Statistical Learning Theory of Quasi-Regular Cases

Many learning machines such as normal mixtures and layered neural networks are not regular but singular statistical models, because the map from a parameter to a probability distribution is not one-to-one. The conventional statistical asymptotic theory can not be applied to such learning machines because the likelihood function can not be approximated by any normal distribution. Recently, new statistical theory has been established based on algebraic geometry and it was clarified that the generalization and training errors are determined by two birational invariants, the real log canonical threshold and the singular fluctuation. However, their concrete values are left unknown. In the present paper, we propose a new concept, a quasi-regular case in statistical learning theory. A quasi-regular case is not a regular case but a singular case, however, it has the same property as a regular case. In fact, we prove that, in a quasi-regular case, two birational invariants are equal to each other, resulting that the symmetry of the generalization and training errors holds. Moreover, the concrete values of two birational invariants are explicitly obtained, the quasi-regular case is useful to study statistical learning theory

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

Molecular Force Fields with Gradient-Domain Machine Learning: Construction and Application to Dynamics of Small Molecules with Coupled Cluster Forces

We present the construction of molecular force fields for small molecules (less than 25 atoms) using the recently developed symmetrized gradient-domain machine learning (sGDML) approach [Chmiela et al., Nat. Commun. 9, 3887 (2018); Sci. Adv. 3, e1603015 (2017)]. This approach is able to accurately reconstruct complex high-dimensional potential-energy surfaces from just a few 100s of molecular conformations extracted from ab initio molecular dynamics trajectories. The data efficiency of the sGDML approach implies that atomic forces for these conformations can be computed with high-level wavefunction-based approaches, such as the "gold standard" CCSD(T) method. We demonstrate that the flexible nature of the sGDML model recovers local and non-local electronic interactions (e.g. H-bonding, proton transfer, lone pairs, changes in hybridization states, steric repulsion and $n\to\pi^*$ interactions) without imposing any restriction on the nature of interatomic potentials. The analysis of sGDML molecular dynamics trajectories yields new qualitative insights into dynamics and spectroscopy of small molecules close to spectroscopic accuracy

Where does good evidence come from?

This paper started as a debate between the two authors. Both authors present a series of propositions about quality standards in education research. Cook’s propositions, as might be expected, concern the importance of experimental trials for establishing the security of causal evidence, but they also include some important practical and acceptable alternatives such as regression discontinuity analysis. Gorard’s propositions, again as might be expected, tend to place experimental trials within a larger mixed method sequence of research activities, treating them as important but without giving them primacy. The paper concludes with a synthesis of these ideas, summarising the many areas of agreement and clarifying the few areas of disagreement. The latter include what proportion of available research funds should be devoted to trials, how urgent the need for more trials is, and whether the call for more truly mixed methods work requires a major shift in the community

Evolution of Coordination in Social Networks: A Numerical Study

Coordination games are important to explain efficient and desirable social behavior. Here we study these games by extensive numerical simulation on networked social structures using an evolutionary approach. We show that local network effects may promote selection of efficient equilibria in both pure and general coordination games and may explain social polarization. These results are put into perspective with respect to known theoretical results. The main insight we obtain is that clustering, and especially community structure in social networks has a positive role in promoting socially efficient outcomes.Comment: preprint submitted to IJMP

A Quasi-Experimental Study of the Classroom Practices of English Language Teachers and the English Language Proficiency of Students, in Primary and Secondary Schools in Bangladesh

English in Action (EIA) is an English language teacher development project based in Bangladesh that was intended to run from 2008 to 2017, but which was extended at the request of the Government of Bangladesh, with additional funding from UKAID, for a further year to 2018. By the time of the design of this study (2014-2015) EIA was drawing to the end of upscaling (phase III, 2011-2014) and entering institutionalisation and sustainability (phase IV, 2014-17, extended 2018). Successive prior studies had indicated substantial success in improving both teachers’ classroom practices and student learning outcomes, over the pre-project baseline (e.g. EIA 2011, 2012). The 2014 Annual Review of EIA recommended that in the final phase, EIA should explore whether it would be possible to carry out a study that compared a ‘counterfactual’ or control-group of teachers and students, to the ‘EIA’ or treatment schools: i.e. a Randomised Control Trial or Quasi-Experimental study. A proposal for a Quasi-Experimental study was developed in collaboration with DFID’s South Asia Research Hub (SARH), which also provided the additional funding necessary to implement such a study. The teachers and students who were the subject of this study, were the fourth cohort to participate in English in Action (together with teachers from ‘control’ schools, in the same Upazilas). This fourth EIA cohort included Schools, Teachers and Students from approximately 200 Upazilas (of approximately 500 in total) across Bangladesh, including some of the most disadvantaged areas (with reference to UNICEF deprivation index), such as Char, Hoar and Monga districts. Teachers took part in a school-based teacher development Programme, learning communicative language teaching approaches through carrying out new classroom activities, guided by teacher development videos that showed teachers, students and schools similar to those across the country. Teachers also had classroom audio resources for use with students. All digital materials were available offline, on teachers own mobile phones, so there is no dilution of the Programmes core messages about teaching and learning, by some intermediary coming between the teacher and the materials. Teachers were supported through these activities, by other teachers in their schools, by their head teachers and by local education officers. Some teachers from each area were also given additional support and guidance from divisional EIA staff, to act as Teacher Facilitators, helping teachers work through activities and share their experiences at local cluster meetings. Whereas previous cohorts of teachers had attended eight local teacher development meetings over their participation in the project, for Cohort Four, this was reduced to four meetings, with a greater emphasis being placed on support in school by head teachers, as well as support from local education officers. This change was part of the move towards institutionalisation and sustainability of project activities within and through government systems and local officers. The purpose of this study was both to provide the evaluation evidence required for the final phase of the EIA project and to contribute to the international body of research evidence on effective practices in teacher development in low-to-middle income country contexts