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Algorithmic learning in a random world / / Vladimir Vovk, Alexander Gammerman, and Glenn Shafer
Algorithmic learning in a random world / / Vladimir Vovk, Alexander Gammerman, and Glenn Shafer
Autore Vovk Vladimir <1960->
Edizione [2nd ed.]
Pubbl/distr/stampa Cham, Switzerland : , : Springer International Publishing, , [2022]
Descrizione fisica 1 online resource (490 pages)
Disciplina 518.1
Soggetto topico Algorithms
Algorithms - Study and teaching
Teoria de la predicció
Algorismes
Processos estocàstics
Soggetto genere / forma Llibres electrònics
ISBN 3-031-06649-9
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Contents -- Preface to the Second Edition -- Preface to the First Edition -- Notation and Abbreviations -- Sets, Bags, and Sequences -- Stochastics -- Machine Learning -- Programming -- Confidence Prediction -- Other Notations -- Abbreviations -- 1 Introduction -- 1.1 Machine Learning -- 1.1.1 Learning Under Randomness -- 1.1.2 Learning Under Unconstrained Randomness -- 1.2 A Shortcoming of Statistical Learning Theory -- 1.2.1 The Hold-Out Estimate of Confidence -- 1.2.2 The Contribution of This Book -- 1.3 The Online Framework -- 1.3.1 Online Learning -- 1.3.2 Online/Offline Compromises -- 1.3.3 One-Off and Offline Learning -- 1.3.4 Induction, Transduction, and the Online Framework -- 1.4 Conformal Prediction -- 1.4.1 Nested Prediction Sets -- 1.4.2 Validity -- 1.4.3 Efficiency -- 1.4.4 Conditionality -- 1.4.5 Flexibility of Conformal Predictors -- 1.5 Probabilistic Prediction Under Unconstrained Randomness -- 1.5.1 Universally Consistent Probabilistic Predictor -- 1.5.2 Probabilistic Prediction Using a Finite Dataset -- 1.5.3 Venn Prediction -- 1.5.4 Conformal Predictive Distributions -- 1.6 Beyond Randomness -- 1.6.1 Testing Randomness -- 1.6.2 Online Compression Models -- 1.7 Context -- Part I Set Prediction -- 2 Conformal Prediction: General Case and Regression -- 2.1 Confidence Predictors -- 2.1.1 Assumptions -- 2.1.2 Simple Predictors and Confidence Predictors -- 2.1.3 Validity -- 2.1.4 Randomized Confidence Predictors -- 2.1.5 Confidence Predictors Over a Finite Horizon -- 2.1.6 One-Off and Offline Confidence Predictors -- 2.2 Conformal Predictors -- 2.2.1 Bags -- 2.2.2 Nonconformity and Conformity -- 2.2.3 p-Values -- 2.2.4 Definition of Conformal Predictors -- 2.2.5 Validity -- 2.2.6 Smoothed Conformal Predictors -- 2.2.7 Finite-Horizon Conformal Prediction -- 2.2.8 One-Off and Offline Conformal Predictors.
2.2.9 General Schemes for Defining Nonconformity -- Conformity to a Bag -- Conformity to a Property -- 2.2.10 Deleted Conformity Measures -- 2.3 Conformalized Ridge Regression -- 2.3.1 Least Squares and Ridge Regression -- 2.3.2 Basic CRR -- 2.3.3 Two Modifications -- 2.3.4 Dual Form Ridge Regression -- 2.4 Conformalized Nearest Neighbours Regression -- 2.5 Efficiency of Conformalized Ridge Regression -- 2.5.1 Hard and Soft Models -- 2.5.2 Bayesian Ridge Regression -- 2.5.3 Efficiency of CRR -- 2.6 Are There Other Ways to Achieve Validity? -- 2.7 Conformal Transducers -- 2.7.1 Definitions and Properties of Validity -- 2.7.2 Normalized Confidence Predictors and Confidence Transducers -- 2.8 Proofs -- 2.8.1 Proof of Theorem 2.2 -- 2.8.2 Proof of Theorem 2.7 -- Regularizing the Rays in Upper CRR -- Proof Proper -- 2.8.3 Proof of Theorem 2.10 -- 2.9 Context -- 2.9.1 Exchangeability vs Randomness -- 2.9.2 Conformal Prediction -- 2.9.3 Two Equivalent Definitions of Nonconformity Measures -- 2.9.4 The Two Meanings of Conformity in Conformal Prediction -- 2.9.5 Examples of Nonconformity Measures -- 2.9.6 Kernel Methods -- 2.9.7 Burnaev-Wasserman Programme -- 2.9.8 Completeness Results -- 3 Conformal Prediction: Classification and General Case -- 3.1 Criteria of Efficiency for Conformal Prediction -- 3.1.1 Basic Criteria -- 3.1.2 Other Prior Criteria -- 3.1.3 Observed Criteria -- 3.1.4 Idealised Setting -- 3.1.5 Conditionally Proper Criteria of Efficiency -- 3.1.6 Criteria of Efficiency that Are not Conditionally Proper -- 3.1.7 Discussion -- 3.2 More Ways of Computing Nonconformity Scores -- 3.2.1 Nonconformity Scores from Nearest Neighbours -- 3.2.2 Nonconformity Scores from Support Vector Machines -- 3.2.3 Reducing Classification Problems to the Binary Case -- 3.3 Weak Teachers -- 3.3.1 Imperfectly Taught Predictors -- 3.3.2 Weak Validity.
3.3.3 Strong Validity -- 3.3.4 Iterated Logarithm Validity -- 3.3.5 Efficiency -- 3.4 Proofs -- 3.4.1 Proofs for Sect.3.1 -- Proof of Theorem 3.1 -- Proof of Theorem 3.2 -- Proof of Theorem 3.3 -- Proof of Theorem 3.4 -- 3.4.2 Proofs for Sect.3.3 -- Proof of Theorem 3.7, Part I -- Proof of Theorem 3.7, Part II -- Proof of Theorem 3.9 -- Proof of Theorem 3.13 -- 3.5 Context -- 3.5.1 Criteria of Efficiency -- 3.5.2 Examples of Nonconformity Measures -- 3.5.3 Universal Predictors -- 3.5.4 Weak Teachers -- 4 Modifications of Conformal Predictors -- 4.1 The Topics of This Chapter -- 4.2 Inductive Conformal Predictors -- 4.2.1 Inductive Conformal Predictors in the Online Mode -- 4.2.2 Inductive Conformal Predictors in the Offline and Semi-Online Modes -- 4.2.3 The General Scheme for Defining Nonconformity -- 4.2.4 Normalization and Hyper-Parameter Selection -- 4.3 Further Ways of Computing Nonconformity Scores -- 4.3.1 Nonconformity Measures Considered Earlier -- 4.3.2 De-Bayesing -- 4.3.3 Neural Networks and Other Multiclass Scoring Classifiers -- 4.3.4 Decision Trees and Random Forests -- 4.3.5 Binary Scoring Classifiers -- 4.3.6 Logistic Regression -- 4.3.7 Regression and Bootstrap -- 4.3.8 Training Inductive Conformal Predictors -- 4.4 Cross-Conformal Prediction -- 4.4.1 Definition of Cross-Conformal Predictors -- 4.4.2 Computational Efficiency -- 4.4.3 Validity and Lack Thereof for Cross-Conformal Predictors -- 4.5 Transductive Conformal Predictors -- 4.5.1 Definition -- 4.5.2 Validity -- 4.6 Conditional Conformal Predictors -- 4.6.1 One-Off Conditional Conformal Predictors -- 4.6.2 Mondrian Conformal Predictors and Transducers -- 4.6.3 Using Mondrian Conformal Transducers for Prediction -- 4.6.4 Generality of Mondrian Taxonomies -- 4.6.5 Conformal Prediction -- 4.6.6 Inductive Conformal Prediction -- 4.6.7 Label-Conditional Conformal Prediction.
4.6.8 Object-Conditional Conformal Prediction -- 4.7 Training-Conditional Validity -- 4.7.1 Conditional Validity -- 4.7.2 Training-Conditional Validity of Inductive Conformal Predictors -- 4.8 Context -- 4.8.1 Computationally Efficient Hedged Prediction -- 4.8.2 Specific Learning Algorithms and Nonconformity Measures -- 4.8.3 Training Conformal Predictors -- 4.8.4 Cross-Conformal Predictors and Alternative Approaches -- 4.8.5 Transductive Conformal Predictors -- 4.8.6 Conditional Conformal Predictors -- Part II Probabilistic Prediction -- 5 Impossibility Results -- 5.1 Introduction -- 5.2 Diverse Datasets -- 5.3 Impossibility of Estimation of Probabilities -- 5.3.1 Binary Case -- 5.3.2 Multiclass Case -- 5.4 Proof of Theorem 5.2 -- 5.4.1 Probability Estimators and Statistical Tests -- 5.4.2 Complete Statistical Tests -- 5.4.3 Restatement of the Theorem in Terms of Statistical Tests -- 5.4.4 The Proof of the Theorem -- 5.5 Context -- 5.5.1 More Advanced Results -- 5.5.2 Density Estimation, Regression Estimation, and Regression with Deterministic Objects -- 5.5.3 Universal Probabilistic Predictors -- 5.5.4 Algorithmic Randomness Perspective -- 6 Probabilistic Classification: Venn Predictors -- 6.1 Introduction -- 6.2 Venn Predictors -- 6.2.1 Validity of One-Off Venn Predictors -- 6.2.2 Are There Other Ways to Achieve Perfect Calibration? -- 6.2.3 Venn Prediction with Binary Labels and No Objects -- 6.3 A Universal Venn Predictor -- 6.4 Venn-Abers Predictors -- 6.4.1 Full Venn-Abers Predictors -- 6.4.2 Inductive Venn-Abers Predictors -- 6.4.3 Probabilistic Predictors Derived from Venn Predictors -- 6.4.4 Cross Venn-Abers Predictors -- 6.4.5 Merging Multiprobability Predictions into a Probabilistic Prediction -- 6.5 Proofs -- 6.5.1 Proof of Theorem 6.4 -- 6.5.2 PAVA and the Proof of Lemma 6.6 -- 6.5.3 Proof of Proposition 6.7 -- 6.6 Context.
6.6.1 Risk and Uncertainty -- 6.6.2 John Venn, Frequentist Probability, and the Problem of the Reference Class -- 6.6.3 Online Venn Predictors Are Calibrated -- 6.6.4 Isotonic Regression -- 7 Probabilistic Regression: Conformal Predictive Systems -- 7.1 Introduction -- 7.2 Conformal Predictive Systems -- 7.2.1 Basic Definitions -- 7.2.2 Properties of Validity -- 7.2.3 Simplest Example: Monotonic Conformity Measures -- 7.2.4 Criterion of Being a CPS -- 7.3 Least Squares Prediction Machine -- 7.3.1 Three Kinds of LSPM -- 7.3.2 The Studentized LSPM in an Explicit Form -- 7.3.3 The Offline Version of the Studentized LSPM -- 7.3.4 The Ordinary LSPM -- 7.3.5 Asymptotic Efficiency of the LSPM -- 7.3.6 Illustrations -- 7.4 Kernel Ridge Regression Prediction Machine -- 7.4.1 Explicit Forms of the KRRPM -- 7.4.2 Limitation of the KRRPM -- 7.5 Nearest Neighbours Prediction Machine -- 7.6 Universal Conformal Predictive Systems -- 7.6.1 Definitions -- 7.6.2 Universal Conformal Predictive Systems -- 7.6.3 Universal Deterministic Predictive Systems -- 7.7 Applications to Decision Making -- 7.7.1 A Standard Problem of Decision Making -- 7.7.2 Examples -- 7.7.3 Asymptotically Efficient Decision Making -- 7.7.4 Dangers of Overfitting -- 7.8 Computationally Efficient Versions -- 7.8.1 Inductive Conformal Predictive Systems -- 7.8.2 Cross-Conformal Predictive Distributions -- 7.8.3 Practical Aspects -- 7.8.4 Beyond Randomness -- 7.9 Proofs and Calculations -- 7.9.1 Proofs for Sect.7.2 -- Proof of Lemma 7.1 -- Proof of Proposition 7.2 -- 7.9.2 Proofs for Sect.7.3 -- Proof of Proposition 7.4 -- Proof of Proposition 7.5 -- Proof of Proposition 7.6 -- Proof of Proposition 7.7 -- Proof of Proposition 7.8 -- Computations for the Studentized LSPM -- The Ordinary LSPM -- Proof of (7.22) -- 7.9.3 Proof of Theorem 7.16 -- 7.9.4 Proofs for Sect.7.8 -- Proof of Proposition 7.17.
Proof of Proposition 7.18.
Record Nr. UNISA-996503551103316
Vovk Vladimir <1960->  
Cham, Switzerland : , : Springer International Publishing, , [2022]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Algorithmic learning in a random world / / Vladimir Vovk, Alexander Gammerman, and Glenn Shafer
Algorithmic learning in a random world / / Vladimir Vovk, Alexander Gammerman, and Glenn Shafer
Autore Vovk Vladimir <1960->
Edizione [2nd ed.]
Pubbl/distr/stampa Cham, Switzerland : , : Springer International Publishing, , [2022]
Descrizione fisica 1 online resource (490 pages)
Disciplina 518.1
Soggetto topico Algorithms
Algorithms - Study and teaching
Teoria de la predicció
Algorismes
Processos estocàstics
Soggetto genere / forma Llibres electrònics
ISBN 3-031-06649-9
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Contents -- Preface to the Second Edition -- Preface to the First Edition -- Notation and Abbreviations -- Sets, Bags, and Sequences -- Stochastics -- Machine Learning -- Programming -- Confidence Prediction -- Other Notations -- Abbreviations -- 1 Introduction -- 1.1 Machine Learning -- 1.1.1 Learning Under Randomness -- 1.1.2 Learning Under Unconstrained Randomness -- 1.2 A Shortcoming of Statistical Learning Theory -- 1.2.1 The Hold-Out Estimate of Confidence -- 1.2.2 The Contribution of This Book -- 1.3 The Online Framework -- 1.3.1 Online Learning -- 1.3.2 Online/Offline Compromises -- 1.3.3 One-Off and Offline Learning -- 1.3.4 Induction, Transduction, and the Online Framework -- 1.4 Conformal Prediction -- 1.4.1 Nested Prediction Sets -- 1.4.2 Validity -- 1.4.3 Efficiency -- 1.4.4 Conditionality -- 1.4.5 Flexibility of Conformal Predictors -- 1.5 Probabilistic Prediction Under Unconstrained Randomness -- 1.5.1 Universally Consistent Probabilistic Predictor -- 1.5.2 Probabilistic Prediction Using a Finite Dataset -- 1.5.3 Venn Prediction -- 1.5.4 Conformal Predictive Distributions -- 1.6 Beyond Randomness -- 1.6.1 Testing Randomness -- 1.6.2 Online Compression Models -- 1.7 Context -- Part I Set Prediction -- 2 Conformal Prediction: General Case and Regression -- 2.1 Confidence Predictors -- 2.1.1 Assumptions -- 2.1.2 Simple Predictors and Confidence Predictors -- 2.1.3 Validity -- 2.1.4 Randomized Confidence Predictors -- 2.1.5 Confidence Predictors Over a Finite Horizon -- 2.1.6 One-Off and Offline Confidence Predictors -- 2.2 Conformal Predictors -- 2.2.1 Bags -- 2.2.2 Nonconformity and Conformity -- 2.2.3 p-Values -- 2.2.4 Definition of Conformal Predictors -- 2.2.5 Validity -- 2.2.6 Smoothed Conformal Predictors -- 2.2.7 Finite-Horizon Conformal Prediction -- 2.2.8 One-Off and Offline Conformal Predictors.
2.2.9 General Schemes for Defining Nonconformity -- Conformity to a Bag -- Conformity to a Property -- 2.2.10 Deleted Conformity Measures -- 2.3 Conformalized Ridge Regression -- 2.3.1 Least Squares and Ridge Regression -- 2.3.2 Basic CRR -- 2.3.3 Two Modifications -- 2.3.4 Dual Form Ridge Regression -- 2.4 Conformalized Nearest Neighbours Regression -- 2.5 Efficiency of Conformalized Ridge Regression -- 2.5.1 Hard and Soft Models -- 2.5.2 Bayesian Ridge Regression -- 2.5.3 Efficiency of CRR -- 2.6 Are There Other Ways to Achieve Validity? -- 2.7 Conformal Transducers -- 2.7.1 Definitions and Properties of Validity -- 2.7.2 Normalized Confidence Predictors and Confidence Transducers -- 2.8 Proofs -- 2.8.1 Proof of Theorem 2.2 -- 2.8.2 Proof of Theorem 2.7 -- Regularizing the Rays in Upper CRR -- Proof Proper -- 2.8.3 Proof of Theorem 2.10 -- 2.9 Context -- 2.9.1 Exchangeability vs Randomness -- 2.9.2 Conformal Prediction -- 2.9.3 Two Equivalent Definitions of Nonconformity Measures -- 2.9.4 The Two Meanings of Conformity in Conformal Prediction -- 2.9.5 Examples of Nonconformity Measures -- 2.9.6 Kernel Methods -- 2.9.7 Burnaev-Wasserman Programme -- 2.9.8 Completeness Results -- 3 Conformal Prediction: Classification and General Case -- 3.1 Criteria of Efficiency for Conformal Prediction -- 3.1.1 Basic Criteria -- 3.1.2 Other Prior Criteria -- 3.1.3 Observed Criteria -- 3.1.4 Idealised Setting -- 3.1.5 Conditionally Proper Criteria of Efficiency -- 3.1.6 Criteria of Efficiency that Are not Conditionally Proper -- 3.1.7 Discussion -- 3.2 More Ways of Computing Nonconformity Scores -- 3.2.1 Nonconformity Scores from Nearest Neighbours -- 3.2.2 Nonconformity Scores from Support Vector Machines -- 3.2.3 Reducing Classification Problems to the Binary Case -- 3.3 Weak Teachers -- 3.3.1 Imperfectly Taught Predictors -- 3.3.2 Weak Validity.
3.3.3 Strong Validity -- 3.3.4 Iterated Logarithm Validity -- 3.3.5 Efficiency -- 3.4 Proofs -- 3.4.1 Proofs for Sect.3.1 -- Proof of Theorem 3.1 -- Proof of Theorem 3.2 -- Proof of Theorem 3.3 -- Proof of Theorem 3.4 -- 3.4.2 Proofs for Sect.3.3 -- Proof of Theorem 3.7, Part I -- Proof of Theorem 3.7, Part II -- Proof of Theorem 3.9 -- Proof of Theorem 3.13 -- 3.5 Context -- 3.5.1 Criteria of Efficiency -- 3.5.2 Examples of Nonconformity Measures -- 3.5.3 Universal Predictors -- 3.5.4 Weak Teachers -- 4 Modifications of Conformal Predictors -- 4.1 The Topics of This Chapter -- 4.2 Inductive Conformal Predictors -- 4.2.1 Inductive Conformal Predictors in the Online Mode -- 4.2.2 Inductive Conformal Predictors in the Offline and Semi-Online Modes -- 4.2.3 The General Scheme for Defining Nonconformity -- 4.2.4 Normalization and Hyper-Parameter Selection -- 4.3 Further Ways of Computing Nonconformity Scores -- 4.3.1 Nonconformity Measures Considered Earlier -- 4.3.2 De-Bayesing -- 4.3.3 Neural Networks and Other Multiclass Scoring Classifiers -- 4.3.4 Decision Trees and Random Forests -- 4.3.5 Binary Scoring Classifiers -- 4.3.6 Logistic Regression -- 4.3.7 Regression and Bootstrap -- 4.3.8 Training Inductive Conformal Predictors -- 4.4 Cross-Conformal Prediction -- 4.4.1 Definition of Cross-Conformal Predictors -- 4.4.2 Computational Efficiency -- 4.4.3 Validity and Lack Thereof for Cross-Conformal Predictors -- 4.5 Transductive Conformal Predictors -- 4.5.1 Definition -- 4.5.2 Validity -- 4.6 Conditional Conformal Predictors -- 4.6.1 One-Off Conditional Conformal Predictors -- 4.6.2 Mondrian Conformal Predictors and Transducers -- 4.6.3 Using Mondrian Conformal Transducers for Prediction -- 4.6.4 Generality of Mondrian Taxonomies -- 4.6.5 Conformal Prediction -- 4.6.6 Inductive Conformal Prediction -- 4.6.7 Label-Conditional Conformal Prediction.
4.6.8 Object-Conditional Conformal Prediction -- 4.7 Training-Conditional Validity -- 4.7.1 Conditional Validity -- 4.7.2 Training-Conditional Validity of Inductive Conformal Predictors -- 4.8 Context -- 4.8.1 Computationally Efficient Hedged Prediction -- 4.8.2 Specific Learning Algorithms and Nonconformity Measures -- 4.8.3 Training Conformal Predictors -- 4.8.4 Cross-Conformal Predictors and Alternative Approaches -- 4.8.5 Transductive Conformal Predictors -- 4.8.6 Conditional Conformal Predictors -- Part II Probabilistic Prediction -- 5 Impossibility Results -- 5.1 Introduction -- 5.2 Diverse Datasets -- 5.3 Impossibility of Estimation of Probabilities -- 5.3.1 Binary Case -- 5.3.2 Multiclass Case -- 5.4 Proof of Theorem 5.2 -- 5.4.1 Probability Estimators and Statistical Tests -- 5.4.2 Complete Statistical Tests -- 5.4.3 Restatement of the Theorem in Terms of Statistical Tests -- 5.4.4 The Proof of the Theorem -- 5.5 Context -- 5.5.1 More Advanced Results -- 5.5.2 Density Estimation, Regression Estimation, and Regression with Deterministic Objects -- 5.5.3 Universal Probabilistic Predictors -- 5.5.4 Algorithmic Randomness Perspective -- 6 Probabilistic Classification: Venn Predictors -- 6.1 Introduction -- 6.2 Venn Predictors -- 6.2.1 Validity of One-Off Venn Predictors -- 6.2.2 Are There Other Ways to Achieve Perfect Calibration? -- 6.2.3 Venn Prediction with Binary Labels and No Objects -- 6.3 A Universal Venn Predictor -- 6.4 Venn-Abers Predictors -- 6.4.1 Full Venn-Abers Predictors -- 6.4.2 Inductive Venn-Abers Predictors -- 6.4.3 Probabilistic Predictors Derived from Venn Predictors -- 6.4.4 Cross Venn-Abers Predictors -- 6.4.5 Merging Multiprobability Predictions into a Probabilistic Prediction -- 6.5 Proofs -- 6.5.1 Proof of Theorem 6.4 -- 6.5.2 PAVA and the Proof of Lemma 6.6 -- 6.5.3 Proof of Proposition 6.7 -- 6.6 Context.
6.6.1 Risk and Uncertainty -- 6.6.2 John Venn, Frequentist Probability, and the Problem of the Reference Class -- 6.6.3 Online Venn Predictors Are Calibrated -- 6.6.4 Isotonic Regression -- 7 Probabilistic Regression: Conformal Predictive Systems -- 7.1 Introduction -- 7.2 Conformal Predictive Systems -- 7.2.1 Basic Definitions -- 7.2.2 Properties of Validity -- 7.2.3 Simplest Example: Monotonic Conformity Measures -- 7.2.4 Criterion of Being a CPS -- 7.3 Least Squares Prediction Machine -- 7.3.1 Three Kinds of LSPM -- 7.3.2 The Studentized LSPM in an Explicit Form -- 7.3.3 The Offline Version of the Studentized LSPM -- 7.3.4 The Ordinary LSPM -- 7.3.5 Asymptotic Efficiency of the LSPM -- 7.3.6 Illustrations -- 7.4 Kernel Ridge Regression Prediction Machine -- 7.4.1 Explicit Forms of the KRRPM -- 7.4.2 Limitation of the KRRPM -- 7.5 Nearest Neighbours Prediction Machine -- 7.6 Universal Conformal Predictive Systems -- 7.6.1 Definitions -- 7.6.2 Universal Conformal Predictive Systems -- 7.6.3 Universal Deterministic Predictive Systems -- 7.7 Applications to Decision Making -- 7.7.1 A Standard Problem of Decision Making -- 7.7.2 Examples -- 7.7.3 Asymptotically Efficient Decision Making -- 7.7.4 Dangers of Overfitting -- 7.8 Computationally Efficient Versions -- 7.8.1 Inductive Conformal Predictive Systems -- 7.8.2 Cross-Conformal Predictive Distributions -- 7.8.3 Practical Aspects -- 7.8.4 Beyond Randomness -- 7.9 Proofs and Calculations -- 7.9.1 Proofs for Sect.7.2 -- Proof of Lemma 7.1 -- Proof of Proposition 7.2 -- 7.9.2 Proofs for Sect.7.3 -- Proof of Proposition 7.4 -- Proof of Proposition 7.5 -- Proof of Proposition 7.6 -- Proof of Proposition 7.7 -- Proof of Proposition 7.8 -- Computations for the Studentized LSPM -- The Ordinary LSPM -- Proof of (7.22) -- 7.9.3 Proof of Theorem 7.16 -- 7.9.4 Proofs for Sect.7.8 -- Proof of Proposition 7.17.
Proof of Proposition 7.18.
Record Nr. UNINA-9910635392203321
Vovk Vladimir <1960->  
Cham, Switzerland : , : Springer International Publishing, , [2022]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Analysis and Data-Based Reconstruction of Complex Nonlinear Dynamical Systems : Using the Methods of Stochastic Processes / / by M. Reza Rahimi Tabar
Analysis and Data-Based Reconstruction of Complex Nonlinear Dynamical Systems : Using the Methods of Stochastic Processes / / by M. Reza Rahimi Tabar
Autore Rahimi Tabar M. Reza
Edizione [1st ed. 2019.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2019
Descrizione fisica 1 online resource (XVIII, 280 p. 41 illus., 22 illus. in color.)
Disciplina 519.2
519.23
Collana Understanding Complex Systems
Soggetto topico Processos estocàstics
Sistemes complexos
Anàlisi de sèries temporals
Statistical physics
Dynamics
System theory
Probabilities
Economics
Computational complexity
Neurosciences
Complex Systems
Probability Theory and Stochastic Processes
Economic Theory/Quantitative Economics/Mathematical Methods
Complexity
Soggetto genere / forma Llibres electrònics
ISBN 3-030-18472-2
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 1 Introduction -- 2 Introduction to Stochastic Processes -- 3 Kramers-Moyal Expansion and Fokker-Planck Equation -- 4 Continuous Stochastic Process -- 5 The Langevin Equation and Wiener Process -- 6 Stochastic Integration, It^o and Stratonovich Calculi -- 7 Equivalence of Langevin and Fokker-Planck Equations -- 8 Examples of Stochastic Calculus -- 9 Langevin Dynamics in Higher Dimensions -- 10 Levy Noise Driven Langevin Equation and its Time Series-Based Reconstruction -- 11 Stochastic Processes with Jumps and Non-Vanishing Higher-Order Kramers-Moyal Coefficients -- 12 Jump-Diffusion Processes -- 13 Two-Dimensional (Bivariate) Jump-Diffusion Processes -- 14 Numerical Solution of Stochastic Differential Equations: Diffusion and Jump-Diffusion Processes -- 15 The Friedrich-Peinke Approach to Reconstruction of Dynamical Equation for Time Series: Complexity in View of Stochastic Processes -- 16 How To Set Up Stochastic Equations For Real-World Processes: Markov-Einstein Time Scale -- 17 Reconstruction of Stochastic Dynamical Equations: Exemplary Stationary Diffusion and Jump-Diffusion Processes -- 18 The Kramers-Moyal Coefficients of Non-Stationary Time series in The Presence of Microstructure (Measurement) Noise -- 19 Influence of Finite Time Step in Estimating of the Kramers-Moyal Coefficients -- 20 Distinguishing Diffusive and Jumpy Behaviors in Real-World Time Series -- 21 Reconstruction of Langevin and Jump-Diffusion Dynamics From Empirical Uni- and Bivariate Time Series -- 22 Applications and Outlook -- 23 Epileptic Brain Dynamics.
Record Nr. UNINA-9910337876203321
Rahimi Tabar M. Reza  
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2019
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Asymptotic properties of permanental sequence : related to birth and death processes and autoregressive Gaussian sequences / / Michael B. Marcus, Jay Rosen
Asymptotic properties of permanental sequence : related to birth and death processes and autoregressive Gaussian sequences / / Michael B. Marcus, Jay Rosen
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2021]
Descrizione fisica 1 online resource (xi, 114 pages)
Disciplina 519.233
Collana Springer briefs in probability and mathematical statistics
Soggetto topico Birth and death processes (Stochastic processes)
Gaussian distribution
Processos estocàstics
Distribució de Gauss
Soggetto genere / forma Llibres electrònics
ISBN 3-030-69485-2
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- 1 Introduction -- 1.1 General Results -- 1.2 Applications -- 2 Birth and Death Processes -- 3 Birth and Death Processes with Emigration -- 4 Birth and Death Processes with Emigration Related to First Order Gaussian Autoregressive Sequences -- 5 Markov Chains with Potentials That Are the Covariances of Higher Order Gaussian Autoregressive Sequences -- 6 Relating Permanental Sequences to Gaussian Sequences -- 7 Permanental Sequences with Kernels That Have Uniformly Bounded Row Sums -- 8 Uniform Markov Chains -- Appendix Bibliography -- -- Index.
Record Nr. UNISA-996466396103316
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Asymptotic properties of permanental sequence : related to birth and death processes and autoregressive Gaussian sequences / / Michael B. Marcus, Jay Rosen
Asymptotic properties of permanental sequence : related to birth and death processes and autoregressive Gaussian sequences / / Michael B. Marcus, Jay Rosen
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2021]
Descrizione fisica 1 online resource (xi, 114 pages)
Disciplina 519.233
Collana Springer briefs in probability and mathematical statistics
Soggetto topico Birth and death processes (Stochastic processes)
Gaussian distribution
Processos estocàstics
Distribució de Gauss
Soggetto genere / forma Llibres electrònics
ISBN 3-030-69485-2
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- 1 Introduction -- 1.1 General Results -- 1.2 Applications -- 2 Birth and Death Processes -- 3 Birth and Death Processes with Emigration -- 4 Birth and Death Processes with Emigration Related to First Order Gaussian Autoregressive Sequences -- 5 Markov Chains with Potentials That Are the Covariances of Higher Order Gaussian Autoregressive Sequences -- 6 Relating Permanental Sequences to Gaussian Sequences -- 7 Permanental Sequences with Kernels That Have Uniformly Bounded Row Sums -- 8 Uniform Markov Chains -- Appendix Bibliography -- -- Index.
Record Nr. UNINA-9910483199403321
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Brownian motion : fluctuations, dynamics, and applications / / Robert M. Mazo
Brownian motion : fluctuations, dynamics, and applications / / Robert M. Mazo
Autore Mazo Robert M
Edizione [1st ed.]
Pubbl/distr/stampa Oxford, : Clarendon Press, 2002
Descrizione fisica 1 online resource (302 p.)
Disciplina 530.42
530.475
Collana Oxford science publications
International series of monographs on physics
Soggetto topico Brownian motion processes
Markov processes
Processos de moviment brownià
Processos estocàstics
Processos de Markov
Mecànica estadística
Difusió
Polímers
Fluctuacions (Física)
Soggetto genere / forma Llibres electrònics
ISBN 9786611998790
9781281998798
1281998796
9780191565083
0191565083
9780199556441
019955644X
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Contents; 1 Historical Background; 1.1 Robert Brown; 1.2 Between Brown and Einstein; 1.3 Albert Einstein; 1.4 Marian von Smoluchowski; 1.5 Molecular Reality; 1.6 The Scope of this Book; 2 Probability Theory; 2.1 Probability; 2.2 Conditional Probability and Independence; 2.3 Random Variables and Probability Distributions; 2.4 Expectations and Particular Distributions; 2.5 Characteristic Function; Sums of Random Variables; 2.6 Conclusion; 3 Stochastic Processes; 3.1 Stochastic Processes; 3.2 Distribution Functions; 3.3 Classification of Stochastic Processes; 3.4 The Fokker-Planck Equation
3.5 Some Special Processes3.6 Calculus of Stochastic Processes; 3.7 Fourier Analysis of Random Processes; 3.8 White Noise; 3.9 Conclusion; 4 Einstein-Smoluchowski Theory; 4.1 What is Brownian Motion?; 4.2 Smoluchowski's Theory; 4.3 Smoluchowski Theory Continued; 4.4 Einstein's Theory; 4.5 Diffusion Coefficient and Friction Constant; 4.6 The Langevin Theory; 5 Stochastic Differential Equations and Integrals; 5.1 The Langevin Equation Revisited; 5.2 Stochastic Differential Equations; 5.3 Which Rule Should Be Used?; 5.4 Some Examples; 6 Functional Integrals; 6.1 Functional Integrals
6.2 The Wiener Integral6.3 Wiener Measure; 6.4 The Feynman-Kac Formula; 6.5 Feynman Path Integrals; 6.6 Evaluation of Wiener Integrals; 6.7 Applications of Functional Integrals; 7 Some Important Special Cases; 7.1 Several Cases of Interest; 7.2 The Free Particle; 7.3 The Distribution of Displacements; 7.4 The Harmonically Bound Particle; 7.5 A Particle in a Constant Force Field; 7.6 The Uniaxial Rotor; 7.7 An Equation for the Distribution of Displacements; 7.8 Discussion; 8 The Smoluchowski Equation; 8.1 The Kramers-Klein Equation; 8.2 The Smoluchowski Equation
8.3 Elimination of Fast Variables8.4 The Smoluchowski Equation Continued; 8.5 Passage over Potential Barriers; 8.6 Concluding Remarks; 9 Random Walk; 9.1 The Random Walk; 9.2 The One-Dimensional Pearson Walk; 9.3 The Biased Random Walk; 9.4 The Persistent Walk; 9.5 Boundaries and First Passage Times; 9.6 Random Remarks on Random Walks; 10 Statistical Mechanics; 10.1 Molecular Distribution Functions; 10.2 The Liouville Equation; 10.3 Projection Operators-The Zwanzig Equation; 10.4 Projection Operators-The Mori Equation; 10.5 Concluding Remarks
11 Stochastic Equations from a Statistical Mechanical Viewpoint11.1 The Langevin Equation A Heuristic View; 11.2 The Fokker-Planck Equation-A Heuristic View; 11.3 What is Wrong with these Derivations?; 11.4 Eliminating Fast Processes; 11.5 The Distribution Function; 11.6 Discussion; 12 Two Exactly Treatable Models; 12.1 Two Illustrative Examples; 12.2 Brownian Motion in a Dilute Gas; 12.3 Discussion; 12.4 The Particle Bound to a Lattice; 12.5 The One-Dimensional Case; 12.6 Discussion; 13 Brownian Motion and Noise; 13.1 Limits on Measurement; 13.2 Oscillations of a Fiber
13.3 A Pneumatic Example
Record Nr. UNINA-9910960525703321
Mazo Robert M  
Oxford, : Clarendon Press, 2002
Materiale a stampa
Lo trovi qui: Univ. Federico II
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Classical and Spatial Stochastic Processes : With Applications to Biology / / by Rinaldo B. Schinazi
Classical and Spatial Stochastic Processes : With Applications to Biology / / by Rinaldo B. Schinazi
Autore Schinazi Rinaldo B
Edizione [3rd ed. 2024.]
Pubbl/distr/stampa Cham : , : Springer Nature Switzerland : , : Imprint : Birkhäuser, , 2024
Descrizione fisica 1 online resource (XII, 286 p. 16 illus.)
Disciplina 519.23
Soggetto topico Stochastic processes
Probabilities
Biomathematics
Biomatemàtica
Processos estocàstics
Stochastic Processes
Probability Theory
Mathematical and Computational Biology
Soggetto genere / forma Llibres electrònics
ISBN 9783031777608
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Finite Markov Chains -- Random walks on finite graphs -- The first appearance of a pattern -- The ruin problem -- The Ehrenfest chain -- The simple symmetric random walk -- Asymmetric and higher dimension random walks -- Discrete time birth and death chains -- Discrete time branching process -- Recurrence on countable spaces -- Stationary distributions on countable spaces -- The Poisson process -- Continuous time birth and death chains -- Continuous time branching processes -- Percolation -- A cellular automaton -- A branching random walk -- The contact process on a homogeneous tree -- Appendix: A little more probability -- Bibliography -- Index.
Record Nr. UNINA-9910919828003321
Schinazi Rinaldo B  
Cham : , : Springer Nature Switzerland : , : Imprint : Birkhäuser, , 2024
Materiale a stampa
Lo trovi qui: Univ. Federico II
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Continuous Time Processes for Finance [[electronic resource] ] : Switching, Self-exciting, Fractional and other Recent Dynamics / / by Donatien Hainaut
Continuous Time Processes for Finance [[electronic resource] ] : Switching, Self-exciting, Fractional and other Recent Dynamics / / by Donatien Hainaut
Autore Hainaut Donatien
Edizione [1st ed. 2022.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022
Descrizione fisica 1 online resource (359 pages)
Disciplina 332.015195
Collana Bocconi & Springer Series, Mathematics, Statistics, Finance and Economics
Soggetto topico Probabilities
Social sciences - Mathematics
Econometrics
Actuarial science
Probability Theory
Mathematics in Business, Economics and Finance
Actuarial Mathematics
Quantitative Economics
Finances
Models matemàtics
Estadística matemàtica
Processos estocàstics
Anàlisi de sèries temporals
Soggetto genere / forma Llibres electrònics
ISBN 9783031063619
9783031063602
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Preface -- Acknowledgements -- Notations -- 1. Switching Models: Properties and Estimation -- 2. Estimation of Continuous Time Processes by Markov Chain Monte Carlo -- 3. Particle Filtering and Estimation -- 4. Modeling of Spillover Effects in Stock Markets -- 5. Non-Markov Models for Contagion and Spillover -- 6. Fractional Brownian Motion -- 7. Gaussian Fields for Asset Prices -- 8. Lévy Interest Rate Models With a Long Memory -- 9. Affine Volterra Processes and Rough Models -- 10. Sub-Diffusion for Illiquid Markets -- 11. A Fractional Dupire Equation for Jump-Diffusions -- References.
Record Nr. UNISA-996485661303316
Hainaut Donatien  
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022
Materiale a stampa
Lo trovi qui: Univ. di Salerno
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Continuous Time Processes for Finance : Switching, Self-exciting, Fractional and other Recent Dynamics / / by Donatien Hainaut
Continuous Time Processes for Finance : Switching, Self-exciting, Fractional and other Recent Dynamics / / by Donatien Hainaut
Autore Hainaut Donatien
Edizione [1st ed. 2022.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022
Descrizione fisica 1 online resource (359 pages)
Disciplina 332.015195
Collana Bocconi & Springer Series, Mathematics, Statistics, Finance and Economics
Soggetto topico Probabilities
Social sciences - Mathematics
Econometrics
Actuarial science
Probability Theory
Mathematics in Business, Economics and Finance
Actuarial Mathematics
Quantitative Economics
Finances
Models matemàtics
Estadística matemàtica
Processos estocàstics
Anàlisi de sèries temporals
Soggetto genere / forma Llibres electrònics
ISBN 9783031063619
9783031063602
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Preface -- Acknowledgements -- Notations -- 1. Switching Models: Properties and Estimation -- 2. Estimation of Continuous Time Processes by Markov Chain Monte Carlo -- 3. Particle Filtering and Estimation -- 4. Modeling of Spillover Effects in Stock Markets -- 5. Non-Markov Models for Contagion and Spillover -- 6. Fractional Brownian Motion -- 7. Gaussian Fields for Asset Prices -- 8. Lévy Interest Rate Models With a Long Memory -- 9. Affine Volterra Processes and Rough Models -- 10. Sub-Diffusion for Illiquid Markets -- 11. A Fractional Dupire Equation for Jump-Diffusions -- References.
Record Nr. UNINA-9910590077503321
Hainaut Donatien  
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Control and system theory of discrete-time stochastic systems / / Jan H. van Schuppen
Control and system theory of discrete-time stochastic systems / / Jan H. van Schuppen
Autore Schuppen J. H. van
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2021]
Descrizione fisica 1 online resource (940 pages)
Disciplina 629.8312
Collana Communications and Control Engineering
Soggetto topico Stochastic control theory
Stochastic systems
Discrete-time systems
Teoria de control
Processos estocàstics
Sistemes estocàstics
Sistemes de temps discret
Soggetto genere / forma Llibres electrònics
ISBN 3-030-66952-1
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNINA-9910495184703321
Schuppen J. H. van  
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui