The exponentially weighted average forecaster in geodesic spaces of non-positive curvature
This paper addresses the problem of prediction with expert advice for outcomes in a geodesic space with non-positive curvature in the sense of Alexandrov. Via geometric considerations, and in particular the notion of barycenters, we extend to this setting the definition and analysis of the classical exponentially weighted average forecaster. We also adapt the principle of online to batch conversion to this setting. We shortly discuss the application of these results in the context of aggregation and for the problem of barycenter estimation.
Many Data Mining tasks deal with data which are presented in high dimensional spaces, and the ‘curse of dimensionality’ phenomena is often an obstacle to the use of many methods for solving these tasks. To avoid these phenomena, various Representation learning algorithms are used as a first key step in solutions of these tasks to transform the original high-dimensional data into their lower-dimensional representations so that as much information about the original data required for the considered Data Mining task is preserved as possible. The above Representation learning problems are formulated as various Dimensionality Reduction problems (Sample Embedding, Data Manifold embedding, Manifold Learning and newly proposed Tangent Bundle Manifold Learning) which are motivated by various Data Mining tasks. A new geometrically motivated algorithm that solves the Tangent Bundle Manifold Learning and gives new solutions for all the considered Dimensionality Reduction problems is presented.
The chapter overviews an approach to teaching writing-for-publication via an online pedagogy for post/graduate research writing.
The paper is devoted to the main aspects of using MOOCs as a part of university curriculum. HSE University has the expertise of implementation of blended learning using our own 53 MOOCs on Coursera and 27 MOOCs on Russian National Open Education Platform and courses of other universities. The emphasis will be on institutional decisions, organizational schemes and management solutions that allow to recognize MOOCs’ results and transfer them into university credits (ESTC).
Learning management systems (LMS) have been proven to encourage a constructive approach to knowledge acquisition and support active learning. One of the keys to successful and efficient use of LMS is how the stakeholders adopt and perceive this learning tool. The present research is therefore motivated by the importance of understanding teachers’ and students’ perceptions of LMS in order to anticipate possible issues (problems) and help to build a productive learning environment and a committed user community. The paper looks at this process at a Russian university (National Research University Higher School of Economics – HSE) where the system is being implemented and examines the following issues: qualification and readiness of the stakeholders to use LMS and their perceptions of the system’s convenience, effectiveness, and usefulness. The research reveals remarkable divergence of students’ and teachers’ perceptions of various aspects of LMS which must be considered when raising the effectiveness of the system and building commitment to e-learning. They are analyzed and explicated in the present paper.
This book constitutes the refereed proceedings of the 6th IAPR TC3 International Workshop on Artificial Neural Networks in Pattern Recognition, ANNPR 2014, held in Montreal, QC, Canada, in October 2014. The 24 revised full papers presented were carefully reviewed and selected from 37 submissions for inclusion in this volume. They cover a large range of topics in the field of learning algorithms and architectures and discussing the latest research, results, and ideas in these areas.
Objects have a variety of different features that can be represented as probability distributions. Recent findings show that in addition to mean and variance, the visual system can also encode the shape of feature distributions for features like color or orientation. In an odd-one-out search task we investigated observers' ability to encode two feature distributions simultaneously. Our stimuli were defined by two distinct features (color and orientation) while only one was relevant to the search task. We investigated whether the irrelevant feature distribution influences learning of the task-relevant distribution and whether observers also encode the irrelevant distribution. Although considerable learning of feature distributions occurred, especially for color, our results also suggest that adding a second irrelevant feature distribution negatively affected the encoding of the relevant one and that little learning of the irrelevant distribution occurred. There was also an asymmetry between the two different features: Searching for the oddly oriented target was more difficult than searching for the oddly colored target, which was reflected in worse learning of the color distribution. Overall, the results demonstrate that it is possible to encode information about two feature distributions simultaneously but also reveal considerable limits to this encoding.
This book constitutes the proceedings of the 6th European Conference on Massive Open Online Courses, EMOOCs 2019, held in Naples, Italy, in May 2019.
The 15 full and 6 short papers presented in this volume were carefully reviewed and selected from 42 submissions. Massive Open Online Courses (MOOCs) have marked a milestone in the use of technology for education. The reach, potential, and possibilities of EMOOCs are immense. But they are not only restricted to global outreach: the same technology can be used to improve teaching on campus and training inside companies and institutions.
The chapter 'Goal Setting and Striving in MOOCs. A Peek inside the Black Box of Learner Behaviour' is open access under a CC BY 4.0 license at link.springer.com.
The problem of minimizing the root mean square deviation of a uniform string with clamped ends from an equilibrium position is investigated. It is assumed that the initial conditions are specified and the ends of the string are clamped. The Fourier method is used, which enables the control problem with a partial differential equation to be reduced to a control problem with a denumerable system of ordinary differential equations. For the optimal control problem in the l2 space obtained, it is proved that the optimal synthesis contains singular trajectories and chattering trajectories. For the initial problem of the optimal control of the vibrations of a string it is also proved that there is a unique solution for which the optimal control has a denumerable number of switchings in a finite time interval.
For a class of optimal control problems and Hamiltonian systems generated by these problems in the space l 2, we prove the existence of extremals with a countable number of switchings on a finite time interval. The optimal synthesis that we construct in the space l 2 forms a fiber bundle with piecewise smooth two-dimensional fibers consisting of extremals with a countable number of switchings over an infinite-dimensional basis of singular extremals.
This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.
In this paper, we construct a new distribution corresponding to a real noble gas as well as the equation of state for it.