Lecture

Support Vector Machines: Theory and Optimization

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In course

MGT-448: Statistical inference and machine learning

This course aims to provide graduate students a thorough grounding in the methods, theory, mathematics and algorithms needed to do research and applications in machine learning. The course covers topics from machine learning, classical statistics, and data ...

Description

This lecture covers the theory and optimization of Support Vector Machines (SVM). It explains the Mercer's Theorem for valid kernels, the concept of Kernel matrix, and the mathematical formulation of SVM. The instructor discusses the hyperplane equation, the role of normal vectors, and the Lagrange Duality in SVM optimization.

Instructor

Negar Kiyavash

Teaching & PhD PhD Students Mohammad Shahverdikondori, Badri Mohammad Reza, Arefe Boushehrian, Sepehr Elahi, Mohammadsadegh Khorasani, Mohammadsaeed Masiha, Amir Mohammad Aboueimehrizi Past EPFL PhD Students Sina Akbari, Ehsan Mokhtarian, Yaroslav Kivva, Fateme Jamshidi Courses Causal inference MGT-416 Students will learn the core concepts and techniques of network analysis with emphasis on causal inference. Theory andapplication will be balanced, with students working directly with networ

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Related concepts (32)

Kernel method

In machine learning, kernel machines are a class of algorithms for pattern analysis, whose best known member is the support-vector machine (SVM). These methods involve using linear classifiers to solve nonlinear problems. The general task of pattern analysis is to find and study general types of relations (for example clusters, rankings, principal components, correlations, classifications) in datasets.

Hyperplane

In geometry, a hyperplane is a subspace whose dimension is one less than that of its ambient space. For example, if a space is 3-dimensional then its hyperplanes are the 2-dimensional planes, while if the space is 2-dimensional, its hyperplanes are the 1-dimensional lines. This notion can be used in any general space in which the concept of the dimension of a subspace is defined. In different settings, hyperplanes may have different properties.

Linear equation

In mathematics, a linear equation is an equation that may be put in the form where are the variables (or unknowns), and are the coefficients, which are often real numbers. The coefficients may be considered as parameters of the equation, and may be arbitrary expressions, provided they do not contain any of the variables. To yield a meaningful equation, the coefficients are required to not all be zero. Alternatively, a linear equation can be obtained by equating to zero a linear polynomial over some field, from which the coefficients are taken.

Mathematical optimization

Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.

Support vector machine

In machine learning, support vector machines (SVMs, also support vector networks) are supervised learning models with associated learning algorithms that analyze data for classification and regression analysis. Developed at AT&T Bell Laboratories by Vladimir Vapnik with colleagues (Boser et al., 1992, Guyon et al., 1993, Cortes and Vapnik, 1995, Vapnik et al., 1997) SVMs are one of the most robust prediction methods, being based on statistical learning frameworks or VC theory proposed by Vapnik (1982, 1995) and Chervonenkis (1974).

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