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]
Yexi Jiang commented on MAHOUT975:

The size of goodLabels in updateRanking is always 1 and it seems that there is no need to
use a loop.
Also, the existing test case cannot been passed. The ArrayIndexOutOfBoundsException are thrown.
> Bug in Gradient Machine  Computation of the gradient
> 
>
> Key: MAHOUT975
> URL: https://issues.apache.org/jira/browse/MAHOUT975
> Project: Mahout
> Issue Type: Bug
> Components: Classification
> Affects Versions: 0.7
> Reporter: Christian Herta
> Assignee: Ted Dunning
> Fix For: Backlog
>
> Attachments: GradientMachine2.java, GradientMachine.patch, MAHOUT975.patch
>
>
> The initialisation to compute the gradient descent weight updates for the output units
should be wrong:
>
> In the comment: "dy / dw is just w since y = x' * w + b."
> This is wrong. dy/dw is x (ignoring the indices). The same initialisation is done in
the code.
> Check by using neural network terminology:
> The gradient machine is a specialized version of a multi layer perceptron (MLP).
> In a MLP the gradient for computing the "weight change" for the output units is:
> dE / dw_ij = dE / dz_i * dz_i / d_ij with z_i = sum_j (w_ij * a_j)
> here: i index of the output layer; j index of the hidden layer
> (d stands for the partial derivatives)
> here: z_i = a_i (no squashing in the output layer)
> with the special loss (cost function) is E = 1  a_g + a_b = 1  z_g + z_b
> with
> g index of output unit with target value: +1 (positive class)
> b: random output unit with target value: 0
> =>
> dE / dw_gj = dE/dz_g * dz_g/dw_gj = 1 * a_j (a_j: activity of the hidden unit
> j)
> dE / dw_bj = dE/dz_b * dz_b/dw_bj = +1 * a_j (a_j: activity of the hidden unit
> j)
> That's the same if the comment would be correct:
> dy /dw = x (x is here the activation of the hidden unit) * (1) for weights to
> the output unit with target value +1.
> 
> In neural network implementations it's common to compute the gradient
> numerically for a test of the implementation. This can be done by:
> dE/dw_ij = (E(w_ij + epsilon) E(w_ij  epsilon) ) / (2* (epsilon))

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