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  1. Mahout
  2. MAHOUT-975

Bug in Gradient Machine - Computation of the gradient



    • Type: Bug
    • Status: Closed
    • Priority: Major
    • Resolution: Won't Fix
    • Affects Version/s: 0.7
    • Fix Version/s: 0.10.0
    • Component/s: Classification
    • Labels:


      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
      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
      dE / dw_bj = -dE/dz_b * dz_b/dw_bj = +1 * a_j (a_j: activity of the hidden unit

      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))


        1. GradientMachine.patch
          3 kB
          Christian Herta
        2. MAHOUT-975.patch
          3 kB
          Suneel Marthi
        3. GradientMachine2.java
          12 kB
          Ted Dunning

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              • Assignee:
                tdunning Ted Dunning
                chrisberlin Christian Herta
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