lab05_1_Logistic_Regression

▷ Classification

• variable is either 0 or 1 (positive / negative)
• Exam : Pass or Fail
• Face : Real or Fake

x_train = [[1, 2], [2, 3], [3, 1], [4, 3], [5, 3], [6, 2]]
y_train = [[0], [0], [0], [1], [1], [1]]

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▷ Logistic vs Linear

What is the difference between logistic and lenear?

• Logistic : Decrete(Counted) ex. Shoe Size, The number of workers in a company
• Linear : Continous(Measured) ex. Time, Weight, Height

Logistic_Y = [[0], [0], [0], [1], [1], [1]] # One Hot
Linear_Y = [828.659973, 833.450012, 819.23999, 828.349976, 831.659973] # Numeric

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▷ Hypothesis Representation

When using linear regression we did $h_Θ(x) = (Θ^TX)$
But start with binary classification, Y is only 0 or 1
So we need new funtion

• For classification hypothesis representation we do $h_Θ(x) = g((Θ^TX))$
• X → Linear function → Logistic function → Decision Boundary → Y ∈ {0, 1}
• Where we define g(z) → z is a real number → $g(z) = e^z/(e^z + 1) = 1/(1 + e^{-z})$
  • As z increases, it becames closer to 1/1+0, so it converges to 1,
  • and as z decreases, it becomes closer to 1/1+infinite, so it converges to 0

import tensorflow as tf
hypothesis = tf.sigmoid(z) # z=tf.matmul(X, Θ) + b
hypothesis = tf.div(1., 1. + tf.exp(z))

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▷ Dicision boundary

• We can set a boundary that separates 0 from 1 by setting 'dicision boundary'