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papers:bottou-lecun-2004 [2014/02/28 20:37] leonb [Notes]		papers:bottou-lecun-2004 [2014/02/28 20:42] leonb [Notes]
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	The ASMB version of this work [[bottou-lecun-2004a\|(Bottou and LeCun, 2005)]] contains the complete proof. The NIPS version was written several months after the ASMB. It contains only a proof sketch but reports experimental results. It also offers a better discussion of the previous results obtained by Murata and Amari (1998) which are in fact much more general than I initially realized. Relative to these results, this work contains three contributions: (a) spelling out the computational consequences of the efficiency results, (b) expressing the solution of the batch learning problems as a stochastic process that is fundamentally similar to a second order stochastic gradient algorithm, and (<html></html>c) providing a more rigorous proof, taking into account, for instance, how the gain matrix approximates the inverse Hessian.		The ASMB version of this work [[bottou-lecun-2004a\|(Bottou and LeCun, 2005)]] contains the complete proof. The NIPS version was written several months after the ASMB. It contains only a proof sketch but reports experimental results. It also offers a better discussion of the previous results obtained by Murata and Amari (1998) which are in fact much more general than I initially realized. Relative to these results, this work contains three contributions: (a) spelling out the computational consequences of the efficiency results, (b) expressing the solution of the batch learning problems as a stochastic process that is fundamentally similar to a second order stochastic gradient algorithm, and (<html></html>c) providing a more rigorous proof, taking into account, for instance, how the gain matrix approximates the inverse Hessian.
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