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Gradient Descent Convergence



2019 Community Moderator ElectionStochastic gradient descent based on vector operations?procedure for gradient descentRegression problem - too complex for gradient descentIntuition in Backpropagation (gradient descent)Algorithm to apply Lasso and Ridge in Gradient descentGradient descent and partial derivativesStochastic Gradient Descent BatchingL-BFGS improvement for stochastic gradient descentLinear classifier and gradient descentHow do I approach learning Data Science/ML the 'rightest' way?










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I'm a double major in Math and CS interested in Machine Learning. I'm currently taking the popular Coursera course by Prof. Andrew. He's talking and explaining Gradient Descent but I can't avoid noticing a few things. With my math background, I know that if I'm trying to find the global min/max of a function, I must first find all the critical points first. The course talks about convergence of GD, but is it really guaranteed to converge to the global min? How do I know it won't get stuck at a saddle point? Wouldn't be safer to do a 2nd derivative test to test it? If my function is differentiable it seems reasonable it converges to a local min, but not to the global min. I have tried looking for a better explanation but everyone seems to take it for granted without questioning. Can someone point me in the right direction?










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$endgroup$
















    0












    $begingroup$


    I'm a double major in Math and CS interested in Machine Learning. I'm currently taking the popular Coursera course by Prof. Andrew. He's talking and explaining Gradient Descent but I can't avoid noticing a few things. With my math background, I know that if I'm trying to find the global min/max of a function, I must first find all the critical points first. The course talks about convergence of GD, but is it really guaranteed to converge to the global min? How do I know it won't get stuck at a saddle point? Wouldn't be safer to do a 2nd derivative test to test it? If my function is differentiable it seems reasonable it converges to a local min, but not to the global min. I have tried looking for a better explanation but everyone seems to take it for granted without questioning. Can someone point me in the right direction?










    share|improve this question









    $endgroup$














      0












      0








      0





      $begingroup$


      I'm a double major in Math and CS interested in Machine Learning. I'm currently taking the popular Coursera course by Prof. Andrew. He's talking and explaining Gradient Descent but I can't avoid noticing a few things. With my math background, I know that if I'm trying to find the global min/max of a function, I must first find all the critical points first. The course talks about convergence of GD, but is it really guaranteed to converge to the global min? How do I know it won't get stuck at a saddle point? Wouldn't be safer to do a 2nd derivative test to test it? If my function is differentiable it seems reasonable it converges to a local min, but not to the global min. I have tried looking for a better explanation but everyone seems to take it for granted without questioning. Can someone point me in the right direction?










      share|improve this question









      $endgroup$




      I'm a double major in Math and CS interested in Machine Learning. I'm currently taking the popular Coursera course by Prof. Andrew. He's talking and explaining Gradient Descent but I can't avoid noticing a few things. With my math background, I know that if I'm trying to find the global min/max of a function, I must first find all the critical points first. The course talks about convergence of GD, but is it really guaranteed to converge to the global min? How do I know it won't get stuck at a saddle point? Wouldn't be safer to do a 2nd derivative test to test it? If my function is differentiable it seems reasonable it converges to a local min, but not to the global min. I have tried looking for a better explanation but everyone seems to take it for granted without questioning. Can someone point me in the right direction?







      machine-learning regression gradient-descent






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