Optimization basics for machine learning
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Optimization basics for machine learning
Course notes onOptimization for Machine LearningGabriel PeyréCNRS & DMAEcole Nonnale Siipcrietire gabriel.peyre@ens.fr https://mathematical-tours.gith Optimization basics for machine learning hub.ioWWW.numerical-tours.com44285AbstractThis document presents first order optimization methods and their applications to machine learning. This is not a course on machine learning (in particular it docs not cover modeling and statistical considerations) and it is focussed on t he use and analysis Optimization basics for machine learning OÍ cheap met hods that can scale to large datasets and models with lots of parameters. These methods are variations around the notion of “gradient deOptimization basics for machine learning
scent”, so that the computation of gradients plays a major role. This course covers basic theoretical properties of optimization problems (in particulCourse notes onOptimization for Machine LearningGabriel PeyréCNRS & DMAEcole Nonnale Siipcrietire gabriel.peyre@ens.fr https://mathematical-tours.gith Optimization basics for machine learning llow and deep networks.Contents1Motivation in Machine Learning11.1Unconstraint optimization....................................................... I1.2Regression...................................................................... 21.3Classification.................................................. Optimization basics for machine learning ................ 22Basics of Convex Analysis22.1Existence of Solutions.......................................................... 22.2Convexity........Optimization basics for machine learning
............................................................... 32.3Convex Sets..................................................................... 1Course notes onOptimization for Machine LearningGabriel PeyréCNRS & DMAEcole Nonnale Siipcrietire gabriel.peyre@ens.fr https://mathematical-tours.gith Optimization basics for machine learning ........................................... 53.3Least Squares................................................................... 63.1Link with I’CA.................................................................. 73.5Classification.........3.6Chain Rule.............4Gradient Descent Algorithm4.1Ste Optimization basics for machine learning epest Descent Direction4.2Gradient Descent............................................................... 10XX o> o15Convergence Analysis115.1QuadratOptimization basics for machine learning
ic Case...................................................................... 115.2General Case.......................................................Course notes onOptimization for Machine LearningGabriel PeyréCNRS & DMAEcole Nonnale Siipcrietire gabriel.peyre@ens.fr https://mathematical-tours.gith Optimization basics for machine learning Bregman Divergences ................................................................. 186.2Mirror descent....................................................................... 196.3Re-parameterized Hows................................................................ 20 Optimization basics for machine learning Course notes onOptimization for Machine LearningGabriel PeyréCNRS & DMAEcole Nonnale Siipcrietire gabriel.peyre@ens.fr https://mathematical-tours.githGọi ngay
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