This book explores the measurement of learning effectiveness and the optimization of knowledge retention by modeling the learning process and building the mathematical foundation of multi-space learning theory. Multi-space learning is defined in this book as a micro-process of human learning that can take place in more than one space, with the goal of effective learning and knowledge retention. This book models the learning process as a temporal sequence of concept learning, drawing on established principles and empirical evidence. It also introduces the matroid to strengthen the mathematical foundation of multi-space learning theory and applies the theory to vocabulary and mathematics learning, respectively. The results show that, for vocabulary learning, the method can be used to estimate the effectiveness of a single learning strategy, to detect the mutual interference that might exist between learning strategies, and to predict the optimal combination of strategies. In mathematical learning, it was found that timing is crucial in both first learning and second learning in scheduling optimization to maximize the intersection effective interval. The title will be of interest to researchers and students in a wide range of areas, including educational technology, learning sciences, mathematical applications, and mathematical psychology.

The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.

Introduces machine learning and its algorithmic paradigms, explaining the principles behind automated learning approaches and the considerations underlying their usage.

Speech and language technologies continue to grow in importance as they are used to create natural and efficient interfaces between people and machines, and to automatically transcribe, extract, analyze, and route information from high-volume streams of spoken and written information. The workshops on Mathematical Foundations of Speech Processing and Natural Language Modeling were held in the Fall of 2000 at the University of Minnesota's NSF-sponsored Institute for Mathematics and Its Applications, as part of a "Mathematics in Multimedia" year-long program. Each workshop brought together researchers in the respective technologies on the one hand, and mathematicians and statisticians on the other hand, for an intensive week of cross-fertilization. There is a long history of benefit from introducing mathematical techniques and ideas to speech and language technologies. Examples include the source-channel paradigm, hidden Markov models, decision trees, exponential models and formal languages theory. It is likely that new mathematical techniques, or novel applications of existing techniques, will once again prove pivotal for moving the field forward. This volume consists of original contributions presented by participants during the two workshops. Topics include language modeling, prosody, acoustic-phonetic modeling, and statistical methodology.

The Conference on Spatial Information Theory – COSIT – grew out of a series of workshops / NATO Advanced Study Institutes / NSF specialist meetings concerned with cognitive and applied aspects of representing large-scale space, particularly geographic space. In these meetings, the need for a well-founded theory of spatial information processing was identified. The COSIT conference series was established in 1993 as a biennial interdisciplinary European conference on the representation and processing of information about large-scale space, after a successful international conference on the topic had been organized by Andrew Frank et al. in Pisa, Italy, in 1992 (frequently referred to as ‘COSIT zero’). After two successful European conferences with strong North-American participation (COSIT ’93, held on the Island of Elba, Italy; COSIT ’95, held in Semmering, Austria), the conference became a truly international enterprise when COSIT ’97 was held in the Laurel Highlands, Pennsylvania, USA. COSIT ’99 will take place in Stade, Germany. All aspects of large-scale space, i. e. spaces too large to be seen from a single vantage point, are addressed in the COSIT conferences. These include spaces of geographic scale, as well as smaller spaces in which humans, animals, or autonomous robots have to find their way around. Spatial information theory also deals with the description of objects, processes, or events in spatial environments and it forms the foundation for the construction of Geographic Information Systems (GIS) and for spatial information and communication system design in general.

Historically and technically important papers range from early work in mathematical control theory to studies in adaptive control processes. Contributors include J. C. Maxwell, H. Nyquist, H. W. Bode, other experts. 1964 edition.

This book constitutes the refereed proceedings of the 20th Annual Conference on Learning Theory, COLT 2007, held in San Diego, CA, USA in June 2007. It covers unsupervised, semisupervised and active learning, statistical learning theory, inductive inference, regularized learning, kernel methods, SVM, online and reinforcement learning, learning algorithms and limitations on learning, dimensionality reduction, as well as open problems.