available from May 2019
FORMAT: Hardback
ISBN: 9781107036161
Methods and perspectives to model and measure productivity and efficiency have made a number of important advances in the last decade. Using the standard and innovative formulations of the theory and practice of efficiency and productivity measurement, Robin C. Sickles and Valentin Zelenyuk provide a comprehensive approach to productivity and efficiency analysis, covering its theoretical underpinnings and its empirical implementation, paying particular attention to the implications of neoclassical economic theory. A distinct feature of the book is that it presents a wide array of theoretical and empirical methods utilized by researchers and practitioners who study productivity issues. An accompanying website includes methods, programming codes that can be used with widely available software like MATLABR and R, and test data for many of the productivity and efficiency estimators discussed in the book. It will be valuable to upper-level undergraduates, graduate students, and professionals.
Provides a self-contained resource for upper-level undergraduates, graduate students, academics, government analysts, and independent researchers
Provides an integrated and synthesized treatment of the topics covered
MATLABR software is readily available so readers can implement the applied productivity and efficiency analysis discussed
Preface
Introduction
1. Production theory: primal approach
2. Production theory: dual approach
3. Efficiency measurement
4. Productivity indexes: part 1
5. Aggregation
6. Functional forms
7. Productivity indexes: part 2
8. Envelopment-type estimators
9. Statistical analysis for DEA and FDH: Part 1
10. Statistical analysis for DEA and FDH: part 2
11. Cross-sectional stochastic frontiers
12. SF models-first generation panel approaches
13. SF models-second generation approaches
14. Endogeneity
15. Dynamic models
16. Shape restrictions and model averaging
17. Measurement, KLEMS, and other data
Afterword.
Part of London Mathematical Society Student Texts
available from October 2019
Hardback ISBN: 9781108483094
Paperback ISBN: 9781108716376
The theory of semigroups of operators is one of the most important themes in modern analysis. Not only does it have great intellectual beauty, but also wide-ranging applications. In this book the author first presents the essential elements of the theory, introducing the notions of semigroup, generator and resolvent, and establishes the key theorems of Hille?Yosida and Lumer?Phillips that give conditions for a linear operator to generate a semigroup. He then presents a mixture of applications and further developments of the theory. This includes a description of how semigroups are used to solve parabolic partial differential equations, applications to Levy and Feller?Markov processes, Koopmanism in relation to dynamical systems, quantum dynamical semigroups, and applications to generalisations of the Riemann?Liouville fractional integral. Along the way the reader encounters several important ideas in modern analysis including Sobolev spaces, pseudo-differential operators and the Nash inequality.
Introduction
1. Semigroups and generators
2. The generation of semigroups
3. Convolution semigroups of measures
4. Self adjoint semigroups and unitary groups
5. Compact and trace class semigroups
6. Perturbation theory
7. Markov and Feller semigroups
8. Semigroups and dynamics
9. Varopoulos semigroups
Notes and further reading
Appendices: A. The space C0(Rd)
B. The Fourier transform
C. Sobolev spaces
D. Probability measures and Kolmogorov's theorem on construction of stochastic processes
E. Absolute continuity, conditional expectation and martingales
F. Stochastic integration and Ito's formula
G. Measures on locally compact spaces: some brief remarks
References
Index.
available from August 2019 FORMAT: HardbackISBN: 9781108482295
Paperback ISBN: 9781108711821
Category theory is unmatched in its ability to organize and layer abstractions and to find commonalities between structures of all sorts. No longer the exclusive preserve of pure mathematicians, it is now proving itself to be a powerful tool in science, informatics, and industry. By facilitating communication between communities and building rigorous bridges between disparate worlds, applied category theory has the potential to be a major organizing force. This book offers a self-contained tour of applied category theory. Each chapter follows a single thread motivated by a real-world application and discussed with category-theoretic tools. We see data migration as an adjoint functor, electrical circuits in terms of monoidal categories and operads, and collaborative design via enriched profunctors. All the relevant category theory, from simple to sophisticated, is introduced in an accessible way with many examples and exercises, making this an ideal guide even for those without experience of university-level mathematics.
Preface
1. Generative effects: orders and Galois connections
2. Resource theories: monoidal preorders and enrichment
3. Databases: categories, functors, and universal constructions
4. Collaborative design: profunctors, categorification, and monoidal categories
5. Signal flow graphs: props, presentations, and proofs
6. Electric circuits: hypergraph categories and operads
7. Logic of behavior: sheaves, toposes, and internal languages
Appendix. Exercise solutions
References
Index.
available from September 2019
Hardback ISBN: 9781107076150
Description
Variational Bayesian learning is one of the most popular methods in machine learning. Designed for researchers and graduate students in machine learning, this book summarizes recent developments in the non-asymptotic and asymptotic theory of variational Bayesian learning and suggests how this theory can be applied in practice. The authors begin by developing a basic framework with a focus on conjugacy, which enables the reader to derive tractable algorithms. Next, it summarizes non-asymptotic theory, which, although limited in application to bilinear models, precisely describes the behavior of the variational Bayesian solution and reveals its sparsity inducing mechanism. Finally, the text summarizes asymptotic theory, which reveals phase transition phenomena depending on the prior setting, thus providing suggestions on how to set hyperparameters for particular purposes. Detailed derivations allow readers to follow along without prior knowledge of the mathematical techniques specific to Bayesian learning.
Table of contents
1. Bayesian learning
2. Variational Bayesian learning
3. VB algorithm for multi-linear models
4. VB Algorithm for latent variable models
5. VB algorithm under No Conjugacy
6. Global VB solution of fully observed matrix factorization
7. Model-induced regularization and sparsity inducing mechanism
8. Performance analysis of VB matrix factorization
9. Global solver for matrix factorization
10. Global solver for low-rank subspace clustering
11. Efficient solver for sparse additive matrix factorization
12. MAP and partially Bayesian learning
13. Asymptotic Bayesian learning theory
14. Asymptotic VB theory of reduced rank regression
15. Asymptotic VB theory of mixture models
16. Asymptotic VB theory of other latent variable models
17. Unified theory.
Part of Cambridge Tracts in Mathematics
available from September 2019
FORMAT: Hardback
ISBN: 9781108419529
This is the first book to provide a comprehensive overview of foundational results and recent progress in the study of random matrices from the classical compact groups, drawing on the subject's deep connections to geometry, analysis, algebra, physics, and statistics. The book sets a foundation with an introduction to the groups themselves and six different constructions of Haar measure. Classical and recent results are then presented in a digested, accessible form, including the following: results on the joint distributions of the entries; an extensive treatment of eigenvalue distributions, including the Weyl integration formula, moment formulae, and limit theorems and large deviations for the spectral measures; concentration of measure with applications both within random matrix theory and in high dimensional geometry; and results on characteristic polynomials with connections to the Riemann zeta function. This book will be a useful reference for researchers and an accessible introduction for students in related fields.
1. Haar measure on the classical compact matrix groups
2. Distribution of the entries
3. Eigenvalue distributions: exact formulas
4. Eigenvalue distributions: asymptotics
5. Concentration of measure
6. Geometric applications of measure concentration
7. Characteristic polynomials and the zeta function.