Universal time-series forecasting with mixture predictors. (2020)

• Record Type: Book
• Further Information: Note: Daniil Ryabko.
• Other Names: Ryabko, Daniil
• Contents: Intro -- Preface -- Contents -- 1 Introduction -- 1.1 General Motivation -- 1.2 Mixture Predictors -- 1.3 Loss: KL Divergence and Total Variation -- 1.4 Some of the Results -- 1.5 Mixture Predictors in the Literature on Sequence Prediction and Related Settings -- 1.6 Organization -- 2 Notation and Definitions -- 2.1 Loss -- 2.1.1 KL Divergence -- 2.1.2 Total Variation -- 2.2 Regret -- 3 Prediction in Total Variation: Characterizations -- 3.1 Optimality of Mixture Predictors -- 3.2 Topological and Algebraic Characterization of Predictability -- 3.3 Examples 3.3.1 Example: Countable Classes of Measures -- 3.3.2 Example: Bernoulli i.i.d. Processes -- 4 Prediction in KL Divergence -- 4.1 Realizable Case: Finite-Time Optimality of Mixture Predictors -- 4.1.1 Finite-Time Upper-Bound and Asymptotic Optimality -- 4.1.2 Lower Bound -- 4.1.3 Examples -- 4.1.3.1 Examples of Sets of Processes with VC=0 -- 4.1.3.2 Examples of Sets of Processes with VC>0 -- 4.1.4 Proof of Theorem 4.1 -- 4.2 Conditions on C Sufficient for Vanishing Loss (VC=0) -- 4.2.1 Separability -- 4.2.1.1 Examples -- 4.2.2 Conditions Based on the Local Behaviour of Measures 4.2.2.1 Examples -- 4.2.3 Optimal Rates of Uniform Convergence -- 4.2.3.1 Examples -- 4.3 Non-Realizable Case and Suboptimality of Mixture Predictors -- 4.3.1 Suboptimality of Mixture Predictors -- 4.3.2 Some Sufficient Conditions on a Set C for the Existence of a Predictor with Vanishing Regret -- 4.3.2.1 Examples: Finite-Memory and Stationary Processes -- 5 Decision-Theoretic Interpretations -- 5.1 Players and Strategies -- 5.2 Minimax -- 5.3 Complete Class -- 5.4 Total Variation -- 6 Middle-Case: Combining Predictors Whose Loss Vanishes 6.1 Examples and an Impossibility Result for Stationary Processes -- 6.2 Proof of Theorem 6.1 -- 7 Conditions Under Which One Measure Is a Predictor for Another -- 7.1 Measuring Performance of Prediction -- 7.2 Preservation of the Predictive Ability Under Summation with an Arbitrary Measure -- 7.3 Dominance with Decreasing Coefficients -- 8 Conclusion and Outlook -- 8.1 Generalizations: Infinite Alphabets and Different Losses -- 8.2 The General Sequence Prediction Questions -- 8.3 Beyond Sequential Prediction -- References
• Publisher Details: Cham : Springer
• Publication Date: 2020
• Copyright Date: 2020
• Extent: 1 online resource (85 pages)
• Subjects: 519.5/5; Time-series analysis -- Data processing; Time-series analysis -- Data processing; Electronic books; Electronic books
• Languages: English
• ISBNs: 9783030543044
• Related ISBNs: 9783030543037
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.