on either values of the summands in the above empirical risk function or values of the gradients of the summands (i.e., the SGD inputs). In particular, second-order optimality is asymptotically achievable without direct calculation of the Hessian matrices of the summands in the empirical risk function. Notes See also Backtracking line search Coordinate descent – changes one coordinate at a time, rather than one example Linear classifier Online machine learning Stochastic hill climbing Stochastic variance reduction References Further reading External links Using stochastic gradient descent in C++, Boost, Ublas for linear regression Machine Learning Algorithms Interactive paper explaining momentum. Stochastic optimization Computational statistics Gradient methods M-estimators Machine learning algorithms Convex optimization Statistical approximations