Logistic Regression

Logistic Regression

Model:

Parameters:

  • is the estimated probability that on features and parameters

Cost Function

    • For = 1,
    • if = 0,

    • if = 0,

    • if = 1,
  • Cost function on single example

    • If y = 1,
    • If y = 0,
  • minimise cost function maximize , penalise by large cost

  • Cost function on m examples

  • maximum likelihood estimation

Gradient Descent

Predict

Z = np.dot(w.T, X) + b

Adjust Weights

np.sum(dz)

BroadCasting

  • matrix(m, n) + vector(1, n) -> matrix(m, n) + matrix(m, n)
  • matrix(m, n) + x -> matrix(m, n) + matrix(m, n)

Decision Boundary

  1. linear

  2. non-linear

Regularization

Cost Function

Cost Function:

Regularization Parameter:

L2 regularization:

Softmax Regression

Activation Function

t =

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