Introduction to Statistical Machine Learning - ANU 2018.pdf

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Sparse Kernel Machines

SVMs and Maximum Margin Classifiers

Lagrange Multipliers

SVMs and Maximum Margin Classifiers: Redux

Soft Margin SVMs: Non-Separable Case

Loss functions

Introduction to Statistical Machine Learning Cheng Soon Ong & Christian Walder Machine Learning Research Group College of Engineering and Computer Science The Australian National University Data61 | CSIRO and Canberra February – June 2018 (Many ﬁgures from C. M. Bishop, "Pattern Recognition and Machine Learning") Introduction to Statistical Machine Learning c2018 Ong & Walder & Webers Data61 | CSIRO The Australian National University Outlines Overview Introduction Linear Algebra Probability Linear Regression 1 Linear Regression 2 Linear Classiﬁcation 1 Linear Classiﬁcation 2 Kernel Methods Sparse Kernel Methods Mixture Models and EM 1 Mixture Models and EM 2 Neural Networks 1 Neural Networks 2 Principal Component Analysis Autoencoders Graphical Models 1 Graphical Models 2 Graphical Models 3 Sampling Sequential Data 1 Sequential Data 2 1of 826

Overview 1 Administration 2 Examples 3 What is common to these examples? 4 Deﬁnition 5 Related Fields 6 Notation for Learning 7 Python 8 Human Learning Introduction to Statistical Machine Learning c2018 Ong & Walder & Webers Data61 | CSIRO The Australian National University Outlines Overview Introduction Linear Algebra Probability Linear Regression 1 Linear Regression 2 Linear Classiﬁcation 1 Linear Classiﬁcation 2 Kernel Methods Sparse Kernel Methods Mixture Models and EM 1 Mixture Models and EM 2 Neural Networks 1 Neural Networks 2 Principal Component Analysis Autoencoders Graphical Models 1 Graphical Models 2 Graphical Models 3 Sampling Sequential Data 1 Sequential Data 2 2of 826

Introduction 9 Polynomial Curve Fitting 10 Probability Theory 11 Probability Densities 12 Expectations and Covariances Introduction to Statistical Machine Learning c2018 Ong & Walder & Webers Data61 | CSIRO The Australian National University Outlines Overview Introduction Linear Algebra Probability Linear Regression 1 Linear Regression 2 Linear Classiﬁcation 1 Linear Classiﬁcation 2 Kernel Methods Sparse Kernel Methods Mixture Models and EM 1 Mixture Models and EM 2 Neural Networks 1 Neural Networks 2 Principal Component Analysis Autoencoders Graphical Models 1 Graphical Models 2 Graphical Models 3 Sampling Sequential Data 1 Sequential Data 2 3of 826

Linear Algebra 13 Motivation 14 Basic Concepts 15 Linear Transformations 16 Trace 17 Inner Product 18 Projection 19 Rank, Determinant, Trace 20 Matrix Inverse 21 Eigenvectors 22 Singular Value Decomposition 23 Gradient 24 Books Introduction to Statistical Machine Learning c2018 Ong & Walder & Webers Data61 | CSIRO The Australian National University Outlines Overview Introduction Linear Algebra Probability Linear Regression 1 Linear Regression 2 Linear Classiﬁcation 1 Linear Classiﬁcation 2 Kernel Methods Sparse Kernel Methods Mixture Models and EM 1 Mixture Models and EM 2 Neural Networks 1 Neural Networks 2 Principal Component Analysis Autoencoders Graphical Models 1 Graphical Models 2 Graphical Models 3 Sampling Sequential Data 1 Sequential Data 2 4of 826

Probability 25 Motivation 26 Boxes with Apples and Oranges 27 Bayes’ Theorem 28 Bayes’ Probabilities 29 Probability Distributions 30 Gaussian Distribution over a Vector 31 Decision Theory 32 Model Selection - Key Ideas Introduction to Statistical Machine Learning c2018 Ong & Walder & Webers Data61 | CSIRO The Australian National University Outlines Overview Introduction Linear Algebra Probability Linear Regression 1 Linear Regression 2 Linear Classiﬁcation 1 Linear Classiﬁcation 2 Kernel Methods Sparse Kernel Methods Mixture Models and EM 1 Mixture Models and EM 2 Neural Networks 1 Neural Networks 2 Principal Component Analysis Autoencoders Graphical Models 1 Graphical Models 2 Graphical Models 3 Sampling Sequential Data 1 Sequential Data 2 5of 826

Linear Regression 1 33 Review 34 Linear Basis Function Models 35 Maximum Likelihood and Least Squares 36 Geometry of Least Squares 37 Sequential Learning 38 Regularized Least Squares 39 Multiple Outputs 40 Loss Function for Regression 41 The Bias-Variance Decomposition Introduction to Statistical Machine Learning c2018 Ong & Walder & Webers Data61 | CSIRO The Australian National University Outlines Overview Introduction Linear Algebra Probability Linear Regression 1 Linear Regression 2 Linear Classiﬁcation 1 Linear Classiﬁcation 2 Kernel Methods Sparse Kernel Methods Mixture Models and EM 1 Mixture Models and EM 2 Neural Networks 1 Neural Networks 2 Principal Component Analysis Autoencoders Graphical Models 1 Graphical Models 2 Graphical Models 3 Sampling Sequential Data 1 Sequential Data 2 6of 826

Linear Regression 2 42 Review 43 Bayesian Regression 44 Sequential Update of the Posterior 45 Predictive Distribution 46 Proof of the Predictive Distribution 47 Predictive Distribution with Simpliﬁed Prior 48 Limitations of Linear Basis Function Models Introduction to Statistical Machine Learning c2018 Ong & Walder & Webers Data61 | CSIRO The Australian National University Outlines Overview Introduction Linear Algebra Probability Linear Regression 1 Linear Regression 2 Linear Classiﬁcation 1 Linear Classiﬁcation 2 Kernel Methods Sparse Kernel Methods Mixture Models and EM 1 Mixture Models and EM 2 Neural Networks 1 Neural Networks 2 Principal Component Analysis Autoencoders Graphical Models 1 Graphical Models 2 Graphical Models 3 Sampling Sequential Data 1 Sequential Data 2 7of 826

Linear Classiﬁcation 1 49 Classiﬁcation 50 Generalised Linear Model 51 Inference and Decision 52 Discriminant Functions Introduction to Statistical Machine Learning c2018 Ong & Walder & Webers Data61 | CSIRO The Australian National University Outlines Overview Introduction Linear Algebra Probability Linear Regression 1 Linear Regression 2 Linear Classiﬁcation 1 Linear Classiﬁcation 2 Kernel Methods Sparse Kernel Methods Mixture Models and EM 1 Mixture Models and EM 2 Neural Networks 1 Neural Networks 2 Principal Component Analysis Autoencoders Graphical Models 1 Graphical Models 2 Graphical Models 3 Sampling Sequential Data 1 Sequential Data 2 8of 826

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