gradientDescent.puml

@startuml
/' 
  PUML: https://gist.github.com/yoga1290/6ea0e57dd493d4148ac7f0183c1647eb
  SVG: http://www.plantuml.com/plantuml/svg/RLDRJzim67tFhpY21spMDCae5yfbT4oRngIrOftQlXGvjPjOoYLAN9N2-E-p7KH2gIhPhh_lN1mVtrIAbMgL9evtW5YfekfxNYGhrOsaYbTXTv6dtYQFMF3vtFTE1FF5yIddlVCZtWjwPsnnklI3iwD5SD8x5U7-KYR2ZKh6fSWK5zL2JswXwN7WELRAAVGWbSmpo4pFB95F0iyEq0zn1V_2hDPwbHNT9r7c5I5SfXq4bDhIJ9T0WWxIFiGZIuj4L1JxKB50maAHL1VEY-EKeX1CEHhHwErz7zvF1lVVCBeVZWO_1kEVmzzxLbhpNgPCnTULZ596dgWM2Jo209-qI45SlKClFTjoqUv7p1Gskhi6JkPZJ3KcR9hRtIEo-VTek9-9nNKWbnOTq0v801VljttQVtabiZHRBBNsVDE2qZa9t0tz24ho26_03VHVKWEqMminMmtFRl-tmpzZ3RyZwmv2G-I2e5gbPBPDg2iVA65-7jBMTtpPkg2lWzjVksweRO9Fj33XTzGZV4rj6gOuF8ILdscr6PsFjuKQTDYWxH68zlz0v9LFvodg8ymbN3FIzomx_FujE5FYBKCJk5T812ipcKKFfIxX47poQY3SMGthxr3d5UjO9W94Ac7gNwZZjDH6fU1oOTQrOerfdwweE-pzT32rKGC9JA3U4aeanTIC9gTcfhZMKUiUcmpww21NiIZNiX9D-ep7BOUuD2ymMwMXA94lcxTeNb-byiAv4HdNB_y_
  PNG: http://www.plantuml.com/plantuml/png/RLDRJzim67tFhpY21spMDCae5yfbT4oRngIrOftQlXGvjPjOoYLAN9N2-E-p7KH2gIhPhh_lN1mVtrIAbMgL9evtW5YfekfxNYGhrOsaYbTXTv6dtYQFMF3vtFTE1FF5yIddlVCZtWjwPsnnklI3iwD5SD8x5U7-KYR2ZKh6fSWK5zL2JswXwN7WELRAAVGWbSmpo4pFB95F0iyEq0zn1V_2hDPwbHNT9r7c5I5SfXq4bDhIJ9T0WWxIFiGZIuj4L1JxKB50maAHL1VEY-EKeX1CEHhHwErz7zvF1lVVCBeVZWO_1kEVmzzxLbhpNgPCnTULZ596dgWM2Jo209-qI45SlKClFTjoqUv7p1Gskhi6JkPZJ3KcR9hRtIEo-VTek9-9nNKWbnOTq0v801VljttQVtabiZHRBBNsVDE2qZa9t0tz24ho26_03VHVKWEqMminMmtFRl-tmpzZ3RyZwmv2G-I2e5gbPBPDg2iVA65-7jBMTtpPkg2lWzjVksweRO9Fj33XTzGZV4rj6gOuF8ILdscr6PsFjuKQTDYWxH68zlz0v9LFvodg8ymbN3FIzomx_FujE5FYBKCJk5T812ipcKKFfIxX47poQY3SMGthxr3d5UjO9W94Ac7gNwZZjDH6fU1oOTQrOerfdwweE-pzT32rKGC9JA3U4aeanTIC9gTcfhZMKUiUcmpww21NiIZNiX9D-ep7BOUuD2ymMwMXA94lcxTeNb-byiAv4HdNB_y_
'/
start
partition initialize {
  :b = 0;
  :w = np.zeros((dim, 1));
  :Y =  (1, m: examples) # the labels;
}

repeat

  partition "FORWARD PROPAGATION" {
    :<math>sigma(z) = 1/( 1 + exp(-z) )</math>;
    :<math> hat y = sigma(W^T X + b)</math>;

    :<math>P(y|x) = {(hat y, if y = 1), (1 - hat y, if y = 0):}</math>
    <math>P(y|x) = hat y ^y (1 - hat y)^(1-y)</math>
    <math>log P(y|x) = y log(hat y) + (1-y) log(1 - hat y)</math>;

    :<math>COST = J(w, b) = - ( sum(Y log(hat y) + (1 - y) log(1 - hat y) ) ) / m</math>;
  }

  partition "BACKWARD PROPAGATION" {

    :<math>dW = (dJ)/(dw) =  (X ** (hat Y - Y)^T) / m</math>;
    :<math>db = (dJ)/(db) = (sum_(i=0)^m (hat y^i - y^i)) / m</math>;

  }

  partition "Update" {
    :W -= learning_rate * dW;
    :b -= learning_rate * db;
  }
repeat while (iterate?)

partition "Prediction" {
  repeat
    :<math>predict(w, b, X) = { (1, if sigma(W^(i) X^(i) + b^(i)) >= 0.5), (0 , otherwise):}</math>;
  repeat while (i < m: number of examples)
}

stop
@enduml