extremely difficult We analysed Py-MS data from 36 different strains of aerobic endospore-forming bacteria encompassing seven different species. These bacteria were grown axenically on nutrient agar and vegetative biomass and spores were analyzed by Curie-point Py-MS. Results We develop a novel genetic algorithm-Bayesian network algorithm that accurately identifies sand selects a small subset of key relevant mass spectra (biomarkers) to be further analysed. Once identified, this subset of relevant biomarkers was then used to identify Bacillus spores successfully and to identify Bacillus species via a Bayesian network model specifically built for this reduced set of features. Conclusions This final compact Bayesian network classification model is parsimonious, computationally fast to run and its graphical visualization allows easy interpretation of the probabilistic relationships among selected biomarkers. In addition, we compare the features selected by the genetic algorithm-Bayesian network approach with the features selected by partial least squares-discriminant analysis (PLS-DA). The classification accuracy results show that the set of features selected by the GA-BN is far superior to PLS-DA

OpenEssayist: a supply and demand learning analytics tool for drafting academic essays

This paper focuses on the use of a natural language analytics engine to provide feedback to students when preparing an essay for summative assessment. OpenEssayist is a real-time learning analytics tool, which operates through the combination of a linguistic analysis engine that processes the text in the essay, and a web application that uses the output of the linguistic analysis engine to generate the feedback. We outline the system itself and present analysis of observed patterns of activity as a cohort of students engaged with the system for their module assignments. We report a significant positive correlation between the number of drafts submitted to the system and the grades awarded for the first assignment. We can also report that this cohort of students gained significantly higher overall grades than the students in the previous cohort, who had no access to OpenEssayist. As a system that is content free, OpenEssayist can be used to support students working in any domain that requires the writing of essays

Promoting student success: Creating conditions so every student can learn

Accommodating diverse learning styles of students has long been espoused as a principle of good practice in undergraduate education. Much progress has been made during the past two decades in using active, collaborative, and problem-based learning, learning communities, student-faculty research, service learning, internships, and other pedagogical innovations to enrich student learning. Variable time blocks are more common--from three hours, to all day, to weekends, to six or eight weeks--to fit the desired outcomes, content, and processes. Peers tutor other students, deepening their own learning in the process. Increasingly sophisticated communication and information technologies provide students access to a broad range of print and visual resources and to an expanded range of human expertise. A wider range of assessment tools document what and how well students are learning. Despite all this activity, at too many schools these and other effective educational practices are underutilized. The suggestions offered here are drawn in large part from a study of 20 diverse four-year colleges and universities that have higher-than-predicted graduation rates and, through the National Survey of Student Engagement, demonstrated that they have effective practices for fostering success among students of differing abilities and aspirations. These institutions clearly communicate that they value high quality undergraduate teaching and learning. They have developed instructional approaches tailored to a wide range of student learning styles, ensuring that students engage with course content and interact in meaningful ways with faculty and peers, inside and outside the classroom