Optimal Bayesian classification

"The most basic problem of engineering is the design of optimal operators. Design takes different forms depending on the random process constituting the scientific model and the operator class of interest. This book treats classification, where the underlying random process is a feature-label d...

Ausführliche Beschreibung

Gespeichert in:
Hauptverfasser:
Dalton, Lori A., Dougherty, Edward R.
Format:
Elektronisch E-Book
Sprache:
Englisch
Veröffentlicht:
2020
Zusammenfassung:
"The most basic problem of engineering is the design of optimal operators. Design takes different forms depending on the random process constituting the scientific model and the operator class of interest. This book treats classification, where the underlying random process is a feature-label distribution, and an optimal operator is a Bayes classifier, which is a classifier minimizing the classification error. With sufficient knowledge we can construct the feature-label distribution and thereby find a Bayes classifier. Rarely, do we possess such knowledge. On the other hand, if we had unlimited data, we could accurately estimate the feature-label distribution and obtain a Bayes classifier. Rarely do we possess sufficient data. The aim of this book is to best use whatever knowledge and data are available to design a classifier. The book takes a Bayesian approach to modeling the feature-label distribution and designs an optimal classifier relative to a posterior distribution governing an uncertainty class of feature-label distributions. In this way it takes full advantage of knowledge regarding the underlying system and the available data. Its origins lie in the need to estimate classifier error when there is insufficient data to hold out test data, in which case an optimal error estimate can be obtained relative to the uncertainty class. A natural next step is to forgo classical ad hoc classifier design and simply find an optimal classifier relative to the posterior distribution over the uncertainty class-this being an optimal Bayesian classifier"--
Umfang:
1 online resource (xv, 362 pages)
Anmerkungen:
"SPIE Digital Library."--Website. - Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader
Preface -- Acknowledgments -- 1. Classification and error estimation: 1.1. Classifiers; 1.2. Constrained classifiers; 1.3. Error estimation; 1.4. Random versus separate sampling; 1.5. Epistemology and validity -- 2. Optimal Bayesian error estimation: 2.1. The Bayesian MMSE error estimator; 2.2. Evaluation of the Bayesian MMSE error estimator; 2.3. Performance evaluation at a fixed point; 2.4. Discrete model; 2.5. Gaussian model; 2.6. Performance in the Gaussian model with LDA; -- 2.7. Consistency of Bayesian error estimation; 2.8. Calibration; 2.9. Optimal Bayesian ROC-based analysis -- 3. Sample-conditioned MSE of error estimation: 3.1. Conditional MSE of error estimators; 3.2. Evaluation of the conditional MSE; 3.3. Discrete model; 3.4. Gaussian model; 3.5. Average performance in the Gaussian model; 3.6. Convergence of the sample-conditioned MSE; 3.7. A performance bound for the discrete model; 3.8. Censored sampling; 3.9. Asymptotic approximation of the RMS -- 4. Optimal Bayesian
5. Optimal Bayesian risk-based multi-class classification: 5.1. Bayes decision theory; 5.2. Bayesian risk estimation; 5.3. Optimal Bayesian risk classification; 5.4. Sample-conditioned MSE of risk estimation; 5.5. Efficient computation; 5.6. Evaluation of posterior mixed moments: discrete model; 5.7. Evaluation of posterior mixed moments: Gaussian models; 5.8. Simulations -- 6. Optimal Bayesian transfer learning: 6.1. Joint prior distribution; 6.2. Posterior distribution in the target domain; 6.3. Optimal Bayesian transfer learning classifier; 6.4. OBTLC with negative binomial distribution -- 7. Construction of prior distributions: 7.1. Prior construction using data from discarded features; 7.2. Prior knowledge from stochastic differential equations; 7.3. Maximal knowledge-driven information prior; 7.4. REMLP for a normal-Wishart prior -- References -- Index
Schriftenreihe:
SPIE Press monograph
ISBN:
9781510630710
1510630724
9781510630727
1510630716
9781510630703
1510630708
9781510630697
Schlagworte:
Bayesian statistical decision theory
Statistical decision
Links: