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My question concerns a specific statement in this paper:

Schraudolph and Graepel address the problem that in stochastic settings of ill-conditioned problems the sampled estimate of the gradient is very unlikely to point in the right direction due to the ill-conditioning of the (estimated) Hessian.

In Chapter 3, the authors claim that directions associated with large eigenvalues of the Hessian (directions of large curvature) can be identified by multiplying the stochastic estimates of Hessian $H$ and gradient $g$.

I don't understand this argument. What point am I missing?

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