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Record Nr. |
UNINA9910483358803321 |
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Autore |
Phillips Jeff M. |
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Titolo |
Mathematical foundations for data analysis / / Jeff M. Phillips |
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Pubbl/distr/stampa |
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Cham, Switzerland : , : Springer, , [2021] |
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©2021 |
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ISBN |
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Descrizione fisica |
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1 online resource (299 pages) |
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Collana |
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Springer Series in the Data Sciences |
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Disciplina |
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Soggetti |
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Data mining - Mathematics |
Machine learning - Mathematics |
Mineria de dades |
Aprenentatge automàtic |
Matemàtica |
Llibres electrònics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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Intro -- Preface -- Acknowledgements -- Contents -- 1 Probability Review -- 1.1 Sample Spaces -- 1.2 Conditional Probability and Independence -- 1.3 Density Functions -- 1.4 Expected Value -- 1.5 Variance -- 1.6 Joint, Marginal, and Conditional Distributions -- 1.7 Bayes' Rule -- 1.7.1 Model Given Data -- 1.8 Bayesian Inference -- Exercises -- 2 Convergence and Sampling -- 2.1 Sampling and Estimation -- 2.2 Probably Approximately Correct (PAC) -- 2.3 Concentration of Measure -- 2.3.1 Markov Inequality -- 2.3.2 Chebyshev Inequality -- 2.3.3 Chernoff-Hoeffding Inequality -- 2.3.4 Union Bound and Examples -- 2.4 Importance Sampling -- 2.4.1 Sampling Without Replacement with Priority Sampling -- Exercises -- 3 Linear Algebra Review -- 3.1 Vectors and Matrices -- 3.2 Addition and Multiplication -- 3.3 Norms -- 3.4 Linear Independence -- 3.5 Rank -- 3.6 Square Matrices and Properties -- 3.7 Orthogonality -- Exercises -- 4 Distances and Nearest Neighbors -- 4.1 Metrics -- 4.2 Lp Distances and their Relatives -- 4.2.1 Lp Distances -- 4.2.2 Mahalanobis Distance -- 4.2.3 Cosine and Angular Distance -- 4.2.4 KL Divergence -- 4.3 Distances for Sets and Strings -- 4.3.1 Jaccard |
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