Remarks on multivariate Gaussian Process

Gaussian processes occupy one of the leading places in modern statistics and probability theory due to their importance and a wealth of strong results. The common use of Gaussian processes is in connection with problems related to estimation, detection, and many statistical or machine learning models. With the fast development of Gaussian process applications, it is necessary to consolidate the fundamentals of vector-valued stochastic processes, in particular multivariate Gaussian processes, which is the essential theory for many applied problems with multiple correlated responses. In this paper, we propose a precise definition of multivariate Gaussian processes based on Gaussian measures on vector-valued function spaces, and provide an existence proof. In addition, several fundamental properties of multivariate Gaussian processes, such as strict stationarity and independence, are introduced. We further derive multivariate Brownian motion including It\^o lemma as a special case of a multivariate Gaussian process, and present a brief introduction to multivariate Gaussian process regression as a useful statistical learning method for multi-output prediction problems

대수기하학적 관점에서의 특이학습이론

학위논문 (석사)-- 서울대학교 대학원 : 자연과학대학 수리과학부, 2018. 2. 김영훈.In this thesis, the goal of singular learning theory and its methods are described. To resolve the singularity problem, we will introduce resolution of singularities, the notion in algebraic geometry. In addition, we will go over some examples of singular learning theory (focus on strictly singular model) and show how to resolve singularities by computation. In particular, in the reduced rank regression model, the process of resolution will be described by taking blow-ups. Finally, we will introduce a determinantal variety, and examine the possibility of connection with the reduced rank regression model.1. Introduction 1 1.1 Main Results 1 1.2 Introduction 4 2. Preliminaries 12 2.1 Elementary Probability Theory 12 2.2 Statistical Learning Theory 19 2.3 Singularity Theory 26 3. Examples of Singular Learning Theory 33 3.1 Bayesian Networks 35 3.2 Hidden Markov Models 39 3.3 Mixtures of Statistical Models 31 3.4 Layered Neural Networks 45 3.5 Boltzmann Machines 50 4. The Reduced Rank Regression 53 4.1 The case when M=N=H and r= 0 54 4.2 Other cases 58 5. Determinantal Variety 62Maste

Extension of the Group Invariance Theorem for Perceptrons

Most of statistical machine learning relies on deep neural nets, whose underlying theory and mathematical properties are currently not well explored. This thesis focuses on the theory of Perceptrons, a form of shallow neural network mostly explored in Minsky & Papert’s book “Perceptrons: an Introduction to Computational Geometry”. Their analysis relied on the use of groups that describe the global symmetries of what is to be computed. However, all real images have an input space with finite length and height, and it is often the case that machine learning systems have disconnected input spaces. This means that real-world systems must actually rely on a concept of local symmetry, if any at all. This paper explores the implications of having a bounded and possibly disconnected input space, and generalizes the Minsky & Papert result, proving that the implications of the group invariance theorem can be retained by using groupoids instead

Pilot Study of the Effects of Supraliminal Bipolar Primes on Occupational Educators\u27 Viewing Time and Perceived Confidence with Desktop Virtual Reality

Virtual reality (VR) has been demonstrated to offer learning benefits over traditional instructional methods in many technical and occupational areas. However, in the framework of Rogers’ innovation diffusion theory, adoption of VR in Career and Technical Education and occupational programs appears to be lagging. This study used experimental methodology to test the possibility of positively influencing the dispositions of occupational educators toward desktop VR through application of prime theory in a context of supplantation and technology self-efficacy theory. Supraliminal bipolar primes were used to test whether a positive disposition more conducive to VR adoption could be created in a sample of 30 occupational educators prior to introduction of a desktop VR presentation, with “disposition” defined as a pair of specific performance measures. Intended as a pilot study, this inquiry used ANOVA and correlation statistical analyses to produce sufficient indications of relationships between positive primes, VR viewing time, and perceived confidence in VR to merit recommendation of further investigation

The development of holistic professional competence through assessment - applying constructivist and reflective assessment practices in a teacher-training programme

Traditional forms of assessment such, as essays and end of term examinations, are still widely used in higher education in Ireland as the sole assessment methods. These forms of assessment, while the may be valid and reliable methods for collecting evidence of acquisition of theoretical knowledge, they rarely afford students the opportunity to apply knowledge to key professional scenarios. The authors draw on their experience as Lecturers and course designers for the module “Curriculum Assessment” which is offered to both, traditional full-time undergraduates and part-time professional educators. This paper describes the introduction of an assessment portfolio designed with the aim to promote the development of professional competence among teacher students and foster professional development among more experienced teachers and trainers in relation to assessment theory and practice. The authors of this paper view research and an integral part of teaching and learning. Therefore a constructivist approach to both teaching and learning and conducting research is essential. Using a mixed methodology approach the authors’ research was conducted using both quantitative and qualitative tools. A primary focus of the research used student reflection to generate relevant data suitable for triangulation; this was then coupled with the module evaluations and statistical data. The introduction of a new assessment format needs to be carefully planned an evaluated. The suitability of the assessment format should be evaluated in terms of the student population, the learning objectives and the learning

Analisis Penerimaan Pengguna Learning Management System Menggunakan Model UTAUT

E-learning is emerging as an important strategy for providing broad and easy access to high quality education. In Indonesia, the concept of e-learning is usually applied in universities to support learning activities and student administration. This study aims to analyze the factors that affect the level of satisfaction by adopting the UTAUT (Unified Theory of Acceptance and Use of Technology) model and seeing the effect of user satisfaction. by intending to continue to use a new technology (e-learning). The UTAUT model was adopted in this study because it has a useful measurement tool for policy makers to assess the likelihood of the successful introduction of new technology. A quantitative research approach with a survey method is used to determine the factors that affect user satisfaction and the intention to use. The quantitative analysis of survey data was carried out using statistical techniques Partial Least Square Structural Equation Modeling (PLS-SEM) and utilizing SmartPLS 3.2.4 software. In this study, two factors were identified that affect user satisfaction, namely effort expectancy. Furthermore, user satisfaction affects intention to use.   Keywords: e-learning, UTAUT, user satisfaction, intention to use, PLS-SE