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What is Learning All about ? Get knowledge of by study, experience, or being taught Become aware by information or from observation Commit to memory Be informed of or receive instruction
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A Possible Definition of Learning Things learn when they change their behavior in a way that makes them perform better in the future. Have your shoes learned the shape of your foot ? In learning the purpose is the learner’s, whereas in training it is the teacher’s
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Our Learning Tasks in the Class Classification (Supervised learning) binary classification problem multi-class classification problem Regression (Supervised learning) Does your machine learn anything from you? Who/which is the better teacher/algorithm?
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The Mathematical Background Material in the Class Calculus (Multi-variable) What is the gradient of function Linear Algebra How to compute the distance between two parallel hyperplanes in ? eigenvalue, positive definite matrix, inner product, projection matrix etc.
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Basic Concepts of Probability and Statistics Basic Concepts of Probability and Statistics Probability: Statistics: Random variables, probability distribution, expected value (mean), variance … Confidence interval, testing hypothesis …
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Classification Problem 2-Category Linearly Separable Case Classification Problem 2-Category Linearly Separable Case A- A+ Malignant Benign
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Support Vector Machines Maximizing the Margin between Bounding Planes A+ A-
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Why Use Support Vector Machines (SVMs)? Powerful tools for Data Mining SVM classifier is an optimally defined surface SVMs have a good geometric interpretation SVMs can be generated very efficiently Can be extended from linear to nonlinear case Typically nonlinear in the input space Linear in a higher dimensional “feature” space Implicitly defined by a kernel function Have a sound theoretical foundation Based on Statistical Learning Theory
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Why We Maximize the Margin? (Based on Statistical Learning Theory) The Structural Risk Minimization (SRM): The expected risk will be less than or equal to empirical risk (training error)+ VC (error) bound
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Two-spiral Dataset (94 White Dots & 94 Red Dots)
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